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Title: Bayesian inference for doubly-intractable likelihoods using the block-Poisson estimator Authors:  Yu Yang - University of New South Wales (Australia) [presenting]
Robert Kohn - University of New South Wales (Australia)
Scott Sisson - University of New South Wales (Austria)
Matias Quiroz - University of Technology Sydney (Australia)
Abstract: Many modeling problems in science involve models with unknown normalizing functions, so-called doubly-intractable models in the Bayesian literature. Inference for such models requires the evaluation of likelihood functions that depend on the parameter of interest. We propose an approach that uses a block-Poisson estimator to estimate the doubly-intractable likelihood unbiasedly. The estimator is not necessarily positive, so the pseudo-marginal MCMC algorithm runs on the absolute value of the likelihood estimate with an importance sampling correction that ensures consistent estimates of the posterior mean of any function. We derive practical guidelines on how to tune the hyper-parameters of the estimator to achieve the optimal balance between sampling efficiency and computational cost. The advantage of the method is demonstrated in three examples. The first example concerns the Ising model, a standard example in this literature. The second example concerns modelling a function with a constrained Gaussian process. The third example concerns estimating the parameters in a model for spherical data.