Global Robust Bayesian Analysis in Large Models

Abstract

This paper develops tools for global prior sensitivity analysis in large Bayesian models. Without imposing parametric restrictions, the framework provides bounds for a wide range of posterior statistics given any prior that is close to the original in relative entropy. The methodology also reveals parts of the prior that are important for the posterior statistics of interest. To implement these calculations in large models, we develop a sequential Monte Carlo algorithm and use approximations to the likelihood and statistic of interest. We use the framework to study error bands for the impulse response of output to a monetary policy shock in the New Keynesian model of Smets and Wouters (2007). The error bands depend asymmetrically on the prior through features of the likelihood that are hard to detect without this formal prior sensitivity analysis.