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<h1 class="title toc-ignore"><code>CASH</code> Simulations</h1>
<h4 class="author"><em>Lei Sun</em></h4>
<h4 class="date"><em>2018-02-10</em></h4>
</div>
<p><strong>Last updated:</strong> 2018-05-15</p>
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2018-05-12
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<td style="text-align:left;">
Update to 1.0
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/cc0ab8379469bc3726f1508cd81e4ecd6fef1b1a/analysis/cash_plots.rmd" target="_blank">cc0ab83</a>
</td>
<td style="text-align:left;">
Lei Sun
</td>
<td style="text-align:left;">
2018-05-11
</td>
<td style="text-align:left;">
update
</td>
</tr>
<tr>
<td style="text-align:left;">
html
</td>
<td style="text-align:left;">
<a href="https://cdn.rawgit.com/LSun/truncash/566a8654839abc68c26d7eeb00980e5cd89b3ab5/docs/cash_plots.html" target="_blank">566a865</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-09
</td>
<td style="text-align:left;">
Build site.
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/f85ff3f95abc912244162392d4d18f73a5794c06/analysis/cash_plots.rmd" target="_blank">f85ff3f</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-09
</td>
<td style="text-align:left;">
wflow_publish(“analysis/cash_plots.rmd”)
</td>
</tr>
<tr>
<td style="text-align:left;">
html
</td>
<td style="text-align:left;">
<a href="https://cdn.rawgit.com/LSun/truncash/564f9cbc4a8c3126ba03c320d03add8cc56c0aad/docs/cash_plots.html" target="_blank">564f9cb</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-06
</td>
<td style="text-align:left;">
Build site.
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/797cd6939f3c430497c03ce97a2093ee9b29f32c/analysis/cash_plots.rmd" target="_blank">797cd69</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-06
</td>
<td style="text-align:left;">
wflow_publish(“analysis/cash_plots.rmd”)
</td>
</tr>
<tr>
<td style="text-align:left;">
html
</td>
<td style="text-align:left;">
<a href="https://cdn.rawgit.com/LSun/truncash/4093362a962261caab72b6d8d091a8d75bf6aa57/docs/cash_plots.html" target="_blank">4093362</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-04-27
</td>
<td style="text-align:left;">
Build site.
</td>
</tr>
<tr>
<td style="text-align:left;">
html
</td>
<td style="text-align:left;">
<a href="https://cdn.rawgit.com/LSun/truncash/37ad45698441ee0ae5eb3202f95e0164d77ef5b7/docs/cash_plots.html" target="_blank">37ad456</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-04-27
</td>
<td style="text-align:left;">
Build site.
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/8c99563f2eef4e5cab124d07550cdea171d4d252/analysis/cash_plots.rmd" target="_blank">8c99563</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-04-27
</td>
<td style="text-align:left;">
wflow_publish(“analysis/cash_plots.rmd”)
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/434b541bdc15b2dc25ba567a00b400a3adca728e/analysis/cash_plots.rmd" target="_blank">434b541</a>
</td>
<td style="text-align:left;">
Lei Sun
</td>
<td style="text-align:left;">
2018-04-13
</td>
<td style="text-align:left;">
FDP q
</td>
</tr>
<tr>
<td style="text-align:left;">
html
</td>
<td style="text-align:left;">
<a href="https://cdn.rawgit.com/LSun/truncash/7e7b2d1056ce9271efcec0a9c683c5ead20fadcc/docs/cash_plots.html" target="_blank">7e7b2d1</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-04-12
</td>
<td style="text-align:left;">
Build site.
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/3a1e4cccb478491f57bfcb67c445abb3ef01b754/analysis/cash_plots.rmd" target="_blank">3a1e4cc</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-04-12
</td>
<td style="text-align:left;">
wflow_publish(“analysis/cash_plots.rmd”)
</td>
</tr>
<tr>
<td style="text-align:left;">
html
</td>
<td style="text-align:left;">
<a href="https://cdn.rawgit.com/LSun/truncash/d022714b2f3ed96ed6023463e86b00853d0e4af7/docs/cash_plots.html" target="_blank">d022714</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-02-22
</td>
<td style="text-align:left;">
cash
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/e94c1d3faaabce53937a14402cbd7a141b7eb094/analysis/cash_plots.rmd" target="_blank">e94c1d3</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-02-22
</td>
<td style="text-align:left;">
cash plots
</td>
</tr>
<tr>
<td style="text-align:left;">
html
</td>
<td style="text-align:left;">
<a href="https://cdn.rawgit.com/LSun/truncash/898349224d5515a514c73d486a1ec606b8ddf32e/docs/cash_plots.html" target="_blank">8983492</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-02-21
</td>
<td style="text-align:left;">
Build site.
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/5902dc9ac06021c1fe2118b450831535b2cd9ecb/analysis/cash_plots.rmd" target="_blank">5902dc9</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-02-21
</td>
<td style="text-align:left;">
wflow_publish(“~/GitHub/truncash/analysis/cash_plots.rmd”)
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/48787a24c36b1a24e129936b2748cc52d1397d8a/analysis/cash_plots.rmd" target="_blank">48787a2</a>
</td>
<td style="text-align:left;">
Lei Sun
</td>
<td style="text-align:left;">
2018-02-16
</td>
<td style="text-align:left;">
cash plots
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/ff78840417d28f89acda4ced9358de7dc499bf01/analysis/cash_plots.rmd" target="_blank">ff78840</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-02-16
</td>
<td style="text-align:left;">
cash_plots
</td>
</tr>
<tr>
<td style="text-align:left;">
html
</td>
<td style="text-align:left;">
<a href="https://cdn.rawgit.com/LSun/truncash/e4ecc944e59aa28a6791b0064a1c4e66a539e9a6/docs/cash_plots.html" target="_blank">e4ecc94</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-02-16
</td>
<td style="text-align:left;">
Build site.
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/2898ce9a1fd6100e144c03e810a018dcbb95a8f2/analysis/cash_plots.rmd" target="_blank">2898ce9</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-02-16
</td>
<td style="text-align:left;">
wflow_publish(“analysis/cash_plots.rmd”)
</td>
</tr>
<tr>
<td style="text-align:left;">
html
</td>
<td style="text-align:left;">
<a href="https://cdn.rawgit.com/LSun/truncash/7c34000d9661213f6beaf89c08f5385487f40c87/docs/cash_plots.html" target="_blank">7c34000</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-02-15
</td>
<td style="text-align:left;">
Build site.
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/cc05dc761a08501debf921040a8c82272670f4de/analysis/cash_plots.rmd" target="_blank">cc05dc7</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-02-15
</td>
<td style="text-align:left;">
wflow_publish(“analysis/cash_plots.rmd”)
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/4d857f76f9fb42a3c75dd097694e2aebcd2a36b9/analysis/cash_plots.rmd" target="_blank">4d857f7</a>
</td>
<td style="text-align:left;">
Lei Sun
</td>
<td style="text-align:left;">
2018-02-14
</td>
<td style="text-align:left;">
plots
</td>
</tr>
<tr>
<td style="text-align:left;">
html
</td>
<td style="text-align:left;">
<a href="https://cdn.rawgit.com/LSun/truncash/f6f0ca05166b95be517673adcc3d213590001693/docs/cash_plots.html" target="_blank">f6f0ca0</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-02-14
</td>
<td style="text-align:left;">
Build site.
