Identification-aware Markov chain Monte Carlo

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 proposal overcomes the issues of being trapped in a local mode and achieves a faster rate of convergence than the existing MCMC techniques including random walk Metropolis-Hastings and Hamiltonian Monte Carlo. The gain in the speed of convergence is more significant as the dimension or cardinality of the identified sets increases. 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.