Last updated: 2018-12-13

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rrmse = function(data, model){
  sqrt(mean((data$B - model$result$PosteriorMean)^2)/mean((data$B - data$Bhat)^2))
}

ROC.table = function(data, model){
  sign.test = data*model$result$PosteriorMean
  thresh.seq = seq(0, 1, by=0.005)[-1]
  m.seq = matrix(0,length(thresh.seq), 2)
  colnames(m.seq) = c('TPR', 'FPR')
  for(t in 1:length(thresh.seq)){
    m.seq[t,] = c(sum(sign.test>0 & model$result$lfsr <= thresh.seq[t])/sum(data!=0),
                  sum(data==0 & model$result$lfsr <=thresh.seq[t])/sum(data==0))
  }
  return(m.seq)
}

library(knitr)
library(kableExtra)

Common noise correlation

We simulate null data which has common noise correlation structure. We fit mash model without and with the estimated correlation structure. There are lots of false positives in the model without the correlation structure. The posterior mean is far from the truth.

library(mvtnorm)
library(mashr)
Loading required package: ashr
set.seed(1)
n = 10000; p = 5
B = matrix(0,n,p)
V = matrix(0.75, p, p); diag(V) = 1
Bhat = rmvnorm(n, sigma = V)
simdata = list(B = B, Bhat = Bhat, Shat = 1)
data = mash_set_data(Bhat, Shat=1)
U.c = cov_canonical(data)
m.ignore = mash(data, U.c, verbose = FALSE)

V.current = estimate_null_correlation(data, U.c)
m.current = V.current$mash.model

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

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

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

tmp = rbind(ign, current, true)
row.names(tmp) = c('ignore', 'current', 'true')
colnames(tmp) = c('loglik', '# signif')
tmp %>% kable() %>% kable_styling()
loglik # signif
ignore -62970.94 2930
current -50426.33 0
true -50432.44 0

RRMSE:

tmp = c(rrmse(simdata, m.ignore), rrmse(simdata, m.current), rrmse(simdata, m.true))
barplot(tmp, names.arg = c('ignore', 'current', 'true'))

Expand here to see past versions of unnamed-chunk-5-1.png:
Version Author Date
66be60b zouyuxin 2018-12-07

Two different noise correlations

Now, we simulate data with 2 noise correlation structures. Half of the null data have no noise correlation, the other half have noise correlation.

Bhat1 = rmvnorm(n/2, sigma = diag(p))
Bhat2 = rmvnorm(n/2, sigma = V)
Bhat = rbind(Bhat1, Bhat2)
simdata = list(B = B, Bhat = Bhat, Shat = 1)

data = mash_set_data(Bhat, Shat=1)
U.c = cov_canonical(data)
m.I = mash(data, U.c, verbose = FALSE)

data.V = mash_update_data(data, V = V)
m.V = mash(data.V, U.c, verbose = FALSE)

V.current = estimate_null_correlation(data, U.c)
m.current = V.current$mash.model

Vtrue = array(0,dim=c(p,p,n))
Vtrue[,,1:(n/2)] = diag(p)
Vtrue[,,(n/2+1): n] = V
data.true = mash_update_data(data, V = Vtrue)
m.true = mash(data.true, U.c, verbose = FALSE, algorithm.version = 'R')

The estimated V is

V.current$V
          [,1]      [,2]      [,3]      [,4]      [,5]
[1,] 1.0000000 0.3866502 0.4018458 0.3783971 0.3990991
[2,] 0.3866502 1.0000000 0.3913344 0.3688566 0.3936946
[3,] 0.4018458 0.3913344 1.0000000 0.4172119 0.3878397
[4,] 0.3783971 0.3688566 0.4172119 1.0000000 0.3830625
[5,] 0.3990991 0.3936946 0.3878397 0.3830625 1.0000000
Ionly = c(get_loglik(m.I), length(get_significant_results(m.I)))

Vonly = c(get_loglik(m.V), length(get_significant_results(m.V)))

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

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

tmp = rbind(Ionly, Vonly, current, true)
row.names(tmp) = c('I only', 'V only', 'current', 'true')
colnames(tmp) = c('loglik', '# signif')
tmp %>% kable() %>% kable_styling()
loglik # signif
I only -67844.31 597
V only -65457.36 1904
current -65793.59 28
true -60618.07 0

RRMSE:

tmp = c(rrmse(simdata, m.I), rrmse(simdata, m.V), rrmse(simdata, m.current), rrmse(simdata, m.true))
barplot(tmp, names.arg = c('I only', 'V only', 'current', 'true'))

Expand here to see past versions of unnamed-chunk-9-1.png:
Version Author Date
66be60b zouyuxin 2018-12-07

Data with signals

set.seed(2018)
B1 = matrix(0, n/2, p)
V.1 = matrix(0,p,p); V.1[1,1] = 1
B2 = rmvnorm(n/2, sigma = V.1)
B = rbind(B1, B2)

V.random = array(0, dim=c(p,p,n))
ind = sample(1:n, n/2)
V.random[,,ind] = V
V.random[,,-ind] = diag(p)

Ehat = matrix(0, n, p)
Ehat[ind,] = rmvnorm(n/2, sigma = V)
Ehat[-ind,] = rmvnorm(n/2, sigma = diag(p))

