To try out some simulations that donâ€™t match the canonical covariance matrices and illustrate how the data driven matrices help.

Here the function `simple_sims_2`

simulates data in five
conditions with just two types of effect:

shared effects only in the first two conditions; and

shared effects only in the last three conditions.

```
library(ashr)
library(mashr)
set.seed(1)
= simple_sims2(1000,1)
simdata = cbind(c(1,1,0,0,0),c(1,1,0,0,0),rep(0,5),rep(0,5),rep(0,5))
true.U1 = cbind(rep(0,5),rep(0,5),c(0,0,1,1,1),c(0,0,1,1,1),c(0,0,1,1,1))
true.U2 = list(true.U1 = true.U1, true.U2 = true.U2) U.true
```

Run 1-by-1 to add the strong signals and ED covariances.

```
= mash_set_data(simdata$Bhat, simdata$Shat)
data .1by1 = mash_1by1(data)
m= get_significant_results(m.1by1)
strong = cov_canonical(data)
U.c = cov_pca(data,5,strong)
U.pca = cov_ed(data,U.pca,strong)
U.ed
# Computes covariance matrices based on extreme deconvolution,
# initialized from PCA.
= mash(data, U.c)
m.c = mash(data, U.ed)
m.ed = mash(data, c(U.c,U.ed))
m.c.ed = mash(data, U.true)
m.true
print(get_loglik(m.c),digits = 10)
print(get_loglik(m.ed),digits = 10)
print(get_loglik(m.c.ed),digits = 10)
print(get_loglik(m.true),digits = 10)
```

The log-likelihood is much better from data-driven than canonical covariances. This is good! Indeed, here the data-driven fit is very slightly better fit than the true matrices, but only very slightly.