Quasi-Newton particle Metropolis-Hastings
This incremental improvement addresses tuning challenges for researchers using Bayesian inference in state space models, particularly with intractable likelihoods.
The authors tackled the problem of poor mixing in Particle Metropolis-Hastings for Bayesian parameter inference in nonlinear state space models by proposing a quasi-Newton inspired proposal that reduces tuning needs, achieving similar or better mixing with less effort.
Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly using tedious pilot runs. Therefore, we consider a new proposal inspired by quasi-Newton algorithms that may achieve similar (or better) mixing with less tuning. An advantage compared to other Hessian based proposals, is that it only requires estimates of the gradient of the log-posterior. A possible application is parameter inference in the challenging class of SSMs with intractable likelihoods. We exemplify this application and the benefits of the new proposal by modelling log-returns of future contracts on coffee by a stochastic volatility model with $α$-stable observations.