Bhat = B + Ehat
simdata = list(B = B, Bhat=Bhat, Shat = 1)
data = mash_set_data(Bhat, Shat=1)
U.c = cov_canonical(data)
m.I = mash(data, U.c, verbose = FALSE)

data.V = mash_update_data(data, V = V)
m.V = mash(data.V, U.c, verbose = FALSE)
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(0.110553314193142,
0.153957533037059, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
V.current = estimate_null_correlation(data, U.c)
m.current = V.current$mash.model

data.true = mash_update_data(data, V = V.random)
m.true = mash(data.true, U.c, verbose = FALSE, algorithm.version = 'R')

The estimated V is

V.current$V
          [,1]      [,2]      [,3]      [,4]      [,5]
[1,] 1.0000000 0.3546903 0.3429767 0.3490963 0.3441630
[2,] 0.3546903 1.0000000 0.3990047 0.3829697 0.3814803
[3,] 0.3429767 0.3990047 1.0000000 0.3706125 0.3784724
[4,] 0.3490963 0.3829697 0.3706125 1.0000000 0.3832408
[5,] 0.3441630 0.3814803 0.3784724 0.3832408 1.0000000
Ionly = c(get_loglik(m.I), length(get_significant_results(m.I)), sum(get_significant_results(m.I) <= n/2))

Vonly = c(get_loglik(m.V), length(get_significant_results(m.V)), sum(get_significant_results(m.V) <= n/2))

current = c(get_loglik(m.current), length(get_significant_results(m.current)), sum(get_significant_results(m.current) <= n/2))

true = c(get_loglik(m.true), length(get_significant_results(m.true)), sum(get_significant_results(m.true) <= n/2))

tmp = rbind(Ionly, Vonly, current, true)
row.names(tmp) = c('I only', 'V only', 'current', 'true')
colnames(tmp) = c('loglik', '# signif', 'false positive')
tmp %>% kable() %>% kable_styling()
loglik # signif false positive
I only -70068.62 741 344
V only -68333.69 2588 999
current -68468.46 114 16
true -63908.31 340 5

RRMSE:

tmp = c(rrmse(simdata, m.I), rrmse(simdata, m.V), rrmse(simdata, m.current), rrmse(simdata, m.true))
barplot(tmp, names.arg = c('I only', 'V only', 'current', 'true'))

Expand here to see past versions of unnamed-chunk-14-1.png:
Version Author Date
66be60b zouyuxin 2018-12-07

ROC:

roc.seq = ROC.table(simdata$B, m.true)
plot(roc.seq[,'FPR'], roc.seq[,'TPR'], type='l', xlab = 'FPR', ylab='TPR',
       main=paste0(' True Pos vs False Pos'), cex=1.5, lwd = 1.5, col = 'cyan')
roc.seq = ROC.table(simdata$B, m.current)
lines(roc.seq[,'FPR'], roc.seq[,'TPR'], col='purple', lwd = 1.5)
roc.seq = ROC.table(simdata$B, m.I)
lines(roc.seq[,'FPR'], roc.seq[,'TPR'], col='red', lwd = 1.5)
roc.seq = ROC.table(simdata$B, m.V)
lines(roc.seq[,'FPR'], roc.seq[,'TPR'], col='darkolivegreen4', lwd = 1.5)
legend('bottomright', c('oracle','current', 'I only', 'V only'), col=c('cyan','purple','red','darkolivegreen4'),
           lty=c(1,1,1,1), lwd=c(1.5,1.5,1.5,1.5))

Expand here to see past versions of unnamed-chunk-15-1.png:
Version Author Date
66be60b zouyuxin 2018-12-07

Session information

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14.1

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] mashr_0.2.19.0555 ashr_2.2-23       mvtnorm_1.0-8     kableExtra_0.9.0 
[5] knitr_1.20       

loaded via a namespace (and not attached):
 [1] lattice_0.20-35   Rmosek_8.0.69     colorspace_1.3-2 
 [4] htmltools_0.3.6   viridisLite_0.3.0 yaml_2.2.0       
 [7] rlang_0.3.0.1     R.oo_1.22.0       pillar_1.3.0     
[10] R.utils_2.7.0     REBayes_1.3       foreach_1.4.4    
[13] plyr_1.8.4        stringr_1.3.1     munsell_0.5.0    
[16] workflowr_1.1.1   rvest_0.3.2       R.methodsS3_1.7.1
[19] codetools_0.2-15  evaluate_0.12     doParallel_1.0.14
[22] pscl_1.5.2        parallel_3.5.1    highr_0.7        
[25] Rcpp_1.0.0        readr_1.1.1       scales_1.0.0     
[28] backports_1.1.2   rmeta_3.0         truncnorm_1.0-8  
[31] abind_1.4-5       hms_0.4.2         digest_0.6.18    
[34] stringi_1.2.4     grid_3.5.1        rprojroot_1.3-2  
[37] tools_3.5.1       magrittr_1.5      tibble_1.4.2     
[40] crayon_1.3.4      whisker_0.3-2     pkgconfig_2.0.2  
[43] MASS_7.3-50       Matrix_1.2-14     SQUAREM_2017.10-1
[46] xml2_1.2.0        assertthat_0.2.0  rmarkdown_1.10   
[49] httr_1.3.1        rstudioapi_0.8    iterators_1.0.10 
[52] R6_2.3.0          git2r_0.23.0      compiler_3.5.1

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