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Introduction

source("code/binomial_mean/binomial_mean_splitting.R")
Loading required package: Rcpp
Loading required package: RcppZiggurat
set.seed(12345)
n = 500
nb = rep(100,n)
w = 0.8
mu = c(rep(0,n*w),rnorm(round(n*(1-w))))
p = sigmoid(mu)
x = rbinom(n,nb,p)
library(ashr)
fit_ash = ashr::ash(rep(0,n),1,lik=lik_binom(x,nb,link='identity'))
fit_split = binomial_mean_splitting(x,nb,printevery = 1,n_gh=10,
                                    b_pm_init = NULL,sigma2_init = NULL,
                                    ebnm_params = list(prior_family='normal_scale_mixture'))
[1] "At iter 1 elbo= -1564.537 sigma2= 0.205"
[1] "At iter 2 elbo= -1505.271 sigma2= 0.159"
[1] "At iter 3 elbo= -1461.715 sigma2= 0.131"
[1] "At iter 4 elbo= -1434.582 sigma2= 0.117"
[1] "At iter 5 elbo= -1419.311 sigma2= 0.11"
[1] "At iter 6 elbo= -1412.213 sigma2= 0.107"
[1] "At iter 7 elbo= -1409.016 sigma2= 0.105"
[1] "At iter 8 elbo= -1407.596 sigma2= 0.105"
[1] "At iter 9 elbo= -1406.97 sigma2= 0.105"
[1] "At iter 10 elbo= -1406.694 sigma2= 0.104"
[1] "At iter 11 elbo= -1406.573 sigma2= 0.104"
[1] "At iter 12 elbo= -1406.519 sigma2= 0.104"
[1] "At iter 13 elbo= -1406.496 sigma2= 0.104"
[1] "At iter 14 elbo= -1406.486 sigma2= 0.104"
[1] "At iter 15 elbo= -1406.481 sigma2= 0.104"
[1] "At iter 16 elbo= -1406.479 sigma2= 0.104"
[1] "At iter 17 elbo= -1406.478 sigma2= 0.104"
[1] "At iter 18 elbo= -1406.478 sigma2= 0.104"
[1] "At iter 19 elbo= -1406.478 sigma2= 0.104"
[1] "At iter 20 elbo= -1406.478 sigma2= 0.104"
[1] "At iter 21 elbo= -1406.478 sigma2= 0.104"
[1] "At iter 22 elbo= -1406.478 sigma2= 0.104"
[1] "At iter 23 elbo= -1406.478 sigma2= 0.104"
fit_GG = binomial_mean_GG(x,nb,printevery = 1,n_gh=10)
[1] "At iter 1 elbo= -1645.672"
[1] "At iter 2 elbo= -1598.219"
[1] "At iter 3 elbo= -1586.716"
[1] "At iter 4 elbo= -1577.111"
[1] "At iter 5 elbo= -1576.244"
[1] "At iter 6 elbo= -1575.846"
[1] "At iter 7 elbo= -1575.346"
[1] "At iter 8 elbo= -1575.346"
plot(x/nb,col='grey80')
lines(p,col='grey80')
lines(fit_ash$result$PosteriorMean,col=2)

plot(x/nb,col='grey80')
lines(p,col='grey80')
lines(fit_split$posterior$mean,col=4)

plot(x/nb,col='grey80')
lines(p,col='grey80')
lines(sigmoid(fit_split$posterior$mean_b),col=4)

plot(x/nb,col='grey80')
lines(p,col='grey80')
lines(fit_GG$posterior$mean,col=3)

set.seed(12345)
n = 500
nb = rep(1,n)
w = 0.8
mu = c(rep(0,n*w),rnorm(round(n*(1-w))))
p = sigmoid(mu)
x = rbinom(n,nb,p)
library(ashr)
fit_ash = ashr::ash(rep(0,n),1,lik=lik_binom(x,nb,link='identity'))
fit_split = binomial_mean_splitting(x,nb,printevery = 1,n_gh=10,
                                    b_pm_init = NULL,sigma2_init = NULL,
                                    ebnm_params = list(prior_family='normal_scale_mixture'))
[1] "At iter 1 elbo= -1072.08 sigma2= 4.761"
[1] "At iter 2 elbo= -1072.08 sigma2= 4.761"
fit_GG = binomial_mean_GG(x,nb,printevery = 1,n_gh=10)
[1] "At iter 1 elbo= -1063.752"
[1] "At iter 2 elbo= -1075.504"
Warning in binomial_mean_GG(x, nb, printevery = 1, n_gh = 10): An iteration
decreases ELBO. This is likely due to numerical issues.
plot(x/nb,col='grey80')
lines(p,col='grey80')
lines(fit_ash$result$PosteriorMean,col=2)

plot(x/nb,col='grey80')
lines(p,col='grey80')
lines(fit_split$posterior$mean,col=4)

plot(x/nb,col='grey80')
lines(p,col='grey80')
lines(sigmoid(fit_split$posterior$mean_b),col=4)

plot(x/nb,col='grey80')
lines(p,col='grey80')
lines(fit_GG$posterior$mean,col=3)


sessionInfo()
R version 4.2.1 (2022-06-23)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04.5 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0

locale:
 [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
 [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
 [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
[10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ashr_2.2-54        Rfast_2.0.6        RcppZiggurat_0.1.6 ebnm_1.0-9        
[5] fastGHQuad_1.0.1   Rcpp_1.0.9         vebpm_0.2.1        workflowr_1.7.0   

loaded via a namespace (and not attached):
 [1] horseshoe_0.2.0    invgamma_1.1       lattice_0.20-45    nleqslv_3.3.3     
 [5] getPass_0.2-2      ps_1.7.1           assertthat_0.2.1   rprojroot_2.0.3   
 [9] digest_0.6.29      utf8_1.2.2         truncnorm_1.0-8    R6_2.5.1          
[13] rootSolve_1.8.2.3  evaluate_0.17      highr_0.9          httr_1.4.4        
[17] ggplot2_3.3.6      pillar_1.8.1       rlang_1.0.6        rstudioapi_0.14   
[21] irlba_2.3.5.1      nloptr_2.0.3       whisker_0.4        callr_3.7.2       
[25] jquerylib_0.1.4    Matrix_1.5-1       rmarkdown_2.17     splines_4.2.1     
[29] stringr_1.4.1      munsell_0.5.0      mixsqp_0.3-43      compiler_4.2.1    
[33] httpuv_1.6.6       xfun_0.33          pkgconfig_2.0.3    SQUAREM_2021.1    
[37] htmltools_0.5.3    tidyselect_1.2.0   tibble_3.1.8       matrixStats_0.62.0
[41] fansi_1.0.3        dplyr_1.0.10       later_1.3.0        grid_4.2.1        
[45] jsonlite_1.8.2     gtable_0.3.1       lifecycle_1.0.3    DBI_1.1.3         
[49] git2r_0.30.1       magrittr_2.0.3     scales_1.2.1       ebpm_0.0.1.3      
[53] cli_3.4.1          stringi_1.7.8      cachem_1.0.6       fs_1.5.2          
[57] promises_1.2.0.1   bslib_0.4.0        generics_0.1.3     vctrs_0.4.2       
[61] trust_0.1-8        tools_4.2.1        glue_1.6.2         parallel_4.2.1    
[65] processx_3.7.0     fastmap_1.1.0      yaml_2.3.5         colorspace_2.0-3  
[69] deconvolveR_1.2-1  knitr_1.40         sass_0.4.2