Bayesian Gibbs Slice Sampler: a Novel Approach to Efficient MCMC

Abstract In this paper, we introduce the Bayesian Gibbs Slice Sampler (BGSS), a novel MCMC algorithm where Bayesian inference is employed to estimate the slice width on each iteration, as well as a conditionally univariate factorization of the parameter space that confer a substantial efficiency to the exploration process. This efficiency can be further improved by using an initial QR decomposition of the explanatory variable matrix. The proposed sampler is both adaptable and computationally eff