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Title: The Block-Poisson estimator for efficient Bayesian inference in intractable models Authors:  Mattias Villani - Stockholm University (Sweden) [presenting]
Matias Quiroz - University of Technology Sydney (Australia)
Robert Kohn - University of New South Wales (Australia)
Minh-Ngoc Tran - University of Sydney (Australia)
Doan Khue Dung Dang - University of New South Wales (Australia)
Abstract: Many applications involve models with intractable likelihood functions, for example random effects models, big data problems with costly likelihood evaluations, and the class of doubly intractable problems where the likelihood contains an intractable normalization constant. We propose an efficient dependent pseudo-marginal Markov Chain Monte Carlo algorithm based on the Block-Poisson estimator of the intractable likelihood. The Block-Poisson estimator is shown to be unbiased and provides a convenient way to introduce dependence between successive likelihood estimates, which is well known to be crucial for pseudo-marginal algorithms to work well with noisy estimates. The Block-Poisson estimator can give occasionally negative estimates and we follow previous research and run our MCMC on the absolute value of the posterior density followed by an importance sampling correction to obtain simulation consistent estimates of posterior expectations of functions. We provide guidelines for optimally tuning the algorithm that balances the computational cost of the likelihood estimator against the loss of efficiency from using noisy estimates and the importance sampling inefficiency resulting from occasional negative estimates. We demonstrate the method on subsampling in big data problems and show dramatical speed-ups compared to regular MCMC and another recently proposed exact subsampling algorithm.