Bayesian Gibbs Slice Sampler: a Novel Approach to Efficient MCMC

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 effective, matching the speed of Latent Slice Sampler (LSS) and delivering results on par with state-of-the-art approaches like the No-U-Turn Sampler (NUTS). We display its capabilities through some simulated scenarios and an empirical application. Overall, BGSS strikes a favourable balance between performance and computational demands, making it a dependable tool for Bayesian inference in econometric contexts. The proposed method enables efficient posterior distribution calculation or approximation, providing reliable inference for model parameters.