Title: The block-Poisson estimator for optimally tuned signed pseudo-marginal MCMC
Authors: Matias Quiroz - University of Technology Sydney (Australia) [presenting]
Minh-Ngoc Tran - University of Sydney (Australia)
Mattias Villani - Stockholm University (Sweden)
Robert Kohn - University of New South Wales (Australia)
Doan Khue Dung Dang - University of New South Wales (Australia)
Abstract: A pseudo-marginal Markov Chain Monte Carlo (MCMC) method is proposed that estimates the likelihood using a block-Poisson estimator. The estimator is a product of Poisson estimators, each based on an independent set of random numbers used to construct the estimator. The construction allows us to update the random numbers in a subset of the blocks in each MCMC iteration, thereby inducing a controllable correlation between the estimates at the current and proposed draw in the Metropolis-Hastings ratio. This makes it possible to use highly variable likelihood estimators (which are computationally much faster) without adversely affecting the sampling efficiency. Poisson estimators are unbiased but not necessarily positive. We therefore follow a previous work and run the MCMC on the absolute value of the estimator, which we term signed pseudo-marginal MCMC, and use an importance sampling correction for occasionally negative likelihood estimates to estimate expectations of any function of the parameters consistently. We provide analytically derived guidelines to select the optimal tuning parameters for the block-Poisson estimator by minimizing the variance of the importance sampling corrected estimator per unit of computing time. We apply the block-Poisson estimator to doubly intractable problems, which are typically challenging to estimate efficiently.