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/3af89d27f95275a2cfeb3d23237e813930357c8c/analysis/cash_plots.rmd" target="_blank">3af89d2</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-02-14
</td>
<td style="text-align:left;">
wflow_publish(“analysis/cash_plots.rmd”)
</td>
</tr>
<tr>
<td style="text-align:left;">
rmd
</td>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/d2473f1d284215968bb9e32a89c65de7a10b877f/analysis/cash_plots.rmd" target="_blank">d2473f1</a>
</td>
<td style="text-align:left;">
Lei Sun
</td>
<td style="text-align:left;">
2018-02-14
</td>
<td style="text-align:left;">
cash_plots
</td>
</tr>
<tr>
<td style="text-align:left;">
html
</td>
<td style="text-align:left;">
<a href="https://cdn.rawgit.com/LSun/truncash/d2473f1d284215968bb9e32a89c65de7a10b877f/docs/cash_plots.html" target="_blank">d2473f1</a>
</td>
<td style="text-align:left;">
Lei Sun
</td>
<td style="text-align:left;">
2018-02-14
</td>
<td style="text-align:left;">
cash_plots
</td>
</tr>
</tbody>
</table>
</ul>
</details>
<hr />
<pre class="r"><code>source("../code/gdfit.R")
source("../code/gdash_lik.R")
source("../code/count_to_summary.R")
library(ashr)
library(locfdr)
library(qvalue)
library(reshape2)
library(ggplot2)
library(grid)
library(gridExtra)
library(RColorBrewer)
library(scales)
library(cowplot)
library(ggpubr)</code></pre>
<pre class="r"><code>mean_sdp <- function (x) {
m <- mean(x)
ymax <- m + sd(x)
return(c(y = m, ymax = ymax, ymin = m))
}
mad.mean <- function (x) {
return(mean(abs(x - median(x))))
}
FDP <- function (FDR, qvalue, beta) {
return(sum(qvalue <= FDR & beta == 0) / max(sum(qvalue <= FDR), 1))
}
pFDP <- function (FDR, qvalue, beta) {
return(sum(qvalue <= FDR & beta == 0) / sum(qvalue <= FDR))
}
power <- function (FDR, qvalue, beta) {
return(sum(qvalue <= FDR & beta != 0) / sum(beta != 0))
}</code></pre>
<pre class="r"><code>r <- readRDS("../data/liver.rds")</code></pre>
<pre class="r"><code>top_genes_index = function (g, X) {
return(order(rowSums(X), decreasing = TRUE)[1 : g])
}
lcpm = function (r) {
R = colSums(r)
t(log2(((t(r) + 0.5) / (R + 1)) * 10^6))
}</code></pre>
<pre class="r"><code>nsamp <- 5
ngene <- 1e4
pi0.vec <- c(0.5, 0.9, 0.99)</code></pre>
<pre class="r"><code>Y = lcpm(r)
subset = top_genes_index(ngene, Y)
r = r[subset,]</code></pre>
<div id="g_1-nleft0-22right" class="section level2">
<h2><span class="math inline">\(g_1 = N\left(0, 2^2\right)\)</span></h2>
<pre class="r"><code>q.vec <- seq(0.001, 0.20, by = 0.001)
method.name <- c("BHq", "qvalue", "locfdr", "ASH", "CASH")</code></pre>
<pre class="r"><code>FDP.array <- pFDP.array <- power.array <- array(0, dim = c(nsim, length(q.vec), length(method.name), length(pi0.vec)))
FDP.summary <- array(0, dim = c(7, length(q.vec), length(method.name), length(pi0.vec)))
pFDP.summary <- power.summary <- array(0, dim = c(5, length(q.vec), length(method.name), length(pi0.vec)))
for (j in seq(length(pi0.vec))) {
for (k in seq(length(method.name))) {
for (i in seq(nsim)) {
FDP.array[i, , k, j] <- sapply(q.vec, FDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
pFDP.array[i, , k, j] <- sapply(q.vec, pFDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
power.array[i, , k, j] <- sapply(q.vec, power, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
}
FDP.summary[, , k, j] <- rbind(
avg <- colMeans(FDP.array[, , k, j], na.rm = TRUE),
sd <- apply(FDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(FDP.array[, , k, j])),
q975 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE),
q750 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.75, na.rm = TRUE),
q250 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.25, na.rm = TRUE)
)
pFDP.summary[, , k, j] <- rbind(
avg <- colMeans(pFDP.array[, , k, j], na.rm = TRUE),
sd <- apply(pFDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(pFDP.array[, , k, j])),
q975 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
power.summary[, , k, j] <- rbind(
avg <- colMeans(power.array[, , k, j], na.rm = TRUE),
sd <- apply(power.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(power.array[, , k, j])),
q975 <- apply(power.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(power.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
}
}</code></pre>
<pre class="r"><code>q <- 0.1
z.over <- 1.05
z.under <- 0.95
method.col <- scales::hue_pal()(5)
# method.col <- c("#377eb8", "#984ea3", "#4daf4a", "#ff7f00", "#e41a1c")</code></pre>
<pre class="r"><code>for (j in seq(length(pi0.vec))) {
sd.z <- sapply(z.pi0.list[[j]], sd)
Noise <- cut(sd.z, breaks = c(0, quantile(sd.z, probs = 1 : 2 / 3), Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
# Noise <- cut(sd.z, breaks = c(0, z.under, z.over, Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
pi0.pi0 <- matrix(unlist(pi0.pi0.list[[j]]), byrow = TRUE, length(pi0.pi0.list[[j]]))
pi0.pi0.noise <- rbind.data.frame(cbind.data.frame(Noise, pi0.pi0), cbind.data.frame(Noise = rep("All", length(Noise)), pi0.pi0))
pi0.plot <- ggplot(data = melt(pi0.pi0.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col[-1]) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = pi0.vec[j], col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name[-1]) +
labs(x = "", y = expression(hat(pi)[0])) +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.summary.pi0 <- aperm(FDP.summary[, , , j], c(2, 1, 3))
FDP.summary.pi0.method <- FDP.summary.pi0[, , 1]
for (kk in 2 : length(method.name)) {
FDP.summary.pi0.method <- rbind.data.frame(FDP.summary.pi0.method, FDP.summary.pi0[, , kk])
}
FDP.summary.pi0.method <- cbind.data.frame(
rep(factor(seq(method.name)), each = dim(FDP.summary.pi0)[1]),
rep(q.vec, length(method.name)),
FDP.summary.pi0.method
)
colnames(FDP.summary.pi0.method) <- c(
"Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.array.pi0 <- aperm(FDP.array[, , , j], c(2, 1, 3))
FDP.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, mean, na.rm = TRUE), c(2, 1, 3)))
sd.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, sd, na.rm = TRUE), c(2, 1, 3)))
n.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, function(x){sum(!is.na(x))}), c(2, 1, 3)))
q975.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.975, na.rm = TRUE), c(2, 1, 3)))
q025.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.025, na.rm = TRUE), c(2, 1, 3)))
q750.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.75, na.rm = TRUE), c(2, 1, 3)))
q250.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.25, na.rm = TRUE), c(2, 1, 3)))
FDP.summary.pi0.method.noise <- cbind.data.frame(
rep(rep(levels(Noise), each = length(q.vec)), length(method.name)),
rep(factor(seq(method.name)), each = length(levels(Noise)) * length(q.vec)),
rep(q.vec, length(levels(Noise)) * length(method.name)),
FDP.pi0.noise,
sd.pi0.noise,
n.pi0.noise,
q975.pi0.noise,
q025.pi0.noise,
q750.pi0.noise,
q250.pi0.noise
)
colnames(FDP.summary.pi0.method.noise) <- c(
"Noise", "Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.summary.pi0.method.noise <- rbind.data.frame(
FDP.summary.pi0.method.noise,
cbind.data.frame(Noise = rep("All", dim(FDP.summary.pi0.method)[1]), FDP.summary.pi0.method)
)
FDR.calib.plot <- ggplot(data = FDP.summary.pi0.method.noise, aes(x = FDR, y = FDP, group = Method, col = Method)) +
geom_line() +
geom_ribbon(aes(ymin = q025, ymax = q975, fill = Method), alpha = 0.35, linetype = "blank") +
scale_color_manual(labels = method.name, values = method.col) +
scale_fill_manual(labels = method.name, values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_abline(slope = 1, intercept = 0, linetype = "dashed", size = 1, col = "black") +
labs(x = "Nominal FDR", y = "FDP") +
theme(legend.position = "top", legend.text = element_text(size = 15), plot.title = element_text(hjust = 0.5, size = 15), axis.title.x = element_text(size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(angle = 45, size = 15), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.q <- FDP.array[, which(round(q.vec, 4) == q), , j]
FDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, FDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), FDP.q))
FDR.plot <- ggplot(data = melt(FDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = q, col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "FDP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
TDP.q <- power.array[, which(round(q.vec, 4) == q), , j]
TDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, TDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), TDP.q))
power.plot <- ggplot(data = melt(TDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "TPP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
joint <- ggarrange(FDR.calib.plot,
pi0.plot + rremove("x.text"),
FDR.plot + rremove("x.text"),
power.plot,
align = "v", ncol = 1, nrow = 4,
heights = c(1.5, 1, 1, 1.2)
)
joint <- annotate_figure(joint,
top = text_grob(bquote(pi[0] == .(pi0.vec[j])), size = 15)
)
print(joint)
ggsave(paste0("../output/fig/g1_pi0_", pi0.vec[j], ".pdf"), joint, height = 10, width = 8)
}</code></pre>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-8-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-8-1.png:</em></summary>
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<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/0eb67ffc48770b8bfe57b04e1c40d06be807a68b/docs/figure/cash_plots.rmd/unnamed-chunk-8-1.png" target="_blank">0eb67ff</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-13
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-8-2.png" width="672" style="display: block; margin: auto;" /></p>
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<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/0eb67ffc48770b8bfe57b04e1c40d06be807a68b/docs/figure/cash_plots.rmd/unnamed-chunk-8-2.png" target="_blank">0eb67ff</a>
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<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-13
</td>
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</table>
</details>
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<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/0eb67ffc48770b8bfe57b04e1c40d06be807a68b/docs/figure/cash_plots.rmd/unnamed-chunk-8-3.png" target="_blank">0eb67ff</a>
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<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-13
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</div>
<div id="bimodal-g_2-0.5-nleft-2-1right-0.5-nleft2-1right" class="section level2">
<h2>Bimodal: <span class="math inline">\(g_2 = 0.5 N\left(-2, 1\right) + 0.5 N\left(2, 1\right)\)</span></h2>
<pre class="r"><code>FDP.array <- pFDP.array <- power.array <- array(0, dim = c(nsim, length(q.vec), length(method.name), length(pi0.vec)))
FDP.summary <- array(0, dim = c(7, length(q.vec), length(method.name), length(pi0.vec)))
