  Probabilistic models are conceptually powerful tools for finding structure in
data, but their practical effectiveness is often limited by our ability to
perform inference in them. Exact inference is frequently intractable, so
approximate inference is often performed using Markov chain Monte Carlo (MCMC).
To achieve the best possible results from MCMC, we want to efficiently simulate
many steps of a rapidly mixing Markov chain which leaves the target
distribution invariant. Of particular interest in this regard is how to take
advantage of multi-core computing to speed up MCMC-based inference, both to
improve mixing and to distribute the computational load. In this paper, we
present a parallelizable Markov chain Monte Carlo algorithm for efficiently
sampling from continuous probability distributions that can take advantage of
hundreds of cores. This method shares information between parallel Markov
chains to build a scale-mixture of Gaussians approximation to the density
function of the target distribution. We combine this approximation with a
recent method known as elliptical slice sampling to create a Markov chain with
no step-size parameters that can mix rapidly without requiring gradient or
curvature computations.
