A flexible particle Markov chain Monte Carlo method
Particle Markov Chain Monte Carlo methods are used to carry out inference in nonlinear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform Bayesian inference using either a particle marginal Metropolis–Hastings (PMMH) algorithm or a particle Gibbs (PG) sampler. This paper shows how the two ways of generating variables mentioned above can be combined in a flexible manner to give sampling schemes that converge to a desired target distribution. The advantage of our approach is that the sampling scheme can be tailored to obtain good results for different applications. For example, when some parameters and the states are highly correlated, such parameters can be generated using PMMH, while all other parameters are generated using PG because it is easier to obtain good proposals for the parameters within the PG framework. We derive some convergence properties of our sampling scheme and also investigate its performance empirically by applying it to univariate and multivariate stochastic volatility models and comparing it to other PMCMC methods proposed in the literature.
KeywordsDiffusion equation Factor stochastic volatility model Metropolis–Hastings Particle Gibbs sampler
The work of the authors was partially supported by an ARC Research Council Grant DP120104014. The work of Robert Kohn and David Gunawan was also partially supported by the ARC Center of Excellence Grant CE140100049.
- Chib, S., Pitt, M.K., Shephard, N.: Likelihood based inference for diffusion driven models. Working Paper (2004)Google Scholar
- Douc, R., Cappé, O.: Comparison of resampling schemes for particle filtering. In: Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005. ISPA 2005, pp. 64–69. IEEE (2005)Google Scholar
- Kleppe, T.S., Yu, J., Skaug, H.: Estimating the GARCH diffusion: simulated maximum likelihood in continuous time. SMU Economics and Statistics Working Paper Series, p. 13 (2010)Google Scholar
- Lindsten, F., B. Schön, T.: On the use of backward simulation in particle Markov chain Monte Carlo methods. arxiv:1110.2873 (2012a)
- Lindsten, F., Schön, T.B.: On the use of backward simulation in the particle Gibbs sampler. In: Proceedings of the 37th International Conference on Acoustics, Speech, and Signal Processing, pp. 3845–3848. ICASSP (2012b)Google Scholar
- Lindsten, F., Bunch, P., Singh, S.S., Schön, T.B.: Particle ancestor sampling for near-degenerate or intractable state transition models. arxiv:1505.0635v1 (2015)
- Van Der Merwe, R., Doucet, A., De Freitas, N., Wan, E.: The unscented particle filter. Advances in neural information processing systems, pp. 584–590 (2001)Google Scholar