pFDP.summary <- power.summary <- array(0, dim = c(5, length(q.vec), length(method.name), length(pi0.vec)))
for (j in seq(length(pi0.vec))) {
for (k in seq(length(method.name))) {
for (i in seq(nsim)) {
FDP.array[i, , k, j] <- sapply(q.vec, FDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
pFDP.array[i, , k, j] <- sapply(q.vec, pFDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
power.array[i, , k, j] <- sapply(q.vec, power, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
}
FDP.summary[, , k, j] <- rbind(
avg <- colMeans(FDP.array[, , k, j], na.rm = TRUE),
sd <- apply(FDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(FDP.array[, , k, j])),
q975 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE),
q750 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.75, na.rm = TRUE),
q250 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.25, na.rm = TRUE)
)
pFDP.summary[, , k, j] <- rbind(
avg <- colMeans(pFDP.array[, , k, j], na.rm = TRUE),
sd <- apply(pFDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(pFDP.array[, , k, j])),
q975 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
power.summary[, , k, j] <- rbind(
avg <- colMeans(power.array[, , k, j], na.rm = TRUE),
sd <- apply(power.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(power.array[, , k, j])),
q975 <- apply(power.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(power.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
}
}</code></pre>
<pre class="r"><code>for (j in seq(length(pi0.vec))) {
sd.z <- sapply(z.pi0.list[[j]], sd)
Noise <- cut(sd.z, breaks = c(0, quantile(sd.z, probs = 1 : 2 / 3), Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
# Noise <- cut(sd.z, breaks = c(0, z.under, z.over, Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
pi0.pi0 <- matrix(unlist(pi0.pi0.list[[j]]), byrow = TRUE, length(pi0.pi0.list[[j]]))
pi0.pi0.noise <- rbind.data.frame(cbind.data.frame(Noise, pi0.pi0), cbind.data.frame(Noise = rep("All", length(Noise)), pi0.pi0))
pi0.plot <- ggplot(data = melt(pi0.pi0.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col[-1]) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = pi0.vec[j], col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name[-1]) +
labs(x = "", y = expression(hat(pi)[0])) +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.summary.pi0 <- aperm(FDP.summary[, , , j], c(2, 1, 3))
FDP.summary.pi0.method <- FDP.summary.pi0[, , 1]
for (kk in 2 : length(method.name)) {
FDP.summary.pi0.method <- rbind.data.frame(FDP.summary.pi0.method, FDP.summary.pi0[, , kk])
}
FDP.summary.pi0.method <- cbind.data.frame(
rep(factor(seq(method.name)), each = dim(FDP.summary.pi0)[1]),
rep(q.vec, length(method.name)),
FDP.summary.pi0.method
)
colnames(FDP.summary.pi0.method) <- c(
"Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.array.pi0 <- aperm(FDP.array[, , , j], c(2, 1, 3))
FDP.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, mean, na.rm = TRUE), c(2, 1, 3)))
sd.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, sd, na.rm = TRUE), c(2, 1, 3)))
n.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, function(x){sum(!is.na(x))}), c(2, 1, 3)))
q975.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.975, na.rm = TRUE), c(2, 1, 3)))
q025.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.025, na.rm = TRUE), c(2, 1, 3)))
q750.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.75, na.rm = TRUE), c(2, 1, 3)))
q250.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.25, na.rm = TRUE), c(2, 1, 3)))
FDP.summary.pi0.method.noise <- cbind.data.frame(
rep(rep(levels(Noise), each = length(q.vec)), length(method.name)),
rep(factor(seq(method.name)), each = length(levels(Noise)) * length(q.vec)),
rep(q.vec, length(levels(Noise)) * length(method.name)),
FDP.pi0.noise,
sd.pi0.noise,
n.pi0.noise,
q975.pi0.noise,
q025.pi0.noise,
q750.pi0.noise,
q250.pi0.noise
)
colnames(FDP.summary.pi0.method.noise) <- c(
"Noise", "Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.summary.pi0.method.noise <- rbind.data.frame(
FDP.summary.pi0.method.noise,
cbind.data.frame(Noise = rep("All", dim(FDP.summary.pi0.method)[1]), FDP.summary.pi0.method)
)
FDR.calib.plot <- ggplot(data = FDP.summary.pi0.method.noise, aes(x = FDR, y = FDP, group = Method, col = Method)) +
geom_line() +
geom_ribbon(aes(ymin = q025, ymax = q975, fill = Method), alpha = 0.35, linetype = "blank") +
scale_color_manual(labels = method.name, values = method.col) +
scale_fill_manual(labels = method.name, values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_abline(slope = 1, intercept = 0, linetype = "dashed", size = 1, col = "black") +
labs(x = "Nominal FDR", y = "FDP") +
theme(legend.position = "top", legend.text = element_text(size = 15), plot.title = element_text(hjust = 0.5, size = 15), axis.title.x = element_text(size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(angle = 45, size = 15), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.q <- FDP.array[, which(round(q.vec, 4) == q), , j]
FDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, FDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), FDP.q))
FDR.plot <- ggplot(data = melt(FDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = q, col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "FDP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
TDP.q <- power.array[, which(round(q.vec, 4) == q), , j]
TDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, TDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), TDP.q))
power.plot <- ggplot(data = melt(TDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "TPP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
joint <- ggarrange(FDR.calib.plot,
pi0.plot + rremove("x.text"),
FDR.plot + rremove("x.text"),
power.plot,
align = "v", ncol = 1, nrow = 4,
heights = c(1.5, 1, 1, 1.2)
)
joint <- annotate_figure(joint,
top = text_grob(bquote(pi[0] == .(pi0.vec[j])), size = 15)
)
print(joint)
ggsave(paste0("../output/fig/g2_pi0_", pi0.vec[j], ".pdf"), joint, height = 10, width = 8)
}</code></pre>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-10-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-10-1.png:</em></summary>
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<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
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</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/27ef9e3a7d9105ef2924cfb810167a16779f2af9/docs/figure/cash_plots.rmd/unnamed-chunk-10-1.png" target="_blank">27ef9e3</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-10-2.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-10-2.png:</em></summary>
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Author
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<th style="text-align:left;">
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</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/27ef9e3a7d9105ef2924cfb810167a16779f2af9/docs/figure/cash_plots.rmd/unnamed-chunk-10-2.png" target="_blank">27ef9e3</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-10-3.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-10-3.png:</em></summary>
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<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/27ef9e3a7d9105ef2924cfb810167a16779f2af9/docs/figure/cash_plots.rmd/unnamed-chunk-10-3.png" target="_blank">27ef9e3</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
</tr>
</tbody>
</table>
</details>
</div>
<div id="spiky-g_3-0.4-nleft0-0.52right-0.2-nleft0-12right-0.2-nleft0-22right-0.2-nleft0-32right" class="section level2">
<h2>Spiky: <span class="math inline">\(g_3 = 0.4 N\left(0, 0.5^2\right) + 0.2 N\left(0, 1^2\right) + 0.2 N\left(0, 2^2\right) + 0.2 N\left(0, 3^2\right)\)</span></h2>
<pre class="r"><code>FDP.array <- pFDP.array <- power.array <- array(0, dim = c(nsim, length(q.vec), length(method.name), length(pi0.vec)))
FDP.summary <- array(0, dim = c(7, length(q.vec), length(method.name), length(pi0.vec)))
pFDP.summary <- power.summary <- array(0, dim = c(5, length(q.vec), length(method.name), length(pi0.vec)))
for (j in seq(length(pi0.vec))) {
for (k in seq(length(method.name))) {
for (i in seq(nsim)) {
FDP.array[i, , k, j] <- sapply(q.vec, FDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
pFDP.array[i, , k, j] <- sapply(q.vec, pFDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
power.array[i, , k, j] <- sapply(q.vec, power, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
}
FDP.summary[, , k, j] <- rbind(
avg <- colMeans(FDP.array[, , k, j], na.rm = TRUE),
sd <- apply(FDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(FDP.array[, , k, j])),
q975 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE),
q750 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.75, na.rm = TRUE),
q250 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.25, na.rm = TRUE)
)
pFDP.summary[, , k, j] <- rbind(
avg <- colMeans(pFDP.array[, , k, j], na.rm = TRUE),
sd <- apply(pFDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(pFDP.array[, , k, j])),
q975 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
power.summary[, , k, j] <- rbind(
avg <- colMeans(power.array[, , k, j], na.rm = TRUE),
sd <- apply(power.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(power.array[, , k, j])),
q975 <- apply(power.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(power.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
}
}</code></pre>
<pre class="r"><code>for (j in seq(length(pi0.vec))) {
sd.z <- sapply(z.pi0.list[[j]], sd)
Noise <- cut(sd.z, breaks = c(0, quantile(sd.z, probs = 1 : 2 / 3), Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
# Noise <- cut(sd.z, breaks = c(0, z.under, z.over, Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
pi0.pi0 <- matrix(unlist(pi0.pi0.list[[j]]), byrow = TRUE, length(pi0.pi0.list[[j]]))
pi0.pi0.noise <- rbind.data.frame(cbind.data.frame(Noise, pi0.pi0), cbind.data.frame(Noise = rep("All", length(Noise)), pi0.pi0))
pi0.plot <- ggplot(data = melt(pi0.pi0.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col[-1]) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = pi0.vec[j], col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name[-1]) +
labs(x = "", y = expression(hat(pi)[0])) +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.summary.pi0 <- aperm(FDP.summary[, , , j], c(2, 1, 3))
FDP.summary.pi0.method <- FDP.summary.pi0[, , 1]
for (kk in 2 : length(method.name)) {
FDP.summary.pi0.method <- rbind.data.frame(FDP.summary.pi0.method, FDP.summary.pi0[, , kk])
}
FDP.summary.pi0.method <- cbind.data.frame(
rep(factor(seq(method.name)), each = dim(FDP.summary.pi0)[1]),
rep(q.vec, length(method.name)),
FDP.summary.pi0.method
)
colnames(FDP.summary.pi0.method) <- c(
"Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.array.pi0 <- aperm(FDP.array[, , , j], c(2, 1, 3))
FDP.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, mean, na.rm = TRUE), c(2, 1, 3)))
sd.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, sd, na.rm = TRUE), c(2, 1, 3)))
n.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, function(x){sum(!is.na(x))}), c(2, 1, 3)))
q975.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.975, na.rm = TRUE), c(2, 1, 3)))
q025.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.025, na.rm = TRUE), c(2, 1, 3)))
q750.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.75, na.rm = TRUE), c(2, 1, 3)))
q250.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.25, na.rm = TRUE), c(2, 1, 3)))
FDP.summary.pi0.method.noise <- cbind.data.frame(
rep(rep(levels(Noise), each = length(q.vec)), length(method.name)),
rep(factor(seq(method.name)), each = length(levels(Noise)) * length(q.vec)),
rep(q.vec, length(levels(Noise)) * length(method.name)),
FDP.pi0.noise,
sd.pi0.noise,
n.pi0.noise,
q975.pi0.noise,
q025.pi0.noise,
q750.pi0.noise,
q250.pi0.noise
)
colnames(FDP.summary.pi0.method.noise) <- c(
"Noise", "Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.summary.pi0.method.noise <- rbind.data.frame(
FDP.summary.pi0.method.noise,
cbind.data.frame(Noise = rep("All", dim(FDP.summary.pi0.method)[1]), FDP.summary.pi0.method)
)
FDR.calib.plot <- ggplot(data = FDP.summary.pi0.method.noise, aes(x = FDR, y = FDP, group = Method, col = Method)) +
geom_line() +
geom_ribbon(aes(ymin = q025, ymax = q975, fill = Method), alpha = 0.35, linetype = "blank") +
scale_color_manual(labels = method.name, values = method.col) +
scale_fill_manual(labels = method.name, values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_abline(slope = 1, intercept = 0, linetype = "dashed", size = 1, col = "black") +
labs(x = "Nominal FDR", y = "FDP") +
theme(legend.position = "top", legend.text = element_text(size = 15), plot.title = element_text(hjust = 0.5, size = 15), axis.title.x = element_text(size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(angle = 45, size = 15), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.q <- FDP.array[, which(round(q.vec, 4) == q), , j]
FDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, FDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), FDP.q))
FDR.plot <- ggplot(data = melt(FDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = q, col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "FDP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
TDP.q <- power.array[, which(round(q.vec, 4) == q), , j]
TDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, TDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), TDP.q))
power.plot <- ggplot(data = melt(TDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "TPP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
joint <- ggarrange(FDR.calib.plot,
pi0.plot + rremove("x.text"),
FDR.plot + rremove("x.text"),
power.plot,
align = "v", ncol = 1, nrow = 4,
heights = c(1.5, 1, 1, 1.2)
)
joint <- annotate_figure(joint,
top = text_grob(bquote(pi[0] == .(pi0.vec[j])), size = 15)
)
print(joint)
ggsave(paste0("../output/fig/g3_pi0_", pi0.vec[j], ".pdf"), joint, height = 10, width = 8)
}</code></pre>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-12-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-12-1.png:</em></summary>
<table style = "border-collapse:separate; border-spacing:5px;">
<thead>
<tr>
<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/27ef9e3a7d9105ef2924cfb810167a16779f2af9/docs/figure/cash_plots.rmd/unnamed-chunk-12-1.png" target="_blank">27ef9e3</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/37ad45698441ee0ae5eb3202f95e0164d77ef5b7/docs/figure/cash_plots.rmd/unnamed-chunk-12-1.png" target="_blank">37ad456</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-04-27
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-12-2.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-12-2.png:</em></summary>
<table style = "border-collapse:separate; border-spacing:5px;">
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<th style="text-align:left;">
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Author
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<th style="text-align:left;">
Date
</th>
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<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/27ef9e3a7d9105ef2924cfb810167a16779f2af9/docs/figure/cash_plots.rmd/unnamed-chunk-12-2.png" target="_blank">27ef9e3</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/37ad45698441ee0ae5eb3202f95e0164d77ef5b7/docs/figure/cash_plots.rmd/unnamed-chunk-12-2.png" target="_blank">37ad456</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-04-27
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-12-3.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-12-3.png:</em></summary>
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Author
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<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/27ef9e3a7d9105ef2924cfb810167a16779f2af9/docs/figure/cash_plots.rmd/unnamed-chunk-12-3.png" target="_blank">27ef9e3</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
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</tbody>
</table>
</details>
</div>
<div id="flattop-g_4-1-13-left-nleft-3-0.52right-nleft-2.5-0.52right-nleft-2-0.52right-nleft-1.5-0.52right-nleft-1-0.52right-nleft-0.5-0.52right-nleft0-0.52right-nleft0.5-0.52right-nleft1-0.52right-nleft1.5-0.52right-nleft2-0.52right-nleft2.5-0.52right-nleft3-0.52right-right" class="section level2">
<h2>Flattop: <span class="math inline">\(g_4 = 1 / 13 \left( N\left(-3, 0.5^2\right) + N\left(-2.5, 0.5^2\right) + N\left(-2, 0.5^2\right) + N\left(-1.5, 0.5^2\right) + N\left(-1, 0.5^2\right) + N\left(-0.5, 0.5^2\right) + N\left(0, 0.5^2\right) + N\left(0.5, 0.5^2\right) + N\left(1, 0.5^2\right) + N\left(1.5, 0.5^2\right) + N\left(2, 0.5^2\right) + N\left(2.5, 0.5^2\right) + N\left(3, 0.5^2\right) \right)\)</span></h2>
<pre class="r"><code>FDP.array <- pFDP.array <- power.array <- array(0, dim = c(nsim, length(q.vec), length(method.name), length(pi0.vec)))
FDP.summary <- array(0, dim = c(7, length(q.vec), length(method.name), length(pi0.vec)))
pFDP.summary <- power.summary <- array(0, dim = c(5, length(q.vec), length(method.name), length(pi0.vec)))
for (j in seq(length(pi0.vec))) {
for (k in seq(length(method.name))) {
for (i in seq(nsim)) {
FDP.array[i, , k, j] <- sapply(q.vec, FDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
pFDP.array[i, , k, j] <- sapply(q.vec, pFDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
power.array[i, , k, j] <- sapply(q.vec, power, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
}
FDP.summary[, , k, j] <- rbind(
avg <- colMeans(FDP.array[, , k, j], na.rm = TRUE),
sd <- apply(FDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(FDP.array[, , k, j])),
q975 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE),
q750 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.75, na.rm = TRUE),
q250 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.25, na.rm = TRUE)
)
pFDP.summary[, , k, j] <- rbind(
avg <- colMeans(pFDP.array[, , k, j], na.rm = TRUE),
sd <- apply(pFDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(pFDP.array[, , k, j])),
q975 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
power.summary[, , k, j] <- rbind(
avg <- colMeans(power.array[, , k, j], na.rm = TRUE),
sd <- apply(power.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(power.array[, , k, j])),
q975 <- apply(power.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(power.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
}
}</code></pre>
<pre class="r"><code>for (j in seq(length(pi0.vec))) {
sd.z <- sapply(z.pi0.list[[j]], sd)
Noise <- cut(sd.z, breaks = c(0, quantile(sd.z, probs = 1 : 2 / 3), Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
# Noise <- cut(sd.z, breaks = c(0, z.under, z.over, Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
pi0.pi0 <- matrix(unlist(pi0.pi0.list[[j]]), byrow = TRUE, length(pi0.pi0.list[[j]]))
pi0.pi0.noise <- rbind.data.frame(cbind.data.frame(Noise, pi0.pi0), cbind.data.frame(Noise = rep("All", length(Noise)), pi0.pi0))
pi0.plot <- ggplot(data = melt(pi0.pi0.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col[-1]) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = pi0.vec[j], col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name[-1]) +
labs(x = "", y = expression(hat(pi)[0])) +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.summary.pi0 <- aperm(FDP.summary[, , , j], c(2, 1, 3))
FDP.summary.pi0.method <- FDP.summary.pi0[, , 1]
for (kk in 2 : length(method.name)) {
FDP.summary.pi0.method <- rbind.data.frame(FDP.summary.pi0.method, FDP.summary.pi0[, , kk])
}
FDP.summary.pi0.method <- cbind.data.frame(
rep(factor(seq(method.name)), each = dim(FDP.summary.pi0)[1]),
rep(q.vec, length(method.name)),
FDP.summary.pi0.method
)
colnames(FDP.summary.pi0.method) <- c(
"Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.array.pi0 <- aperm(FDP.array[, , , j], c(2, 1, 3))
FDP.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, mean, na.rm = TRUE), c(2, 1, 3)))
sd.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, sd, na.rm = TRUE), c(2, 1, 3)))
n.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, function(x){sum(!is.na(x))}), c(2, 1, 3)))
q975.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.975, na.rm = TRUE), c(2, 1, 3)))
q025.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.025, na.rm = TRUE), c(2, 1, 3)))
q750.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.75, na.rm = TRUE), c(2, 1, 3)))
q250.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.25, na.rm = TRUE), c(2, 1, 3)))
FDP.summary.pi0.method.noise <- cbind.data.frame(
rep(rep(levels(Noise), each = length(q.vec)), length(method.name)),
rep(factor(seq(method.name)), each = length(levels(Noise)) * length(q.vec)),
rep(q.vec, length(levels(Noise)) * length(method.name)),
FDP.pi0.noise,
sd.pi0.noise,
n.pi0.noise,
q975.pi0.noise,
q025.pi0.noise,
q750.pi0.noise,
q250.pi0.noise
)
colnames(FDP.summary.pi0.method.noise) <- c(
"Noise", "Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.summary.pi0.method.noise <- rbind.data.frame(
FDP.summary.pi0.method.noise,
cbind.data.frame(Noise = rep("All", dim(FDP.summary.pi0.method)[1]), FDP.summary.pi0.method)
)
FDR.calib.plot <- ggplot(data = FDP.summary.pi0.method.noise, aes(x = FDR, y = FDP, group = Method, col = Method)) +
geom_line() +
geom_ribbon(aes(ymin = q025, ymax = q975, fill = Method), alpha = 0.35, linetype = "blank") +
scale_color_manual(labels = method.name, values = method.col) +
