ABSTRACT
Efficient computational methods to sample from the posterior distribution of models are key to the use of Bayesian variable selection in practice. Adaptive Monte Carlo are a promising approach to build such methods. We review the use of these methods in generalised linear models with a particular focus on linear and logistic regression. We illustrate how these methods can be applied to simulated data and to two contrasting real-life examples. Firstly, we consider a high-dimensional example with an application to fine mapping in genomics with 10,995 observations and 5766 covariates (SNPs). Secondly, we consider an application to a complex model of environmental DNA which contains five logistic regressions and two sets of latent variables.
