A Bayesian comparison in Stan and NIMBLE by trimmed mean regression

Abstract

The Bayesian statistical paradigm has successful applications across various research fields, including medicine, machine learning, artificial intelligence, and more. Motivated by the arising impact of Bayesian computing, the thesis compares two contemporary Bayesian specialized computational tools, Stan and NIMBLE. Both have remained under active development, although they are enjoying the merit of freeing the practitioners and analysts from complicated statistical posterior inference by automating the construction of samplers. The comparison between Stan and NIMBLE is focused on the samplers. Their performances are illustrated by the implementation of weakly informative and informative Bayesian estimation under the trimmed mean regression model by numerical studies, respectively. The informative estimation requires a resampling scheme. We replace Stan with R in comparison since resampling is problematic in Stan. We assess performance of Bayesian inference in both parameter estimation and MCMC diagnostics, for the comparison among Stan, NIMBLE, and R program. We conclude that, both Bayesian computing tools can automate posterior approximation accurately and conveniently compared with pure R programming by parameters hand-tuning plus mathematical derivation. RStan is efficient in parallel computing but needs contrivance tackling discrete parameters owning to Hamiltonian Monte Carlo sampling. NIMBLE aims to serving users who are accustomed to R software but less efficient.