On Gibbs Sampling for Structured Bayesian Models Discussion of paper by Zanella and Roberts

TL;DR

This paper discusses extensions of Gibbs sampling for structured Bayesian models, exploring multigrid decompositions in various complex hierarchical and mixed effects models to gain deeper insights.

Contribution

It introduces potential extensions of multigrid decomposition techniques to new classes of hierarchical Bayesian models.

Findings

Multigrid decomposition can be applied to vector hierarchical models.

Extensions to linear mixed effects models are feasible.

Partial centering parametrizations benefit from multigrid insights.

Abstract

This article is a discussion of Zanella and Roberts' paper: Multilevel linear models, gibbs samplers and multigrid decompositions. We consider several extensions in which the multigrid decomposition would bring us interesting insights, including vector hierarchical models, linear mixed effects models and partial centering parametrizations.