Multivariate Bayesian variable selection regression

Multivariate EBNM based prior for M&M

Running the mixture prior pipeline with this notebook.

Method

I ran two versions of parameters: when per variable PVE = 0.05, a realistic scenario for eQTL studies, and when PVE 0.15 for very strong effect.

The results are shown for ED implemented in mashr package. FLASH, FLASH with non-negative factor constraint and PCA (k=3) as well as XtX are included in the ED. We hope ED does decent job for scenario 1 and good job for secnario 2.

Conclusion

The result is mostly as expected:

  • FLASH can capture simulated singleton effects
  • FLASH cannot capture simulated singleton effects with weights 0.01, unless the PVE per variable is large (PVE = 0.15 in my setting).

The truth

In [5]:
%preview ../../mvSuSiE_output/prior_simulation_artificial_mixture_50.pdf -s png
> ../../mvSuSiE_output/prior_simulation_artificial_mixture_50.pdf (217.5 KiB):
In [7]:
%preview ../../mvSuSiE_output/prior_simulation_gtex_mixture.pdf -s png
> ../../mvSuSiE_output/prior_simulation_gtex_mixture.pdf (176.0 KiB):

Results for PVE = 0.15

Results are saved to this repo. Here are some previous:

In [2]:
%preview ../../mvSuSiE_output/artificial_mixture_identity_ed_bovy.pdf -s png
> ../../mvSuSiE_output/artificial_mixture_identity_ed_bovy.pdf (422.6 KiB):
In [3]:
%preview ../../mvSuSiE_output/gtex_mixture_identity_ed_bovy.pdf -s png
> ../../mvSuSiE_output/gtex_mixture_identity_ed_bovy.pdf (353.9 KiB):

Results for PVE = 0.05

In [1]:
%preview ../../dsc/mnm_prototype/mnm_sumstats/artificial_mixture_identity.ed_bovy.pdf -s png
> ../../dsc/mnm_prototype/mnm_sumstats/artificial_mixture_identity.ed_bovy.pdf (95.1 KiB):
In [2]:
%preview ../../dsc/mnm_prototype/mnm_sumstats/gtex_mixture_identity.ed_bovy.pdf -s png
> ../../dsc/mnm_prototype/mnm_sumstats/gtex_mixture_identity.ed_bovy.pdf (156.3 KiB):
Copyright © 2016-2020 Gao Wang et al at Stephens Lab, University of Chicago