A General Framework for the Parametrization of Hierarchical Models

TL;DR

This paper introduces a unified framework for parametrizing hierarchical models using centering and noncentering techniques, improving MCMC efficiency and robustness across various models.

Contribution

It provides a comprehensive theory and practical recipes for constructing effective centered and noncentered parametrizations, including novel partially noncentered methods.

Findings

Theoretical analysis of convergence time for Gibbs samplers with different parametrizations.

Guidelines for choosing between centering and noncentering based on model characteristics.

Development of robust Gibbs sampler algorithms insensitive to data variations.

Abstract

In this paper, we describe centering and noncentering methodology as complementary techniques for use in parametrization of broad classes of hierarchical models, with a view to the construction of effective MCMC algorithms for exploring posterior distributions from these models. We give a clear qualitative understanding as to when centering and noncentering work well, and introduce theory concerning the convergence time complexity of Gibbs samplers using centered and noncentered parametrizations. We give general recipes for the construction of noncentered parametrizations, including an auxiliary variable technique called the state-space expansion technique. We also describe partially noncentered methods, and demonstrate their use in constructing robust Gibbs sampler algorithms whose convergence properties are not overly sensitive to the data.