The discovery of genomic polymorphisms influencing gene expression (also known as expression quantitative trait loci or eQTLs) can be formulated as a sparse Bayesian multivariate/multiple regression problem. An important aspect in the development of such models is the implementation of bespoke inference methodologies, a process which can become quite laborious, when multiple candidate models are being considered. We describe automatic, black-box inference in such models using Stan, a popular probabilistic programming language. The utilization of systems like Stan can facilitate model prototyping and testing, thus accelerating the data modeling process. The code described in this chapter can be found at https://github.com/dvav/eQTLBookChapter .
Keywords: Bayesian variable selection; Black-box Bayesian inference; Global-local shrinkage; Horseshoe prior; Probabilistic programming; R; RNA-seq; Stan; eQTL mapping.