Last updated: 2020-12-21

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Knit directory: mash_application/analysis/

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Rmd 6106162 zouyuxin 2020-12-21 wflow_publish(“analysis/EstimateCorNullProblem.Rmd”)
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Rmd 6353efc zouyuxin 2019-01-23 wflow_publish(“analysis/EstimateCorNullProblem.Rmd”)

library(mashr)
Loading required package: ashr
library(mvtnorm)
library(knitr)
library(kableExtra)

We simulate 1000 data from \[ \hat{b}|b \sim N_{5}(\hat{b}; b, \left(\begin{matrix} 1 & & 0.3 & &\\ & & \ddots & \\ & & 0.3 & & 1 \end{matrix}\right)) \]

\[ b \sim \delta_{0} \]

\(\Rightarrow\) \[ \hat{b} \sim N_{5}(0, \left(\begin{matrix} 1 & & 0.3 & &\\ & & \ddots & \\ & & 0.3 & & 1 \end{matrix}\right)) \]

set.seed(1)
n = 1000; p = 5
Sigma = matrix(0.3, p,p)
diag(Sigma) = 1
B = matrix(0,n,p)
Bhat = rmvnorm(n, sigma = Sigma)
simdata = list(B = B, Bhat = Bhat, Shat = 1)

We compare methods that ignoring the correlation, estimating the correlation using simple method (estimate_null_correlation_simple), estimating the correlation with em, and the truth.

data = mash_set_data(Bhat, Shat=1)
U.c = cov_canonical(data)
m.ignore = mash(data, U.c, verbose = FALSE, optmethod = 'mixSQP')

V.simple = estimate_null_correlation_simple(data)
data.simple = mash_update_data(data, V = V.simple)
m.simple = mash(data.simple, U.c, verbose = FALSE, optmethod = 'mixSQP')

V.em = estimate_null_correlation(data, Ulist = U.c, details = T)
m.em = V.em$mash.model

data.true = mash_update_data(data, V = Sigma)
m.true = mash(data.true, U.c, verbose = FALSE, optmethod = 'mixSQP')
ign = c(get_loglik(m.ignore), length(get_significant_results(m.ignore)))

simple = c(get_loglik(m.simple), length(get_significant_results(m.simple)))

em = c(get_loglik(m.em), length(get_significant_results(m.em)))

true = c(get_loglik(m.true), length(get_significant_results(m.true)))

tmp = rbind(ign, simple, em, true)
row.names(tmp) = c('ignore', 'simple', 'em', 'true')
colnames(tmp) = c('loglik', '# signif')
tmp %>% kable() %>% kable_styling()
loglik # signif
ignore -7000.556 59
simple -6913.520 0
em -6905.050 0
true -6908.123 0
par(mfrow= c(1,2))
barplot(get_estimated_pi(m.ignore), las=2, cex.names = 0.7, main='Ignore')
barplot(get_estimated_pi(m.true), las=2, cex.names = 0.7, main='True')

Version Author Date
ce8ebdc zouyuxin 2019-01-23

sessionInfo()
R version 4.0.3 (2020-10-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur 10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/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] kableExtra_1.3.1 knitr_1.30       mvtnorm_1.1-1    mashr_0.2.40    
[5] ashr_2.2-51      workflowr_1.6.2 

loaded via a namespace (and not attached):
 [1] xfun_0.19         lattice_0.20-41   colorspace_2.0-0  vctrs_0.3.5      
 [5] htmltools_0.5.0   viridisLite_0.3.0 yaml_2.2.1        rlang_0.4.9      
 [9] mixsqp_0.3-46     later_1.1.0.1     pillar_1.4.7      glue_1.4.2       
[13] lifecycle_0.2.0   plyr_1.8.6        stringr_1.4.0     munsell_0.5.0    
[17] rvest_0.3.6       evaluate_0.14     httpuv_1.5.4      invgamma_1.1     
[21] irlba_2.3.3       highr_0.8         Rcpp_1.0.5        promises_1.1.1   
[25] scales_1.1.1      rmeta_3.0         webshot_0.5.2     truncnorm_1.0-8  
[29] abind_1.4-5       fs_1.5.0          digest_0.6.27     stringi_1.5.3    
[33] grid_4.0.3        rprojroot_2.0.2   tools_4.0.3       magrittr_2.0.1   
[37] tibble_3.0.4      crayon_1.3.4      whisker_0.4       pkgconfig_2.0.3  
[41] ellipsis_0.3.1    Matrix_1.2-18     SQUAREM_2020.5    xml2_1.3.2       
[45] assertthat_0.2.1  rmarkdown_2.5     httr_1.4.2        rstudioapi_0.13  
[49] R6_2.5.0          git2r_0.27.1      compiler_4.0.3