scale_fill_manual(labels = method.name, values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_abline(slope = 1, intercept = 0, linetype = "dashed", size = 1, col = "black") +
labs(x = "Nominal FDR", y = "FDP") +
theme(legend.position = "top", legend.text = element_text(size = 15), plot.title = element_text(hjust = 0.5, size = 15), axis.title.x = element_text(size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(angle = 45, size = 15), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.q <- FDP.array[, which(round(q.vec, 4) == q), , j]
FDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, FDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), FDP.q))
FDR.plot <- ggplot(data = melt(FDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = q, col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "FDP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
TDP.q <- power.array[, which(round(q.vec, 4) == q), , j]
TDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, TDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), TDP.q))
power.plot <- ggplot(data = melt(TDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "TPP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
joint <- ggarrange(FDR.calib.plot,
pi0.plot + rremove("x.text"),
FDR.plot + rremove("x.text"),
power.plot,
align = "v", ncol = 1, nrow = 4,
heights = c(1.5, 1, 1, 1.2)
)
joint <- annotate_figure(joint,
top = text_grob(bquote(pi[0] == .(pi0.vec[j])), size = 15)
)
print(joint)
ggsave(paste0("../output/fig/g4_pi0_", pi0.vec[j], ".pdf"), joint, height = 10, width = 8)
}</code></pre>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-14-1.png" width="672" style="display: block; margin: auto;" /></p>
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</div>
<div id="near-normal-g_5-0.6-nleft0-12right-0.4-nleft0-32right" class="section level2">
<h2>Near normal: <span class="math inline">\(g_5 = 0.6 N\left(0, 1^2\right) + 0.4 N\left(0, 3^2\right)\)</span></h2>
<pre class="r"><code>FDP.array <- pFDP.array <- power.array <- array(0, dim = c(nsim, length(q.vec), length(method.name), length(pi0.vec)))
FDP.summary <- array(0, dim = c(7, length(q.vec), length(method.name), length(pi0.vec)))
pFDP.summary <- power.summary <- array(0, dim = c(5, length(q.vec), length(method.name), length(pi0.vec)))
for (j in seq(length(pi0.vec))) {
for (k in seq(length(method.name))) {
for (i in seq(nsim)) {
FDP.array[i, , k, j] <- sapply(q.vec, FDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
pFDP.array[i, , k, j] <- sapply(q.vec, pFDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
power.array[i, , k, j] <- sapply(q.vec, power, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
}
FDP.summary[, , k, j] <- rbind(
avg <- colMeans(FDP.array[, , k, j], na.rm = TRUE),
sd <- apply(FDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(FDP.array[, , k, j])),
q975 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE),
q750 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.75, na.rm = TRUE),
q250 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.25, na.rm = TRUE)
)
pFDP.summary[, , k, j] <- rbind(
avg <- colMeans(pFDP.array[, , k, j], na.rm = TRUE),
sd <- apply(pFDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(pFDP.array[, , k, j])),
q975 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
power.summary[, , k, j] <- rbind(
avg <- colMeans(power.array[, , k, j], na.rm = TRUE),
sd <- apply(power.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(power.array[, , k, j])),
q975 <- apply(power.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(power.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
}
}</code></pre>
<pre class="r"><code>for (j in seq(length(pi0.vec))) {
sd.z <- sapply(z.pi0.list[[j]], sd)
Noise <- cut(sd.z, breaks = c(0, quantile(sd.z, probs = 1 : 2 / 3), Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
# Noise <- cut(sd.z, breaks = c(0, z.under, z.over, Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
pi0.pi0 <- matrix(unlist(pi0.pi0.list[[j]]), byrow = TRUE, length(pi0.pi0.list[[j]]))
pi0.pi0.noise <- rbind.data.frame(cbind.data.frame(Noise, pi0.pi0), cbind.data.frame(Noise = rep("All", length(Noise)), pi0.pi0))
pi0.plot <- ggplot(data = melt(pi0.pi0.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col[-1]) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = pi0.vec[j], col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name[-1]) +
labs(x = "", y = expression(hat(pi)[0])) +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.summary.pi0 <- aperm(FDP.summary[, , , j], c(2, 1, 3))
FDP.summary.pi0.method <- FDP.summary.pi0[, , 1]
for (kk in 2 : length(method.name)) {
FDP.summary.pi0.method <- rbind.data.frame(FDP.summary.pi0.method, FDP.summary.pi0[, , kk])
}
FDP.summary.pi0.method <- cbind.data.frame(
rep(factor(seq(method.name)), each = dim(FDP.summary.pi0)[1]),
rep(q.vec, length(method.name)),
FDP.summary.pi0.method
)
colnames(FDP.summary.pi0.method) <- c(
"Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.array.pi0 <- aperm(FDP.array[, , , j], c(2, 1, 3))
FDP.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, mean, na.rm = TRUE), c(2, 1, 3)))
sd.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, sd, na.rm = TRUE), c(2, 1, 3)))
n.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, function(x){sum(!is.na(x))}), c(2, 1, 3)))
q975.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.975, na.rm = TRUE), c(2, 1, 3)))
q025.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.025, na.rm = TRUE), c(2, 1, 3)))
q750.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.75, na.rm = TRUE), c(2, 1, 3)))
q250.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.25, na.rm = TRUE), c(2, 1, 3)))
FDP.summary.pi0.method.noise <- cbind.data.frame(
rep(rep(levels(Noise), each = length(q.vec)), length(method.name)),
rep(factor(seq(method.name)), each = length(levels(Noise)) * length(q.vec)),
rep(q.vec, length(levels(Noise)) * length(method.name)),
FDP.pi0.noise,
sd.pi0.noise,
n.pi0.noise,
q975.pi0.noise,
q025.pi0.noise,
q750.pi0.noise,
q250.pi0.noise
)
colnames(FDP.summary.pi0.method.noise) <- c(
"Noise", "Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.summary.pi0.method.noise <- rbind.data.frame(
FDP.summary.pi0.method.noise,
cbind.data.frame(Noise = rep("All", dim(FDP.summary.pi0.method)[1]), FDP.summary.pi0.method)
)
FDR.calib.plot <- ggplot(data = FDP.summary.pi0.method.noise, aes(x = FDR, y = FDP, group = Method, col = Method)) +
geom_line() +
geom_ribbon(aes(ymin = q025, ymax = q975, fill = Method), alpha = 0.35, linetype = "blank") +
scale_color_manual(labels = method.name, values = method.col) +
scale_fill_manual(labels = method.name, values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_abline(slope = 1, intercept = 0, linetype = "dashed", size = 1, col = "black") +
labs(x = "Nominal FDR", y = "FDP") +
theme(legend.position = "top", legend.text = element_text(size = 15), plot.title = element_text(hjust = 0.5, size = 15), axis.title.x = element_text(size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(angle = 45, size = 15), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.q <- FDP.array[, which(round(q.vec, 4) == q), , j]
FDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, FDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), FDP.q))
FDR.plot <- ggplot(data = melt(FDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = q, col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "FDP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
TDP.q <- power.array[, which(round(q.vec, 4) == q), , j]
TDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, TDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), TDP.q))
power.plot <- ggplot(data = melt(TDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "TPP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
joint <- ggarrange(FDR.calib.plot,
pi0.plot + rremove("x.text"),
FDR.plot + rremove("x.text"),
power.plot,
align = "v", ncol = 1, nrow = 4,
heights = c(1.5, 1, 1, 1.2)
)
joint <- annotate_figure(joint,
top = text_grob(bquote(pi[0] == .(pi0.vec[j])), size = 15)
)
print(joint)
ggsave(paste0("../output/fig/g5_pi0_", pi0.vec[j], ".pdf"), joint, height = 10, width = 8)
}</code></pre>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-16-1.png" width="672" style="display: block; margin: auto;" /></p>
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<a href="https://github.com/LSun/truncash/blob/27ef9e3a7d9105ef2924cfb810167a16779f2af9/docs/figure/cash_plots.rmd/unnamed-chunk-16-1.png" target="_blank">27ef9e3</a>
</td>
<td style="text-align:left;">
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</td>
<td style="text-align:left;">
2018-05-14
</td>
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</table>
</details>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-16-2.png" width="672" style="display: block; margin: auto;" /></p>
<details>
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</details>
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<a href="https://github.com/LSun/truncash/blob/27ef9e3a7d9105ef2924cfb810167a16779f2af9/docs/figure/cash_plots.rmd/unnamed-chunk-16-3.png" target="_blank">27ef9e3</a>
</td>
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</div>
<div id="big-normal-g_6-nleft0-52right" class="section level2">
<h2>Big normal: <span class="math inline">\(g_6 = N\left(0, 5^2\right)\)</span></h2>
<pre class="r"><code>FDP.array <- pFDP.array <- power.array <- array(0, dim = c(nsim, length(q.vec), length(method.name), length(pi0.vec)))
FDP.summary <- array(0, dim = c(7, length(q.vec), length(method.name), length(pi0.vec)))
pFDP.summary <- power.summary <- array(0, dim = c(5, length(q.vec), length(method.name), length(pi0.vec)))
for (j in seq(length(pi0.vec))) {
for (k in seq(length(method.name))) {
for (i in seq(nsim)) {
FDP.array[i, , k, j] <- sapply(q.vec, FDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
pFDP.array[i, , k, j] <- sapply(q.vec, pFDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
power.array[i, , k, j] <- sapply(q.vec, power, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
}
FDP.summary[, , k, j] <- rbind(
avg <- colMeans(FDP.array[, , k, j], na.rm = TRUE),
sd <- apply(FDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(FDP.array[, , k, j])),
q975 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE),
q750 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.75, na.rm = TRUE),
q250 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.25, na.rm = TRUE)
)
pFDP.summary[, , k, j] <- rbind(
avg <- colMeans(pFDP.array[, , k, j], na.rm = TRUE),
sd <- apply(pFDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(pFDP.array[, , k, j])),
q975 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
