Variance adaptive shrinkage (vash): flexible empirical Bayes estimation of variances

Genomic studies often involve estimation of variances of thousands of genes (or other genomic units) from just a few measurements on each. For example, variance estimation is an important step in gene expression analyses aimed at identifying differentially expressed genes. 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. This distributional assumption is relatively inflexible; for example, it may not capture 'outlying' genes whose variances are considerably bigger than usual. Here we describe a more flexible EB method, capable of capturing a much wider range of distributions. Indeed, the main assumption is that the distribution of the variances is unimodal (or, as an alternative, that the distribution of the precisions is unimodal). We argue that the unimodal assumption provides an attractive compromise between flexibility, computational tractability and statistical efficiency.