An Automated Prior Robustness Analysis in Bayesian Model Comparison

The marginal likelihood is the gold standard for Bayesian model comparison although it
is well-known that the value of marginal likelihood could be sensitive to the choice of
prior hyperparameters. Most models require computationally intense simulation-based
methods to evaluate the typically high-dimensional integral of the marginal likelihood
expression. Hence, despite the recognition that prior sensitivity analysis is important in
this context, it is rarely done in practice. In this paper we develop efficient and feasible
methods to compute the sensitivities of marginal likelihood, obtained via two common
simulation-based methods, with respect to any prior hyperparameter alongside the
MCMC estimation algorithm. Our approach builds on Automatic Differentiation (AD),
which has only recently been introduced to the more computationally intensive setting of
Markov chain Monte Carlo simulation. We illustrate our approach with two empirical
applications in the context of widely used multivariate time series models.