Changye Wu

Changye Wu, Pierre Pudlo, Christian P. Robert et al.

We introduce a Hamiltonian Monte Carlo (HMC) methodology based on a randomized selection of integration times, referred to as eHMC, where "e" stands for empirical. The approach relies on an offline calibration phase that leverages importance sampling to construct an empirical distribution on discretization parameters, thereby eliminating the need for manual burn-in diagnostics and online adaptation. The proposal distribution used in the calibration stage is obtained via a Population Monte Carlo scheme combined with tempering and flexible parametric variational families such as normalizing flows. The resulting algorithm defines a mixture of HMC kernels with a fixed mixing distribution, preserving the target distribution. Numerical experiments on benchmarks demonstrate that eHMC achieves competitive or improved efficiency compared to the No-U-Turn Sampler (NUTS) when accounting for computational cost. These results suggest that offline calibration combined with randomized integration schemes provides a viable alternative to adaptive HMC methods.

Wu Changye, Christian P. Robert

For Bayesian computation in big data contexts, the divide-and-conquer MCMC concept splits the whole data set into batches, runs MCMC algorithms separately over each batch to produce samples of parameters, and combines them to produce an approximation of the target distribution. In this article, we embed random forests into this framework and use each subposterior/partial-posterior as a proposal distribution to implement importance sampling. Unlike the existing divide-and-conquer MCMC, our methods are based on scaled subposteriors, whose scale factors are not necessarily restricted to being equal to one or to the number of subsets. Through several experiments, we show that our methods work well with models ranging from Gaussian cases to strongly non-Gaussian cases, and include model misspecification.