Analysis of Next Generation Sequencing Data Using Integrated Nested Laplace Approximation (INLA)

Integrated Nested Laplace Approximation (INLA), implemented in the R-package r-inla, is a very versatile methodology for the Bayesian analysis of next generation sequencing count data: it can account for zero-inflation, random effects and correlation across genomic features. We demonstrate its use and provide some insights on its approximations of marginal posteriors. In high-dimension settings like these, INLA is in particular attractive in combination with empirical Bayes. We show how to apply this by estimating priors from the output of INLA. We extend this methodology to estimation of joint priors for a limited number of parameters, which effectuates multivariate shrinkage. Joint priors are useful for appropriate inference when two or more parameters are likely to be strongly correlated. Two examples serve as illustrations: (1) joint inference for differential zero-inflation and means between two groups; (2) correlated group effects on mRNA expression. For both simulated and real data we show that multivariate shrinkage may lead to improved marker selection. We end with a discussion on the use of this INLA-based method within the spectrum of other available methods.