Abstract

Consensus Monte Carlo is an algorithm for conducting Monte Carlo based Bayesian inference on large data sets distributed across many worker machines in a data center. The algorithm operates by running a separate Monte Carlo algorithm on each worker machine, which only sees a portion of the full data set. The worker-level posterior samples are then combined to form a Monte Carlo approximation to the full posterior distribution based on the complete data set. We compare several methods of carrying out the combination, including a new method based on approximating worker-level simulations using a mixture of multivariate Gaussian distributions. We find that resampling and kernel density based methods break down after 10 or sometimes fewer dimensions, while the new mixture-based approach works well, but the necessary mixture models take too long to fit.