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Title: Efficiently combining pseudo marginal and particle Gibbs sampling Authors:  Robert Kohn - University of New South Wales (Australia) [presenting]
Abstract: Particle Markov Chain Monte Carlo (PMCMC) is a general approach to carry out Bayesian inference in non-linear and non-Gaussian state space models. We show how to scale up PMCMC in terms of the number of parameters and number of time points by generating parameters that are highly correlated with the states with the states integrated out using a pseudo marginal step while the rest of the parameters are generated conditional on the states using particle Gibbs. We make the PMCMC scalable in the number of observations by using the same random numbers in the Metropolis-Hastings ratio of the pseudo marginal step. We do so by expressing the target density of the PMCMC in terms of the basic uniform or standard normal random numbers rather than in terms of the particles, as has been done till now, and develop a constrained version of conditional sequential Monte Carlo algorithm. We illustrate the methods using a high dimensional factor stochastic volatility having both a large number of parameters and a large number of latent states and show that our proposed method makes the computation much more efficient.