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<h1 class="title toc-ignore">Simulation with Realistic Standard Error: Small SNR</h1>
<h4 class="author"><em>Lei Sun</em></h4>
<h4 class="date"><em>2017-05-28</em></h4>
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<p><strong>Last updated:</strong> 2018-05-15</p>
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<hr />
<div id="introduction" class="section level2">
<h2>Introduction</h2>
<p>Identifiability of small effects from correlation.</p>
<pre class="r"><code>library(ashr)
library(edgeR)
library(limma)
library(pROC)</code></pre>
<pre class="r"><code>source("../code/gdash.R")</code></pre>
</div>
<div id="read-in-data" class="section level2">
<h2>Read in data</h2>
<pre class="r"><code>data = readRDS("../data/liver.rds")
ngene = 1e4
data = top_gene_selection(ngene, data)$data</code></pre>
</div>
<div id="snr--10-sparse-mixture" class="section level2">
<h2>SNR = -10, Sparse mixture</h2>
<p><span class="math display">\[g = 0.9\delta_0 + 0.1N\left(0, \sigma^2\right) \ .\]</span></p>
<p><img src="figure/simulation_real_se_2.rmd/-10 plotting-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/simulation_real_se_2.rmd/-10 plotting-2.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="figure/simulation_real_se_2.rmd/-10 auc plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="figure/simulation_real_se_2.rmd/-10%20average%20fdp%20plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
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<div id="snr--10-sparse-strong" class="section level2">
<h2>SNR = -10, Sparse & strong</h2>
<p><span class="math display">\[g = 0.99\delta_0 + 0.01N\left(0, \left(3.16\sigma\right)^2\right) \ .\]</span></p>
<p><img src="figure/simulation_real_se_2.rmd/-10S plotting-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/simulation_real_se_2.rmd/-10S plotting-2.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="figure/simulation_real_se_2.rmd/-10S auc plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="figure/simulation_real_se_2.rmd/-10S%20average%20fdp%20plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
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LSun
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2017-12-21
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<a href="https://github.com/LSun/truncash/blob/2457dfb432060da5bab169d19cba264b032869fb/docs/figure/simulation_real_se_2.rmd/-10S average fdp plotting-1.png" target="_blank">2457dfb</a>
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<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/simulation_real_se_2.rmd/-10S average fsp plotting-1.png" target="_blank">0f36d99</a>
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LSun
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2017-12-21
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<a href="https://github.com/LSun/truncash/blob/2457dfb432060da5bab169d19cba264b032869fb/docs/figure/simulation_real_se_2.rmd/-10S average fsp plotting-1.png" target="_blank">2457dfb</a>
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LSun
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2017-06-01
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</details>
</div>
<div id="snr--10-dense-weak" class="section level2">
<h2>SNR = -10, Dense & weak</h2>
<p><span class="math display">\[g = 0.1\delta_0 + 0.9N\left(0, \left(0.33\sigma\right)^2\right) \ .\]</span></p>
<p><img src="figure/simulation_real_se_2.rmd/-10W plotting-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/simulation_real_se_2.rmd/-10W plotting-2.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="figure/simulation_real_se_2.rmd/-10W auc plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="figure/simulation_real_se_2.rmd/-10W%20average%20fdp%20plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
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<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/simulation_real_se_2.rmd/-10W average fdp plotting-1.png" target="_blank">0f36d99</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-12-21
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/2457dfb432060da5bab169d19cba264b032869fb/docs/figure/simulation_real_se_2.rmd/-10W average fdp plotting-1.png" target="_blank">2457dfb</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-06-01
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/simulation_real_se_2.rmd/-10W%20average%20fsp%20plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
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<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/simulation_real_se_2.rmd/-10W average fsp plotting-1.png" target="_blank">0f36d99</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-12-21
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/2457dfb432060da5bab169d19cba264b032869fb/docs/figure/simulation_real_se_2.rmd/-10W average fsp plotting-1.png" target="_blank">2457dfb</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-06-01
</td>
</tr>
</tbody>
</table>
</details>
</div>
<div id="snr--3-sparse-mixture" class="section level2">
<h2>SNR = -3, Sparse mixture</h2>
<p><span class="math display">\[g = 0.5\delta_0 + 0.5N\left(0, \sigma^2\right) \ .\]</span></p>
<p><img src="figure/simulation_real_se_2.rmd/-3 plotting-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/simulation_real_se_2.rmd/-3 plotting-2.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="figure/simulation_real_se_2.rmd/-3 auc plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="figure/simulation_real_se_2.rmd/-3%20average%20fdp%20plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
