Bayesian Gibbs Slice Sampler: A Novel Approach to Efficient MCMC and Its Application to Sovereign Credit Rating Determinants

In this paper, we introduce the Bayesian Gibbs Slice Sampler (BGSS), a novel MCMC algorithm inspired in the Latent Slice Sampling (LSS) framework, where Bayesian inference is employed to refine the proposal distribution required to accommodate the single adjustment parameter. Unlike methods based on gradient calculations or those requiring complex, hard-to-optimize adaptive proposals, BGSS naturally incorporates Bayes’ theorem during the chain adaptation phase to learn about the target distribution. Subsequently, it generates nearly independent proposals derived from a conditionally univariate factorization of the parameter space, along with a QR decomposition, thus conferring substantial efficiency to the exploration process. The proposed sampler is both adaptable and computationally effective, matching the speed of LSS and delivering results on par with state-of-the-art approaches like the No-U-Turn Sampler (NUTS). We display its capabilities through simulated and real-world applications, highlighting an analysis of sovereign credit ratings and illustrating how BGSS can model the influence of macroeconomic fundamentals over multiple time horizons. Overall, BGSS strikes a favourable balance between performance and computational demands, making it a dependable tool for Bayesian inference in econometric contexts.