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Activity Number:
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57
- Frontiers in Bayesian Computing
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Type:
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Contributed
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Date/Time:
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Monday, August 3, 2020 : 10:00 AM to 2:00 PM
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Sponsor:
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Section on Bayesian Statistical Science
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Abstract #313409
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Title:
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On Scalable Particle Markov Chain Monte Carlo
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Author(s):
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Christopher Carter* and David Gunawan and Robert Kohn
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Companies:
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University of New South Wales and University of Wollongong and University of New South Wales
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Keywords:
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Correlated pseudo marginal Metropolis-Hastings;
Factor stochastic volatility model;
Particle Gibbs sampler
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Abstract:
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Particle Markov Chain Monte Carlo (PMCMC) is a general approach to carry out Bayesian inference in non-linear and non-Gaussian state space models. Our article shows how to scale up PMCMC in terms of the number of parameters by generating parameters that are highly correlated with the states using a pseudo marginal step which has the states integrated out, while the rest of the parameters are generated conditional on the states using particle Gibbs and in the number of observations by using the same random numbers in the Metropolis-Hastings ratio of the pseudo marginal step. We express the target density of the PMCMC in terms of the basic uniform or standard normal random numbers used in the sequential Monte Carlo algorithm, rather than in terms of the particles. We derive some theoretical properties of our sampling scheme and also investigate its performance empirically by applying it to univariate and multivariate stochastic volatility models having both a large number of parameters and a large number of latent states and show that our proposed sampling scheme is much more efficient than other competing PMCMC methods.
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Authors who are presenting talks have a * after their name.
