A Tutorial on Bayesian Linear Regression with Compositional Predictors Using JAGS

Abstract

This tutorial offers an exploration of advanced Bayesian methodologies for compositional data analysis, specifically the Bayesian Lasso and Bayesian Spike-and-Slab Lasso (SSL) techniques. Our focus is on a novel Bayesian methodology that integrates Lasso and SSL priors, enhancing both parameter estimation and variable selection for linear regression with compositional predictors. The tutorial is structured to streamline the learning process, breaking down complex analyses into a series of straightforward steps. We demonstrate these methods using R and JAGS, employing simulated datasets to illustrate key concepts. Our objective is to provide a clear and comprehensive understanding of these sophisticated Bayesian techniques, preparing readers to adeptly navigate and apply these methods in their own compositional data analysis endeavors.