power.summary[, , k, j] <- rbind(
avg <- colMeans(power.array[, , k, j], na.rm = TRUE),
sd <- apply(power.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(power.array[, , k, j])),
q975 <- apply(power.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(power.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
}
}</code></pre>
<pre class="r"><code>for (j in seq(length(pi0.vec))) {
sd.z <- sapply(z.pi0.list[[j]], sd)
Noise <- cut(sd.z, breaks = c(0, quantile(sd.z, probs = 1 : 2 / 3), Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
# Noise <- cut(sd.z, breaks = c(0, z.under, z.over, Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
pi0.pi0 <- matrix(unlist(pi0.pi0.list[[j]]), byrow = TRUE, length(pi0.pi0.list[[j]]))
pi0.pi0.noise <- rbind.data.frame(cbind.data.frame(Noise, pi0.pi0), cbind.data.frame(Noise = rep("All", length(Noise)), pi0.pi0))
pi0.plot <- ggplot(data = melt(pi0.pi0.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col[-1]) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = pi0.vec[j], col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name[-1]) +
labs(x = "", y = expression(hat(pi)[0])) +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.summary.pi0 <- aperm(FDP.summary[, , , j], c(2, 1, 3))
FDP.summary.pi0.method <- FDP.summary.pi0[, , 1]
for (kk in 2 : length(method.name)) {
FDP.summary.pi0.method <- rbind.data.frame(FDP.summary.pi0.method, FDP.summary.pi0[, , kk])
}
FDP.summary.pi0.method <- cbind.data.frame(
rep(factor(seq(method.name)), each = dim(FDP.summary.pi0)[1]),
rep(q.vec, length(method.name)),
FDP.summary.pi0.method
)
colnames(FDP.summary.pi0.method) <- c(
"Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.array.pi0 <- aperm(FDP.array[, , , j], c(2, 1, 3))
FDP.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, mean, na.rm = TRUE), c(2, 1, 3)))
sd.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, sd, na.rm = TRUE), c(2, 1, 3)))
n.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, function(x){sum(!is.na(x))}), c(2, 1, 3)))
q975.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.975, na.rm = TRUE), c(2, 1, 3)))
q025.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.025, na.rm = TRUE), c(2, 1, 3)))
q750.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.75, na.rm = TRUE), c(2, 1, 3)))
q250.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.25, na.rm = TRUE), c(2, 1, 3)))
FDP.summary.pi0.method.noise <- cbind.data.frame(
rep(rep(levels(Noise), each = length(q.vec)), length(method.name)),
rep(factor(seq(method.name)), each = length(levels(Noise)) * length(q.vec)),
rep(q.vec, length(levels(Noise)) * length(method.name)),
FDP.pi0.noise,
sd.pi0.noise,
n.pi0.noise,
q975.pi0.noise,
q025.pi0.noise,
q750.pi0.noise,
q250.pi0.noise
)
colnames(FDP.summary.pi0.method.noise) <- c(
"Noise", "Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.summary.pi0.method.noise <- rbind.data.frame(
FDP.summary.pi0.method.noise,
cbind.data.frame(Noise = rep("All", dim(FDP.summary.pi0.method)[1]), FDP.summary.pi0.method)
)
FDR.calib.plot <- ggplot(data = FDP.summary.pi0.method.noise, aes(x = FDR, y = FDP, group = Method, col = Method)) +
geom_line() +
geom_ribbon(aes(ymin = q025, ymax = q975, fill = Method), alpha = 0.35, linetype = "blank") +
scale_color_manual(labels = method.name, values = method.col) +
scale_fill_manual(labels = method.name, values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_abline(slope = 1, intercept = 0, linetype = "dashed", size = 1, col = "black") +
labs(x = "Nominal FDR", y = "FDP") +
theme(legend.position = "top", legend.text = element_text(size = 15), plot.title = element_text(hjust = 0.5, size = 15), axis.title.x = element_text(size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(angle = 45, size = 15), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.q <- FDP.array[, which(round(q.vec, 4) == q), , j]
FDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, FDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), FDP.q))
FDR.plot <- ggplot(data = melt(FDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = q, col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "FDP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
TDP.q <- power.array[, which(round(q.vec, 4) == q), , j]
TDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, TDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), TDP.q))
power.plot <- ggplot(data = melt(TDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "TPP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
joint <- ggarrange(FDR.calib.plot,
pi0.plot + rremove("x.text"),
FDR.plot + rremove("x.text"),
power.plot,
align = "v", ncol = 1, nrow = 4,
heights = c(1.5, 1, 1, 1.2)
)
joint <- annotate_figure(joint,
top = text_grob(bquote(pi[0] == .(pi0.vec[j])), size = 15)
)
print(joint)
ggsave(paste0("../output/fig/g6_pi0_", pi0.vec[j], ".pdf"), joint, height = 10, width = 8)
}</code></pre>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-18-1.png" width="672" style="display: block; margin: auto;" /></p>
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<a href="https://github.com/LSun/truncash/blob/27ef9e3a7d9105ef2924cfb810167a16779f2af9/docs/figure/cash_plots.rmd/unnamed-chunk-18-1.png" target="_blank">27ef9e3</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/37ad45698441ee0ae5eb3202f95e0164d77ef5b7/docs/figure/cash_plots.rmd/unnamed-chunk-18-1.png" target="_blank">37ad456</a>
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LSun
</td>
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<a href="https://github.com/LSun/truncash/blob/37ad45698441ee0ae5eb3202f95e0164d77ef5b7/docs/figure/cash_plots.rmd/unnamed-chunk-18-2.png" target="_blank">37ad456</a>
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LSun
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2018-04-27
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</div>
<div id="skew-g_7-14-nleft-2-22right-14-nleft-1-1.52right-13-nleft0-12right-1-6-nleft1-12right" class="section level2">
<h2>Skew: <span class="math inline">\(g_7 = 1/4 N\left(-2, 2^2\right) + 1/4 N\left(-1, 1.5^2\right) + 1/3 N\left(0, 1^2\right) + 1 / 6 N\left(1, 1^2\right)\)</span></h2>
<pre class="r"><code>FDP.array <- pFDP.array <- power.array <- array(0, dim = c(nsim, length(q.vec), length(method.name), length(pi0.vec)))
FDP.summary <- array(0, dim = c(7, length(q.vec), length(method.name), length(pi0.vec)))
pFDP.summary <- power.summary <- array(0, dim = c(5, length(q.vec), length(method.name), length(pi0.vec)))
for (j in seq(length(pi0.vec))) {
for (k in seq(length(method.name))) {
for (i in seq(nsim)) {
FDP.array[i, , k, j] <- sapply(q.vec, FDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
pFDP.array[i, , k, j] <- sapply(q.vec, pFDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
power.array[i, , k, j] <- sapply(q.vec, power, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
}
FDP.summary[, , k, j] <- rbind(
avg <- colMeans(FDP.array[, , k, j], na.rm = TRUE),
sd <- apply(FDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(FDP.array[, , k, j])),
q975 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE),
q750 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.75, na.rm = TRUE),
q250 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.25, na.rm = TRUE)
)
pFDP.summary[, , k, j] <- rbind(
avg <- colMeans(pFDP.array[, , k, j], na.rm = TRUE),
sd <- apply(pFDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(pFDP.array[, , k, j])),
q975 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
power.summary[, , k, j] <- rbind(
avg <- colMeans(power.array[, , k, j], na.rm = TRUE),
sd <- apply(power.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(power.array[, , k, j])),
q975 <- apply(power.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(power.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
}
}</code></pre>
<pre class="r"><code>for (j in seq(length(pi0.vec))) {
sd.z <- sapply(z.pi0.list[[j]], sd)
Noise <- cut(sd.z, breaks = c(0, quantile(sd.z, probs = 1 : 2 / 3), Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
# Noise <- cut(sd.z, breaks = c(0, z.under, z.over, Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
pi0.pi0 <- matrix(unlist(pi0.pi0.list[[j]]), byrow = TRUE, length(pi0.pi0.list[[j]]))
pi0.pi0.noise <- rbind.data.frame(cbind.data.frame(Noise, pi0.pi0), cbind.data.frame(Noise = rep("All", length(Noise)), pi0.pi0))
pi0.plot <- ggplot(data = melt(pi0.pi0.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col[-1]) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = pi0.vec[j], col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name[-1]) +
labs(x = "", y = expression(hat(pi)[0])) +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.summary.pi0 <- aperm(FDP.summary[, , , j], c(2, 1, 3))
FDP.summary.pi0.method <- FDP.summary.pi0[, , 1]
for (kk in 2 : length(method.name)) {
FDP.summary.pi0.method <- rbind.data.frame(FDP.summary.pi0.method, FDP.summary.pi0[, , kk])
}
FDP.summary.pi0.method <- cbind.data.frame(
rep(factor(seq(method.name)), each = dim(FDP.summary.pi0)[1]),
rep(q.vec, length(method.name)),
FDP.summary.pi0.method
)
colnames(FDP.summary.pi0.method) <- c(
"Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.array.pi0 <- aperm(FDP.array[, , , j], c(2, 1, 3))
FDP.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, mean, na.rm = TRUE), c(2, 1, 3)))
sd.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, sd, na.rm = TRUE), c(2, 1, 3)))
n.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, function(x){sum(!is.na(x))}), c(2, 1, 3)))
q975.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.975, na.rm = TRUE), c(2, 1, 3)))
q025.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.025, na.rm = TRUE), c(2, 1, 3)))
q750.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.75, na.rm = TRUE), c(2, 1, 3)))
q250.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.25, na.rm = TRUE), c(2, 1, 3)))
FDP.summary.pi0.method.noise <- cbind.data.frame(
rep(rep(levels(Noise), each = length(q.vec)), length(method.name)),
rep(factor(seq(method.name)), each = length(levels(Noise)) * length(q.vec)),
rep(q.vec, length(levels(Noise)) * length(method.name)),
FDP.pi0.noise,
sd.pi0.noise,
n.pi0.noise,
q975.pi0.noise,
q025.pi0.noise,
q750.pi0.noise,
q250.pi0.noise
)
colnames(FDP.summary.pi0.method.noise) <- c(
"Noise", "Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.summary.pi0.method.noise <- rbind.data.frame(
FDP.summary.pi0.method.noise,
cbind.data.frame(Noise = rep("All", dim(FDP.summary.pi0.method)[1]), FDP.summary.pi0.method)
)
FDR.calib.plot <- ggplot(data = FDP.summary.pi0.method.noise, aes(x = FDR, y = FDP, group = Method, col = Method)) +
geom_line() +
geom_ribbon(aes(ymin = q025, ymax = q975, fill = Method), alpha = 0.35, linetype = "blank") +
