Pairwise Sharing

Last updated: 2018-11-08

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library(mashr)

Loading required package: ashr

library(corrplot)

corrplot 0.84 loaded

set.seed(1)
simdata = simple_sims(500,5,1)
data = mash_set_data(simdata$Bhat, simdata$Shat)
U.c = cov_canonical(data)
m = mash(data, U.c, algorithm.version = 'R', posterior_samples = 100)

 - Computing 2000 x 151 likelihood matrix.
 - Likelihood calculations took 0.09 seconds.
 - Fitting model with 151 mixture components.
 - Model fitting took 0.27 seconds.
 - Computing posterior matrices.
 - Computation allocated took 3.03 seconds.

The posterior samples is a \(2000\times 5 \times 100\) array. The get_pairwise_sharing_from_samples computes the proportion as \[ \begin{align*} &\text{Proportion of effects have the same sign for condition r, r'} \\ &= \frac{1}{2000} \sum_{j=1}^{2000}\mathbb{E}\left[\mathbb{I}(b_{jr}, b_{jr'} \text{ have same sign}) \right] \\ &\approx \frac{1}{2000} \sum_{j=1}^{2000} \frac{1}{100} \sum_{m=1}^{100} \mathbb{I}(b_{jr}^{(m)}, b_{jr'}^{(m)} \text{ have same sign}) \end{align*} \]

Pairwise sharing by Sign from get_pairwise_sharing_from_samples

x = get_pairwise_sharing_from_samples(m, factor=0)
corrplot(x, method='color', cl.lim=c(0,1), type='upper', addCoef.col = "black", tl.col="black", tl.srt=45, title = 'Pairwise Sharing by Sign', mar = c(4,0,4,0))

The diagonal elements are less than 1, because when we compute the probability of sharing for each effect, we don’t count a sample with all 0s as sharing (\(\mathbb{I}(b_{jr}^{(m)} = 0, b_{jr'}^{(m)} = 0 \text{ have same sign}) = 0\)).

Pairwise sharing by Sign from get_pairwise_sharing

x = get_pairwise_sharing(m, factor=0, lfsr_thresh = 1)
corrplot(x, method='color', cl.lim=c(0,1), type='upper', addCoef.col = "black", tl.col="black", tl.srt=45, title = 'Pairwise Sharing by Sign', mar = c(4,0,4,0))

The diagonal elements are 1, because we include the effects close to 0 as sharing.

sessionInfo()

R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/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] corrplot_0.84     mashr_0.2.18.0476 ashr_2.2-23      

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.19      compiler_3.5.1    git2r_0.23.0     
 [4] plyr_1.8.4        workflowr_1.1.1   R.methodsS3_1.7.1
 [7] R.utils_2.7.0     iterators_1.0.10  tools_3.5.1      
[10] digest_0.6.18     evaluate_0.12     lattice_0.20-35  
[13] Matrix_1.2-14     foreach_1.4.4     yaml_2.2.0       
[16] parallel_3.5.1    mvtnorm_1.0-8     stringr_1.3.1    
[19] knitr_1.20        REBayes_1.3       rprojroot_1.3-2  
[22] grid_3.5.1        rmarkdown_1.10    rmeta_3.0        
[25] magrittr_1.5      whisker_0.3-2     backports_1.1.2  
[28] codetools_0.2-15  htmltools_0.3.6   MASS_7.3-50      
[31] abind_1.4-5       assertthat_0.2.0  stringi_1.2.4    
[34] Rmosek_8.0.69     doParallel_1.0.14 pscl_1.5.2       
[37] truncnorm_1.0-8   SQUAREM_2017.10-1 R.oo_1.22.0      

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