Title: Automated sensitivity computations for Bayesian Markov chain Monte Carlo inference: A new approach
Authors: Liana Jacobi - University Melbourne (Australia)
Dan Zhu - Monash University (Australia) [presenting]
Abstract: An efficient numerical approach is introduced to implement a comprehensive sensitivity analysis of MCMC output with respect all input parameters, i.e. prior hyper-parameters and chain starting values. Building on recent developments of automatic differentiation (AD) in the classical simulation setting, we develop an AD MCMC scheme that is applicable to MCMC algorithms composed of both continuous and dis-continuous high-dimensional mappings. It enables the computation the of sensitivities based on exact (up to computer floating point error) first-order derivatives of MCMC draws alongside the estimation algorithm. The new approach makes it computationally feasible to (i) undertake a complete local robustness analysis of a wide range of posterior output with respect to all prior input parameters; and (ii) assess algorithm performance, in particular convergence behaviour, via the evolution of starting value sensitivities. We discuss a wide range of prior robustness measures, including new measures relating to overall model robustness and quantile robustness. In addition, convergence diagnostics based on the evolution of overall starting value sensitivities are introduced. Performance and applications of the method are illustrated in simulated and real data examples.