scale_color_manual(labels = method.name, values = method.col) +
scale_fill_manual(labels = method.name, values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_abline(slope = 1, intercept = 0, linetype = "dashed", size = 1, col = "black") +
labs(x = "Nominal FDR", y = "FDP") +
theme(legend.position = "top", legend.text = element_text(size = 15), plot.title = element_text(hjust = 0.5, size = 15), axis.title.x = element_text(size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(angle = 45, size = 15), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.q <- FDP.array[, which(round(q.vec, 4) == q), , j]
FDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, FDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), FDP.q))
FDR.plot <- ggplot(data = melt(FDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = q, col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "FDP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
TDP.q <- power.array[, which(round(q.vec, 4) == q), , j]
TDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, TDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), TDP.q))
power.plot <- ggplot(data = melt(TDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "TPP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
joint <- ggarrange(FDR.calib.plot,
pi0.plot + rremove("x.text"),
FDR.plot + rremove("x.text"),
power.plot,
align = "v", ncol = 1, nrow = 4,
heights = c(1.5, 1, 1, 1.2)
)
joint <- annotate_figure(joint,
top = text_grob(bquote(pi[0] == .(pi0.vec[j])), size = 15)
)
print(joint)
ggsave(paste0("../output/fig/g7_pi0_", pi0.vec[j], ".pdf"), joint, height = 10, width = 8)
}</code></pre>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-20-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-20-1.png:</em></summary>
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<a href="https://github.com/LSun/truncash/blob/27ef9e3a7d9105ef2924cfb810167a16779f2af9/docs/figure/cash_plots.rmd/unnamed-chunk-20-1.png" target="_blank">27ef9e3</a>
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<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
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<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/37ad45698441ee0ae5eb3202f95e0164d77ef5b7/docs/figure/cash_plots.rmd/unnamed-chunk-20-1.png" target="_blank">37ad456</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-04-27
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-20-2.png" width="672" style="display: block; margin: auto;" /></p>
<details>
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<a href="https://github.com/LSun/truncash/blob/27ef9e3a7d9105ef2924cfb810167a16779f2af9/docs/figure/cash_plots.rmd/unnamed-chunk-20-2.png" target="_blank">27ef9e3</a>
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<td style="text-align:left;">
LSun
</td>
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2018-05-14
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</details>
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<a href="https://github.com/LSun/truncash/blob/27ef9e3a7d9105ef2924cfb810167a16779f2af9/docs/figure/cash_plots.rmd/unnamed-chunk-20-3.png" target="_blank">27ef9e3</a>
</td>
<td style="text-align:left;">
LSun
</td>
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</div>
<div id="small-normal-g_8-nleft0-12right" class="section level2">
<h2>Small normal: <span class="math inline">\(g_8 = N\left(0, 1^2\right)\)</span></h2>
<pre class="r"><code>FDP.array <- pFDP.array <- power.array <- array(0, dim = c(nsim, length(q.vec), length(method.name), length(pi0.vec)))
FDP.summary <- array(0, dim = c(7, length(q.vec), length(method.name), length(pi0.vec)))
pFDP.summary <- power.summary <- array(0, dim = c(5, length(q.vec), length(method.name), length(pi0.vec)))
for (j in seq(length(pi0.vec))) {
for (k in seq(length(method.name))) {
for (i in seq(nsim)) {
FDP.array[i, , k, j] <- sapply(q.vec, FDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
pFDP.array[i, , k, j] <- sapply(q.vec, pFDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
power.array[i, , k, j] <- sapply(q.vec, power, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
}
FDP.summary[, , k, j] <- rbind(
avg <- colMeans(FDP.array[, , k, j], na.rm = TRUE),
sd <- apply(FDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(FDP.array[, , k, j])),
q975 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE),
q750 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.75, na.rm = TRUE),
q250 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.25, na.rm = TRUE)
)
pFDP.summary[, , k, j] <- rbind(
avg <- colMeans(pFDP.array[, , k, j], na.rm = TRUE),
sd <- apply(pFDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(pFDP.array[, , k, j])),
q975 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
power.summary[, , k, j] <- rbind(
avg <- colMeans(power.array[, , k, j], na.rm = TRUE),
sd <- apply(power.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(power.array[, , k, j])),
q975 <- apply(power.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(power.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
}
}</code></pre>
<pre class="r"><code>for (j in seq(length(pi0.vec))) {
sd.z <- sapply(z.pi0.list[[j]], sd)
Noise <- cut(sd.z, breaks = c(0, quantile(sd.z, probs = 1 : 2 / 3), Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
# Noise <- cut(sd.z, breaks = c(0, z.under, z.over, Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
pi0.pi0 <- matrix(unlist(pi0.pi0.list[[j]]), byrow = TRUE, length(pi0.pi0.list[[j]]))
pi0.pi0.noise <- rbind.data.frame(cbind.data.frame(Noise, pi0.pi0), cbind.data.frame(Noise = rep("All", length(Noise)), pi0.pi0))
pi0.plot <- ggplot(data = melt(pi0.pi0.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col[-1]) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = pi0.vec[j], col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name[-1]) +
labs(x = "", y = expression(hat(pi)[0])) +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.summary.pi0 <- aperm(FDP.summary[, , , j], c(2, 1, 3))
FDP.summary.pi0.method <- FDP.summary.pi0[, , 1]
for (kk in 2 : length(method.name)) {
FDP.summary.pi0.method <- rbind.data.frame(FDP.summary.pi0.method, FDP.summary.pi0[, , kk])
}
FDP.summary.pi0.method <- cbind.data.frame(
rep(factor(seq(method.name)), each = dim(FDP.summary.pi0)[1]),
rep(q.vec, length(method.name)),
FDP.summary.pi0.method
)
colnames(FDP.summary.pi0.method) <- c(
"Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.array.pi0 <- aperm(FDP.array[, , , j], c(2, 1, 3))
FDP.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, mean, na.rm = TRUE), c(2, 1, 3)))
sd.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, sd, na.rm = TRUE), c(2, 1, 3)))
n.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, function(x){sum(!is.na(x))}), c(2, 1, 3)))
q975.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.975, na.rm = TRUE), c(2, 1, 3)))
q025.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.025, na.rm = TRUE), c(2, 1, 3)))
q750.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.75, na.rm = TRUE), c(2, 1, 3)))
q250.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.25, na.rm = TRUE), c(2, 1, 3)))
FDP.summary.pi0.method.noise <- cbind.data.frame(
rep(rep(levels(Noise), each = length(q.vec)), length(method.name)),
rep(factor(seq(method.name)), each = length(levels(Noise)) * length(q.vec)),
rep(q.vec, length(levels(Noise)) * length(method.name)),
FDP.pi0.noise,
sd.pi0.noise,
n.pi0.noise,
q975.pi0.noise,
q025.pi0.noise,
q750.pi0.noise,
q250.pi0.noise
)
colnames(FDP.summary.pi0.method.noise) <- c(
"Noise", "Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.summary.pi0.method.noise <- rbind.data.frame(
FDP.summary.pi0.method.noise,
cbind.data.frame(Noise = rep("All", dim(FDP.summary.pi0.method)[1]), FDP.summary.pi0.method)
)
FDR.calib.plot <- ggplot(data = FDP.summary.pi0.method.noise, aes(x = FDR, y = FDP, group = Method, col = Method)) +
geom_line() +
geom_ribbon(aes(ymin = q025, ymax = q975, fill = Method), alpha = 0.35, linetype = "blank") +
scale_color_manual(labels = method.name, values = method.col) +
scale_fill_manual(labels = method.name, values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_abline(slope = 1, intercept = 0, linetype = "dashed", size = 1, col = "black") +
labs(x = "Nominal FDR", y = "FDP") +
theme(legend.position = "top", legend.text = element_text(size = 15), plot.title = element_text(hjust = 0.5, size = 15), axis.title.x = element_text(size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(angle = 45, size = 15), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.q <- FDP.array[, which(round(q.vec, 4) == q), , j]
FDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, FDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), FDP.q))
FDR.plot <- ggplot(data = melt(FDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = q, col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "FDP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
TDP.q <- power.array[, which(round(q.vec, 4) == q), , j]
TDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, TDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), TDP.q))
power.plot <- ggplot(data = melt(TDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "TPP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
joint <- ggarrange(FDR.calib.plot,
pi0.plot + rremove("x.text"),
FDR.plot + rremove("x.text"),
power.plot,
align = "v", ncol = 1, nrow = 4,
heights = c(1.5, 1, 1, 1.2)
)
joint <- annotate_figure(joint,
top = text_grob(bquote(pi[0] == .(pi0.vec[j])), size = 15)
)
print(joint)
ggsave(paste0("../output/fig/g8_pi0_", pi0.vec[j], ".pdf"), joint, height = 10, width = 8)
}</code></pre>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-22-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-22-1.png:</em></summary>
<table style = "border-collapse:separate; border-spacing:5px;">
<thead>
<tr>
<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/b7cf71b4d05a1ea70fdad8da02796d7c0ddc50e8/docs/figure/cash_plots.rmd/unnamed-chunk-22-1.png" target="_blank">b7cf71b</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/37ad45698441ee0ae5eb3202f95e0164d77ef5b7/docs/figure/cash_plots.rmd/unnamed-chunk-22-1.png" target="_blank">37ad456</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-04-27
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-22-2.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-22-2.png:</em></summary>
<table style = "border-collapse:separate; border-spacing:5px;">
<thead>
<tr>
<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/b7cf71b4d05a1ea70fdad8da02796d7c0ddc50e8/docs/figure/cash_plots.rmd/unnamed-chunk-22-2.png" target="_blank">b7cf71b</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-22-3.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-22-3.png:</em></summary>
