Adaptive Pseudo-Marginal Algorithm

The Pseudo-Marginal (PM) algorithm is a popular Markov chain Monte Carlo (MCMC) method used to sample from a target distribution when its density is inaccessible, but can be estimated with a non-negative unbiased estimator. Its performance depends on a key parameter, N, the number of iterations (or particles) used to approximate the target density. Larger values of N yield more accurate estimates but at increased running time. Previous studies has provided guidelines for selecting an optimal value of N to balance this tradeoff. However, this approach involves multiple steps and manual adjustments. To overcome these limitations, we introduce an adaptive version of the PM algorithm, where N is automatically adjusted during the iterative process toward its optimal value, thus eliminating the need for manual intervention. This algorithm ensures convergence under certain conditions. On two examples, including a real data problem on pulmonary infection in preschool children, the proposed algorithm compares favorably to the existing approach.