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The Correlated Pseudo-Marginal Method

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SINW01 - Scalable statistical inference

Joint work with George Deligiannidis and Michael Pitt

The pseudo-marginal algorithm is a popular Metropolis–Hastings-type scheme which samples asymptotically from a target probability density when we are only able to estimate unbiasedly an unnormalised version of it. However, for the performance of this scheme not to degrade as the number T of data points increases, it is typically necessary for the number N of Monte Carlo samples to be proportional to T to control the relative variance of the likelihood ratio estimator appearing in the acceptance probability of this algorithm. The correlated pseudo-marginal algorithm is a modification of the pseudo-marginal method using a likelihood ratio estimator computed using two correlated likelihood estimators. For random effects models, we show under regularity conditions that the parameters of this scheme can be selected such that the relative variance of this likelihood ratio estimator is controlled when N increases sublinearly with T and we provide guidelines on how to optimise the parameters of the algorithm based on a non-standard weak convergence analysis. The efficiency of computations for Bayesian inference relative to the pseudo-marginal method empirically increases with T and is higher than two orders of magnitude in some of our examples.

This talk is part of the Isaac Newton Institute Seminar Series series.

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