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We propose an importance sampling (IS)-based transport map Hamiltonian MonteCarlo procedure for performing full Bayesian analysis in general nonlinearhigh-dimensional hierarchical models. Using IS techniques to construct atransport map, the proposed method transforms the typically highly challengingtarget distribution of a hierarchical model into a target which is easilysampled using standard Hamiltonian Monte Carlo. Conventional applications ofhigh-dimensional IS, where infinite variance of IS weights can be a seriousproblem, require computationally costly high-fidelity IS distributions. Anappealing property of our method is that the IS distributions employed can beof rather low fidelity, making it computationally cheap. We illustrate ouralgorithm in applications to challenging dynamic state-space models, where itexhibits very high simulation efficiency compared to relevant benchmarks, evenfor variants of the proposed method implemented using a few dozen lines of codein the Stan statistical software.

Importance Sampling-based Transport Map Hamiltonian Monte Carlo for Bayesian Hierarchical Models