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<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/simulation_real_se_2.rmd/-3 average fdp plotting-1.png" target="_blank">0f36d99</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-12-21
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/2457dfb432060da5bab169d19cba264b032869fb/docs/figure/simulation_real_se_2.rmd/-3 average fdp plotting-1.png" target="_blank">2457dfb</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-06-01
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/simulation_real_se_2.rmd/-3%20average%20fsp%20plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
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<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/simulation_real_se_2.rmd/-3 average fsp plotting-1.png" target="_blank">0f36d99</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-12-21
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/2457dfb432060da5bab169d19cba264b032869fb/docs/figure/simulation_real_se_2.rmd/-3 average fsp plotting-1.png" target="_blank">2457dfb</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-06-01
</td>
</tr>
</tbody>
</table>
</details>
</div>
<div id="snr--3-sparse-strong" class="section level2">
<h2>SNR = -3, Sparse & strong</h2>
<p><span class="math display">\[g = 0.6\delta_0 + 0.3N\left(0, \left(0.82\sigma\right)^2\right) + 0.1N\left(0, \left(1.73\sigma\right)^2\right) \ .\]</span></p>
<p><img src="figure/simulation_real_se_2.rmd/-3S plotting-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/simulation_real_se_2.rmd/-3S plotting-2.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="figure/simulation_real_se_2.rmd/-3S auc plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="figure/simulation_real_se_2.rmd/-3S%20average%20fdp%20plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
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</th>
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</thead>
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<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/simulation_real_se_2.rmd/-3S average fdp plotting-1.png" target="_blank">0f36d99</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-12-21
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/2457dfb432060da5bab169d19cba264b032869fb/docs/figure/simulation_real_se_2.rmd/-3S average fdp plotting-1.png" target="_blank">2457dfb</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-06-01
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/simulation_real_se_2.rmd/-3S%20average%20fsp%20plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
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<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/simulation_real_se_2.rmd/-3S average fsp plotting-1.png" target="_blank">0f36d99</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-12-21
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/2457dfb432060da5bab169d19cba264b032869fb/docs/figure/simulation_real_se_2.rmd/-3S average fsp plotting-1.png" target="_blank">2457dfb</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-06-01
</td>
</tr>
</tbody>
</table>
</details>
</div>
<div id="snr--3-dense-weak" class="section level2">
<h2>SNR = -3, Dense & weak</h2>
<p><span class="math display">\[g = 0.1\delta_0 + 0.9N\left(0, \left(0.75\sigma^2\right)^2\right) \ .\]</span></p>
<p><img src="figure/simulation_real_se_2.rmd/-3W plotting-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/simulation_real_se_2.rmd/-3W plotting-2.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="figure/simulation_real_se_2.rmd/-3W auc plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
<p><img src="figure/simulation_real_se_2.rmd/-3W%20average%20fdp%20plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
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<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/simulation_real_se_2.rmd/-3W average fdp plotting-1.png" target="_blank">0f36d99</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-12-21
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/2457dfb432060da5bab169d19cba264b032869fb/docs/figure/simulation_real_se_2.rmd/-3W average fdp plotting-1.png" target="_blank">2457dfb</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-06-01
</td>
</tr>
</tbody>
</table>
</details>
<p><img src="figure/simulation_real_se_2.rmd/-3W%20average%20fsp%20plotting-1.png" width="672" style="display: block; margin: auto;" /></p>
<details>
<summary><em>Expand here to see past versions of -3W average fsp plotting-1.png:</em></summary>
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Author
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</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/0f36d998db26444c5dd01502ea1af7fbd1129b22/docs/figure/simulation_real_se_2.rmd/-3W average fsp plotting-1.png" target="_blank">0f36d99</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-12-21
</td>
</tr>
<tr>
<td style="text-align:left;">
<a href="https://github.com/LSun/truncash/blob/2457dfb432060da5bab169d19cba264b032869fb/docs/figure/simulation_real_se_2.rmd/-3W average fsp plotting-1.png" target="_blank">2457dfb</a>
</td>
<td style="text-align:left;">
LSun
</td>
<td style="text-align:left;">
2017-06-01
</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] stats graphics grDevices utils datasets methods base
loaded via a namespace (and not attached):
[1] workflowr_1.0.1 Rcpp_0.12.16 digest_0.6.15
[4] rprojroot_1.3-2 R.methodsS3_1.7.1 backports_1.1.2
[7] git2r_0.21.0 magrittr_1.5 evaluate_0.10.1
[10] stringi_1.1.6 whisker_0.3-2 R.oo_1.21.0
[13] R.utils_2.6.0 rmarkdown_1.9 tools_3.4.3
[16] stringr_1.3.0 yaml_2.1.18 compiler_3.4.3
[19] htmltools_0.3.6 knitr_1.20 </code></pre>
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