<table style = "border-collapse:separate; border-spacing:5px;">
<thead>
<tr>
<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/b7cf71b4d05a1ea70fdad8da02796d7c0ddc50e8/docs/figure/cash_plots.rmd/unnamed-chunk-22-3.png" target="_blank">b7cf71b</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
</tr>
</tbody>
</table>
</details>
</div>
<div id="small-normal-g_9-nleft0-1.52right" class="section level2">
<h2>Small normal: <span class="math inline">\(g_9 = N\left(0, 1.5^2\right)\)</span></h2>
<pre class="r"><code>FDP.array <- pFDP.array <- power.array <- array(0, dim = c(nsim, length(q.vec), length(method.name), length(pi0.vec)))
FDP.summary <- array(0, dim = c(7, length(q.vec), length(method.name), length(pi0.vec)))
pFDP.summary <- power.summary <- array(0, dim = c(5, length(q.vec), length(method.name), length(pi0.vec)))
for (j in seq(length(pi0.vec))) {
for (k in seq(length(method.name))) {
for (i in seq(nsim)) {
FDP.array[i, , k, j] <- sapply(q.vec, FDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
pFDP.array[i, , k, j] <- sapply(q.vec, pFDP, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
power.array[i, , k, j] <- sapply(q.vec, power, qvalue = qvalue.pi0.list[[j]][[i]][, k], beta = beta.pi0.list[[j]][[i]])
}
FDP.summary[, , k, j] <- rbind(
avg <- colMeans(FDP.array[, , k, j], na.rm = TRUE),
sd <- apply(FDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(FDP.array[, , k, j])),
q975 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE),
q750 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.75, na.rm = TRUE),
q250 <- apply(FDP.array[, , k, j], 2, quantile, probs = 0.25, na.rm = TRUE)
)
pFDP.summary[, , k, j] <- rbind(
avg <- colMeans(pFDP.array[, , k, j], na.rm = TRUE),
sd <- apply(pFDP.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(pFDP.array[, , k, j])),
q975 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(pFDP.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
power.summary[, , k, j] <- rbind(
avg <- colMeans(power.array[, , k, j], na.rm = TRUE),
sd <- apply(power.array[, , k, j], 2, sd, na.rm = TRUE),
n <- colSums(!is.na(power.array[, , k, j])),
q975 <- apply(power.array[, , k, j], 2, quantile, probs = 0.975, na.rm = TRUE),
q025 <- apply(power.array[, , k, j], 2, quantile, probs = 0.025, na.rm = TRUE)
)
}
}</code></pre>
<pre class="r"><code>for (j in seq(length(pi0.vec))) {
sd.z <- sapply(z.pi0.list[[j]], sd)
Noise <- cut(sd.z, breaks = c(0, quantile(sd.z, probs = 1 : 2 / 3), Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
# Noise <- cut(sd.z, breaks = c(0, z.under, z.over, Inf), labels = c("Deflated Noise", "In-between", "Inflated Noise"))
pi0.pi0 <- matrix(unlist(pi0.pi0.list[[j]]), byrow = TRUE, length(pi0.pi0.list[[j]]))
pi0.pi0.noise <- rbind.data.frame(cbind.data.frame(Noise, pi0.pi0), cbind.data.frame(Noise = rep("All", length(Noise)), pi0.pi0))
pi0.plot <- ggplot(data = melt(pi0.pi0.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col[-1]) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = pi0.vec[j], col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name[-1]) +
labs(x = "", y = expression(hat(pi)[0])) +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.summary.pi0 <- aperm(FDP.summary[, , , j], c(2, 1, 3))
FDP.summary.pi0.method <- FDP.summary.pi0[, , 1]
for (kk in 2 : length(method.name)) {
FDP.summary.pi0.method <- rbind.data.frame(FDP.summary.pi0.method, FDP.summary.pi0[, , kk])
}
FDP.summary.pi0.method <- cbind.data.frame(
rep(factor(seq(method.name)), each = dim(FDP.summary.pi0)[1]),
rep(q.vec, length(method.name)),
FDP.summary.pi0.method
)
colnames(FDP.summary.pi0.method) <- c(
"Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.array.pi0 <- aperm(FDP.array[, , , j], c(2, 1, 3))
FDP.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, mean, na.rm = TRUE), c(2, 1, 3)))
sd.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, sd, na.rm = TRUE), c(2, 1, 3)))
n.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, function(x){sum(!is.na(x))}), c(2, 1, 3)))
q975.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.975, na.rm = TRUE), c(2, 1, 3)))
q025.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.025, na.rm = TRUE), c(2, 1, 3)))
q750.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.75, na.rm = TRUE), c(2, 1, 3)))
q250.pi0.noise <- as.vector(aperm(apply(FDP.array.pi0, c(1, 3), tapply, Noise, quantile, probs = 0.25, na.rm = TRUE), c(2, 1, 3)))
FDP.summary.pi0.method.noise <- cbind.data.frame(
rep(rep(levels(Noise), each = length(q.vec)), length(method.name)),
rep(factor(seq(method.name)), each = length(levels(Noise)) * length(q.vec)),
rep(q.vec, length(levels(Noise)) * length(method.name)),
FDP.pi0.noise,
sd.pi0.noise,
n.pi0.noise,
q975.pi0.noise,
q025.pi0.noise,
q750.pi0.noise,
q250.pi0.noise
)
colnames(FDP.summary.pi0.method.noise) <- c(
"Noise", "Method", "FDR", "FDP", "sd", "n", "q975", "q025", "q750", "q250"
)
FDP.summary.pi0.method.noise <- rbind.data.frame(
FDP.summary.pi0.method.noise,
cbind.data.frame(Noise = rep("All", dim(FDP.summary.pi0.method)[1]), FDP.summary.pi0.method)
)
FDR.calib.plot <- ggplot(data = FDP.summary.pi0.method.noise, aes(x = FDR, y = FDP, group = Method, col = Method)) +
geom_line() +
geom_ribbon(aes(ymin = q025, ymax = q975, fill = Method), alpha = 0.35, linetype = "blank") +
scale_color_manual(labels = method.name, values = method.col) +
scale_fill_manual(labels = method.name, values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_abline(slope = 1, intercept = 0, linetype = "dashed", size = 1, col = "black") +
labs(x = "Nominal FDR", y = "FDP") +
theme(legend.position = "top", legend.text = element_text(size = 15), plot.title = element_text(hjust = 0.5, size = 15), axis.title.x = element_text(size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(angle = 45, size = 15), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
FDP.q <- FDP.array[, which(round(q.vec, 4) == q), , j]
FDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, FDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), FDP.q))
FDR.plot <- ggplot(data = melt(FDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
geom_hline(yintercept = q, col = "black", linetype = "dashed", size = 1) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "FDP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
TDP.q <- power.array[, which(round(q.vec, 4) == q), , j]
TDP.q.noise <- rbind.data.frame(cbind.data.frame(Noise, TDP.q), cbind.data.frame(Noise = rep("All", length(Noise)), TDP.q))
power.plot <- ggplot(data = melt(TDP.q.noise, id.vars = "Noise"), aes(x = variable, y = value, col = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom = "point", shape = 13, size = 3) +
scale_color_manual(values = method.col) +
facet_wrap(~Noise, nrow = 1, ncol = 4) +
scale_x_discrete(labels = method.name) +
labs(x = "", y = "TPP") +
theme(legend.position = "none", plot.title = element_text(hjust = 0.5, size = 15), axis.title.y = element_text(size = 15), axis.text.x = element_text(size = 15, angle = 45, hjust = 1), axis.text.y = element_text(size = 15), strip.text = element_text(size = 15))
joint <- ggarrange(FDR.calib.plot,
pi0.plot + rremove("x.text"),
FDR.plot + rremove("x.text"),
power.plot,
align = "v", ncol = 1, nrow = 4,
heights = c(1.5, 1, 1, 1.2)
)
joint <- annotate_figure(joint,
top = text_grob(bquote(pi[0] == .(pi0.vec[j])), size = 15)
)
print(joint)
ggsave(paste0("../output/fig/g9_pi0_", pi0.vec[j], ".pdf"), joint, height = 10, width = 8)
}</code></pre>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-24-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-24-1.png:</em></summary>
<table style = "border-collapse:separate; border-spacing:5px;">
<thead>
<tr>
<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/b7cf71b4d05a1ea70fdad8da02796d7c0ddc50e8/docs/figure/cash_plots.rmd/unnamed-chunk-24-1.png" target="_blank">b7cf71b</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/564f9cbc4a8c3126ba03c320d03add8cc56c0aad/docs/figure/cash_plots.rmd/unnamed-chunk-24-1.png" target="_blank">564f9cb</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-06
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-24-2.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-24-2.png:</em></summary>
<table style = "border-collapse:separate; border-spacing:5px;">
<thead>
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<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/b7cf71b4d05a1ea70fdad8da02796d7c0ddc50e8/docs/figure/cash_plots.rmd/unnamed-chunk-24-2.png" target="_blank">b7cf71b</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/cash_plots.rmd/unnamed-chunk-24-3.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of unnamed-chunk-24-3.png:</em></summary>
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<thead>
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<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/b7cf71b4d05a1ea70fdad8da02796d7c0ddc50e8/docs/figure/cash_plots.rmd/unnamed-chunk-24-3.png" target="_blank">b7cf71b</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2018-05-14
</td>
</tr>
</tbody>
</table>
</details>
</div>
<div id="session-information" class="section level2">
<h2>Session information</h2>
<pre class="r"><code>sessionInfo()</code></pre>
<pre><code>R version 3.4.3 (2017-11-30)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.4
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] grid stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] ggpubr_0.1.6 magrittr_1.5 cowplot_0.9.2
[4] scales_0.5.0 RColorBrewer_1.1-2 gridExtra_2.3
[7] ggplot2_2.2.1 reshape2_1.4.3 qvalue_2.10.0
[10] locfdr_1.1-8 ashr_2.2-2 Rmosek_8.0.69
[13] CVXR_0.95 REBayes_1.2 Matrix_1.2-12
[16] SQUAREM_2017.10-1 EQL_1.0-0 ttutils_1.0-1
[19] PolynomF_1.0-1
loaded via a namespace (and not attached):
[1] purrr_0.2.4 splines_3.4.3 lattice_0.20-35
[4] colorspace_1.3-2 htmltools_0.3.6 yaml_2.1.18
[7] gmp_0.5-13.1 rlang_0.1.6 R.oo_1.21.0
[10] pillar_1.0.1 glue_1.2.0 Rmpfr_0.6-1
[13] R.utils_2.6.0 bit64_0.9-7 bindrcpp_0.2
[16] bindr_0.1 scs_1.1-1 foreach_1.4.4
[19] plyr_1.8.4 stringr_1.3.0 munsell_0.4.3
[22] gtable_0.2.0 workflowr_1.0.1 R.methodsS3_1.7.1
[25] codetools_0.2-15 evaluate_0.10.1 labeling_0.3
[28] knitr_1.20 doParallel_1.0.11 pscl_1.5.2
[31] parallel_3.4.3 Rcpp_0.12.16 backports_1.1.2
[34] truncnorm_1.0-7 bit_1.1-12 digest_0.6.15
[37] stringi_1.1.6 dplyr_0.7.4 rprojroot_1.3-2
[40] ECOSolveR_0.4 tools_3.4.3 lazyeval_0.2.1
[43] tibble_1.4.1 pkgconfig_2.0.1 whisker_0.3-2
[46] MASS_7.3-47 assertthat_0.2.0 rmarkdown_1.9
[49] iterators_1.0.9 R6_2.2.2 git2r_0.21.0
[52] compiler_3.4.3 </code></pre>
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