Variance Adaptive Shrinkage (vash): Flexible Empirical Bayes estimation of variances

Abstract

MotivationWe consider the problem of estimating variances on a large number of \"similar\" units, when there are relatively few observations on each unit. This problem is important in genomics, for example, where it is often desired to estimate variances for thousands of genes (or some other genomic unit) from just a few measurements on each. A common approach to this problem is to use an Empirical Bayes (EB) method that assumes the variances among genes follow an inverse-gamma distribution. Here we describe a more flexible EB method, whose main assumption is that the distribution of the variances (or, as an alternative, the precisions) is unimodal.\n\nResultsWe show that this more flexible assumption provides competitive performance with existing methods when the variances truly come from an inverse-gamma distribution, and can outperform them when the distribution of the variances is more complex. In analyses of several human gene expression datasets from the Genotype Tissues Expression (GTEx) consortium, we find that our more flexible model often fits the data appreciably better than the single inverse gamma distribution. At the same time we find that, for variance estimation, the differences between methods is often small, suggesting that the simpler methods will often suffice in practice.\n\nAvailabilityOur methods are implemented in an R package vashr available from http://github.com/mengyin/vashr.