CASH Simulation, Part 6: Simulated vs Read data

Last updated: 2018-05-15

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rmd	cc0ab83	Lei Sun	2018-05-11	update
html	0f36d99	LSun	2017-12-21	Build site.
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Simulated correlated data

\[ z_i = L_i^Tx / \sqrt{L_i^TL_i} \ , \] where both \(x\) and \(L_i\) are \(d\)-dimentional independent \(N(0,1)\) random variates, and a large number of \(z_i\) are generated by the same \(x\) and different, independent \(L_i\).

Observation

After extensive exploratory simulations, it seems completely simulated data give cleaner results than simulated real data, which is expected.

source("../code/gdash_lik.R")

set.seed(777)
z.mat <- se.mat <- matrix(0, ncol = 1e4, nrow = 1e3)
for (i in 1 : nrow(z.mat)) {
  L <- matrix(rnorm(1e4 * 10), ncol = 10)
  z.mat[i, ] <- L %*% rnorm(10) / sqrt(rowSums(L^2))
  se.mat[i, ] <- sqrt(rchisq(1e4, 1))
}

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.5, 0.3, 0.2), g.sd = c(0, 1, 2), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.5, 0.4, 0.1), g.sd = c(0, 1, 2), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.6, 0.3, 0.1), g.sd = c(0, 1, 2), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.1), g.sd = c(0, 1), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.1), g.sd = c(0, 2), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.1), g.sd = c(0, 3), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.05, 0.05), g.sd = c(0, 1, 2), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.05, 0.05), g.sd = c(0, 1, 3), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.5, 0.5), g.sd = c(0, 1), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.5, 0.5), g.sd = c(0, 2), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.5, 0.5), g.sd = c(0, 3), relative_to_noise = FALSE)

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Read data

z.real <- readRDS("../output/z_null_liver_777.rds")
se.real <- readRDS("../output/sebetahat_null_liver_777.rds")

Simulation

cashSim(z.real, se.real,
        nsim = 200, ngene = 1000,
        g.pi = c(0.5, 0.5), g.sd = c(0, 1), relative_to_noise = TRUE)

Simulation

cashSim(z.real, se.real,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.1), g.sd = c(0, 1), relative_to_noise = TRUE)

Simulation

cashSim(z.real, se.real,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.1), g.sd = c(0, 2), relative_to_noise = TRUE)

Session information

sessionInfo()

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] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ashr_2.2-2        Rmosek_8.0.69     PolynomF_1.0-1    CVXR_0.95        
[5] REBayes_1.2       Matrix_1.2-12     SQUAREM_2017.10-1 EQL_1.0-0        
[9] ttutils_1.0-1    

loaded via a namespace (and not attached):
 [1] gmp_0.5-13.1      Rcpp_0.12.16      compiler_3.4.3   
 [4] git2r_0.21.0      workflowr_1.0.1   R.methodsS3_1.7.1
 [7] R.utils_2.6.0     iterators_1.0.9   tools_3.4.3      
[10] digest_0.6.15     bit_1.1-12        evaluate_0.10.1  
[13] lattice_0.20-35   foreach_1.4.4     yaml_2.1.18      
[16] parallel_3.4.3    Rmpfr_0.6-1       ECOSolveR_0.4    
[19] stringr_1.3.0     knitr_1.20        rprojroot_1.3-2  
[22] bit64_0.9-7       grid_3.4.3        R6_2.2.2         
[25] rmarkdown_1.9     magrittr_1.5      whisker_0.3-2    
[28] MASS_7.3-47       backports_1.1.2   codetools_0.2-15 
[31] htmltools_0.3.6   scs_1.1-1         stringi_1.1.6    
[34] pscl_1.5.2        doParallel_1.0.11 truncnorm_1.0-7  
[37] R.oo_1.21.0

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CASH Simulation, Part 6: Simulated vs Read data

Lei Sun

2017-11-19

Simulated correlated data

Observation

Simulation

Simulation

Simulation

Simulation

Simulation

Simulation

Simulation

Simulation

Simulation

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Simulation

Read data

Simulation

Simulation

Simulation

Session information