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1 : 0.0112765123515512 ; 2 : 1.60751487400088 ; 3 : 0.361378958092869 ; 4 : 1.65789257614746 ; 5 : 0.670189379060472 ; 6 : 0.75997503879673 ; 7 : 0.557659272292024 ; 8 : -0.0586994517219462 ; 9 : 0.175073181131849 ; 10 : -0.132350826272713 ;</code></pre> <p><img src="figure/smemo_2.rmd/fitting%20gaussian%20derivatives-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/smemo_2.rmd/fitting%20gaussian%20derivatives-2.png" width="672" style="display: block; margin: auto;" /></p> </div> <div id="discovered-by-bh-and-ash" class="section level2"> <h2>Discovered by <code>BH</code> and <code>ASH</code></h2> <p>Feeding summary statistics to <code>BH</code> and <code>ASH</code>, both give thousands of discoveries.</p> <pre class="r"><code>fit.BH = p.adjust((1 - pnorm(abs(z))) * 2, method = "BH") ## Number of discoveries by BH sum(fit.BH <= 0.05)</code></pre> <pre><code>[1] 2541</code></pre> <pre class="r"><code>fit.ash = ashr::ash(betahat, sebetahat, method = "fdr") ## Number of discoveries by ASH sum(get_svalue(fit.ash) <= 0.05)</code></pre> <pre><code>[1] 6440</code></pre> </div> <div id="fitting-ash-first-or-gaussian-derivatives-first" class="section level2"> <h2>Fitting <code>ASH</code> first or Gaussian derivatives first</h2> <p>Using default setting <span class="math inline">\(L = 10\)</span>, <span class="math inline">\(\lambda = 10\)</span>, <span class="math inline">\(\rho = 0.5\)</span>, compare the <code>GD-ASH</code> results by fitting <code>ASH</code> first vs fitting <code>GD</code> first. They indeed arrive at different local minima.</p> <pre class="r"><code>fit.gdash.ASH <- gdash(betahat, sebetahat, gd.priority = FALSE) ## Regularized log-likelihood by fitting ASH first fit.gdash.ASH$loglik</code></pre> <pre><code>[1] -12483.86</code></pre> <pre class="r"><code>fit.gdash.GD <- gdash(betahat, sebetahat) ## Regularized log-likelihood by fitting GD first fit.gdash.GD$loglik</code></pre> <pre><code>[1] -22136.92</code></pre> </div> <div id="gd-ash-with-larger-penalties-on-w" class="section level2"> <h2><code>GD-ASH</code> with larger penalties on <span class="math inline">\(w\)</span></h2> <p>Using <span class="math inline">\(\lambda = 50\)</span>, <span class="math inline">\(\rho = 0.1\)</span>, fitting <code>ASH</code> first and <code>GD</code> first give the same result, and produce 1400+ discoveries with <span class="math inline">\(q\)</span> values <span class="math inline">\(\leq 0.05\)</span>, all of which are discovered by <code>BH</code>.</p> <pre class="r"><code>L = 10 lambda = 50 rho = 0.1 fit.gdash.ASH <- gdash(betahat, sebetahat, gd.ord = L, w.lambda = lambda, w.rho = rho, gd.priority = FALSE) ## Regularized log-likelihood by fitting ASH first fit.gdash.ASH$loglik</code></pre> <pre><code>[1] -13651.59</code></pre> <pre class="r"><code>## Number of discoveries sum(fit.gdash.ASH$qvalue <= 0.05)</code></pre> <pre><code>[1] 1431</code></pre> <pre class="r"><code>fit.gdash.GD <- gdash(betahat, sebetahat, gd.ord = L, w.lambda = lambda, w.rho = rho, gd.priority = TRUE) ## Regularized log-likelihood by fitting GD first fit.gdash.GD$loglik</code></pre> <pre><code>[1] -13651.59</code></pre> <pre class="r"><code>## Number of discoveries sum(fit.gdash.GD$qvalue <= 0.05)</code></pre> <pre><code>[1] 1431</code></pre> <pre><code>GD Coefficients:</code></pre> <pre><code>0 : 1 ; 1 : -0.0475544308510135 ; 2 : 0.707888470469342 ; 3 : 0.149489828947119 ; 4 : -8.97499076623316e-14 ; 5 : 0.109281416075664 ; 6 : -3.00530934822662e-13 ; 7 : 0.0783545592042359 ; 8 : -2.99572304462426e-13 ; 9 : 0.0911488252640105 ; 10 : -2.99578347875936e-13 ;</code></pre> <p><img src="figure/smemo_2.rmd/GD-ASH%20discoveries%20histogram-1.png" width="672" style="display: block; margin: auto;" /></p> </div> <div id="session-information" class="section level2"> <h2>Session information</h2> <!-- Insert the session information into the document --> <pre class="r"><code>sessionInfo()</code></pre> <pre><code>R version 3.4.2 (2017-09-28) Platform: x86_64-apple-darwin15.6.0 (64-bit) Running under: macOS Sierra 10.12.6 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_2.1-27 Rmosek_7.1.3 PolynomF_0.94 cvxr_0.0.0.9400 [5] REBayes_0.85 Matrix_1.2-11 SQUAREM_2017.10-1 EQL_1.0-0 [9] ttutils_1.0-1 loaded via a namespace (and not attached): [1] Rcpp_0.12.13 knitr_1.17 magrittr_1.5 [4] edgeR_3.20.1 MASS_7.3-47 pscl_1.5.2 [7] doParallel_1.0.11 lattice_0.20-35 foreach_1.4.3 [10] stringr_1.2.0 tools_3.4.2 parallel_3.4.2 [13] grid_3.4.2 git2r_0.19.0 iterators_1.0.8 [16] htmltools_0.3.6 assertthat_0.2.0 yaml_2.1.14 [19] rprojroot_1.2 digest_0.6.12 gmp_0.5-13.1 [22] codetools_0.2-15 evaluate_0.10.1 rmarkdown_1.6 [25] limma_3.34.0 stringi_1.1.5 compiler_3.4.2 [28] backports_1.1.1 locfit_1.5-9.1 truncnorm_1.0-7 </code></pre> </div> <hr> <p> This <a href="http://rmarkdown.rstudio.com">R Markdown</a> site was created with <a href="https://github.com/jdblischak/workflowr">workflowr</a> </p> <hr> <!-- To enable disqus, uncomment the section below and provide your disqus_shortname --> <!-- disqus <div id="disqus_thread"></div> <script type="text/javascript"> /* * * CONFIGURATION VARIABLES: EDIT BEFORE PASTING INTO YOUR WEBPAGE * * */ var disqus_shortname = 'rmarkdown'; 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