Accelerating delayed-acceptance Markov chain Monte Carlo algorithms

Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and computationally cheaper version) of said distribution. DA-MCMC accelerates MCMC sampling in complex applications, while still targeting the exact distribution. We design a computationally faster, albeit approximate, DA-MCMC algorithm. We consider parameter inference in a Bayesian setting where a surrogate likelihood function is introduced in the delayed-acceptance scheme. When the evaluation of the likelihood function is computationally intensive, our scheme produces a 2-4 times speed-up, compared to standard DA-MCMC. However, the acceleration is highly problem dependent. Inference results for the standard delayed-acceptance algorithm and our approximated version are similar, indicating that our algorithm can return reliable Bayesian inference. As a computationally intensive case study, we introduce a novel stochastic differential equation model for protein folding data.Comment: 40 pages, 21 figures, 10 table

Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a thermodynamic integration scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods

Hierarchical Implicit Models and Likelihood-Free Variational Inference

Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for theories which encompass our understanding of the physical world. Despite this fundamental nature, the use of implicit models remains limited due to challenges in specifying complex latent structure in them, and in performing inferences in such models with large data sets. In this paper, we first introduce hierarchical implicit models (HIMs). HIMs combine the idea of implicit densities with hierarchical Bayesian modeling, thereby defining models via simulators of data with rich hidden structure. Next, we develop likelihood-free variational inference (LFVI), a scalable variational inference algorithm for HIMs. Key to LFVI is specifying a variational family that is also implicit. This matches the model's flexibility and allows for accurate approximation of the posterior. We demonstrate diverse applications: a large-scale physical simulator for predator-prey populations in ecology; a Bayesian generative adversarial network for discrete data; and a deep implicit model for text generation.Comment: Appears in Neural Information Processing Systems, 201