Identification-aware Markov chain Monte Carlo

TL;DR

This paper introduces an identification-aware MCMC method that effectively explores multi-modal and flat posterior regions in non-identified models, improving convergence and uncovering complex posterior structures.

Contribution

It develops a novel MCMC approach leveraging observationally equivalent parameter sets, enhancing exploration in non-identified models and outperforming existing methods.

Findings

Eliminates mode entrapment in complex posteriors

Achieves convergence rates bounded away from zero

Uncovers non-trivial modes in SVMA models

Abstract

Leaving posterior sensitivity concerns aside, non-identifiability of the parameters does not raise a difficulty for Bayesian inference as far as the posterior is proper, but multi-modality or flat regions of the posterior induced by the lack of identification leaves a challenge for modern Bayesian computation. Sampling methods often struggle with slow or non-convergence when dealing with multiple modes or flat regions of the target distributions. This paper develops a novel Markov chain Monte Carlo (MCMC) approach for non-identified models, leveraging the knowledge of observationally equivalent sets of parameters, and highlights an important role that identification plays in modern Bayesian analysis. We show that our identification-aware proposal eliminates mode entrapment, achieving a convergence rate uniformly bounded away from zero, in sharp contrast to the exponentially decaying rates characterizing standard Random Walk Metropolis and Hamiltonian Monte Carlo. Simulation studies show its superior performance compared to other popular computational methods including Hamiltonian Monte Carlo and sequential Monte Carlo. We also demonstrate that our method uncovers non-trivial modes in the target distribution in a structural vector moving-average (SVMA) application.