Global Consensus Monte Carlo

Variational Consensus Monte Carlo

Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large datasets typical of modern machine learning. The recently proposed consensus Monte Carlo algorithm removes this limitation by partitioning the data and drawing sam...

Consensus Monte Carlo using expectation propagation∗

The article under discussion considers algorithms for performing inference on large or unwieldy datasets by partitioning the data, analyzing each piece separately, and then putting the inferences together. This is an active area of research in computational statistics (see, for example, Tresp, 2000, Ahn, Korattikara, and Welling, 2012, Gershman, Hoffman, and Blei, 2012, Korattikara, Chen, and W...

Monte-carlo Methods in Global Illumination

Monte Carlo vs. Fuzzy Monte Carlo Simulation for Uncertainty and Global Sensitivity Analysis

Monte Carlo simulation (MCS) has been widely used for the uncertainty propagations of building simulation tools. In general, most unknown inputs for the MCS are regarded as single probability distributions based on experts’ subjective judgements and assumptions, when simulation information and measured data are inaccurate and insufficient. However, this can lead to meaningless and untrustworthy...

Importance Weighted Consensus Monte Carlo for Distributed Bayesian Inference

The recent explosion in big data has created a significant challenge for efficient and scalable Bayesian inference. In this paper, we consider a divide-and-conquer setting in which the data is partitioned into different subsets with communication constraints, and a proper combination strategy is used to aggregate the Monte Carlo samples drawn from the local posteriors based on the dataset subse...