Constructing Metropolis-Hastings proposals using damped BFGS updates

TL;DR

This paper introduces a novel method for tuning Metropolis-Hastings proposals by incorporating Hessian information via damped BFGS updates, improving sampling efficiency in Bayesian system identification.

Contribution

It proposes a new approach to adaptively tune MH proposals using damped BFGS updates to incorporate curvature information, enhancing convergence.

Findings

Improved mixing of MH chains with the proposed method

Enhanced efficiency in Bayesian parameter estimation

Empirical validation shows better convergence rates

Abstract

The computation of Bayesian estimates of system parameters and functions of them on the basis of observed system performance data is a common problem within system identification. This is a previously studied issue where stochastic simulation approaches have been examined using the popular Metropolis--Hastings (MH) algorithm. This prior study has identified a recognised difficulty of tuning the {proposal distribution so that the MH method provides realisations with sufficient mixing to deliver efficient convergence. This paper proposes and empirically examines a method of tuning the proposal using ideas borrowed from the numerical optimisation literature around efficient computation of Hessians so that gradient and curvature information of the target posterior can be incorporated in the proposal.