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Quasi-Newton particle Metropolis-Hastings

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  • Johan Dahlin
  • Fredrik Lindsten
  • Thomas B. Schon

Abstract

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 $\alpha$-stable observations.

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  • Johan Dahlin & Fredrik Lindsten & Thomas B. Schon, 2015. "Quasi-Newton particle Metropolis-Hastings," Papers 1502.03656, arXiv.org, revised Sep 2015.
    • Handle: RePEc:arx:papers:1502.03656
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    References listed on IDEAS

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    1. Thomas A. Dean & Sumeetpal S. Singh & Ajay Jasra & Gareth W. Peters, 2014. "Parameter Estimation for Hidden Markov Models with Intractable Likelihoods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 970-987, December.
    2. repec:dau:papers:123456789/5724 is not listed on IDEAS
    3. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
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