Particle Metropolis-Hastings using gradient and Hessian information

Abstract

Particle Metropolis-Hastings (PMH) allows for Bayesian parameter inference in nonlinear state space models by combining Markov chain Monte Carlo (MCMC) and particle filtering. The latter is used to estimate the intractable likelihood. In its original formulation, PMH makes use of a marginal MCMC proposal for the parameters, typically a Gaussian random walk. However, this can lead to a poor exploration of the parameter space and an inefficient use of the generated particles. We propose a number of alternative versions of PMH that incorporate gradient and Hessian information about the posterior into the proposal. This information is more or less obtained as a byproduct of the likelihood estimation. Indeed, we show how to estimate the required information using a fixed-lag particle smoother, with a computational cost growing linearly in the number of particles. We conclude that the proposed methods can: (i) decrease the length of the burn-in phase, (ii) increase the mixing of the Markov chain at the stationary phase, and (iii) make the proposal distribution scale invariant which simplifies tuning.

27 pages, 5 figures, 2 tables. The final publication is available at Springer via: http://dx.doi.org/10.1007/s11222-014-9510-0

References in corpus (2)

• The pseudo-marginal approach for efficient Monte Carlo computations
• Sequential Monte Carlo smoothing with application to parameter estimation in non-linear state space models

Cited by in corpus (7)

• On Particle Methods for Parameter Estimation in State-Space Models
• Particle Filters and Data Assimilation
• Sequential Monte Carlo Methods for System Identification
• Probabilistic learning of nonlinear dynamical systems using sequential Monte Carlo
• Efficient Learning of the Parameters of Non-Linear Models using Differentiable Resampling in Particle Filters
• Effect Handlers for Programmable Inference
• Quasi-Newton particle Metropolis-Hastings