Accelerating Pseudo-Marginal MCMC using Gaussian Processes

Pseudo-marginal methods such as the grouped independence Metropolis-Hastings (GIMH) and Markov chain within Metropolis (MCWM) algorithms have been introduced in the literature as an approach to perform Bayesian inference in latent variable models. These methods replace intractable likelihood calculations with unbiased estimates within Markov chain Monte Carlo algorithms. The GIMH method has the posterior of interest as its limiting distribution, but suffers from poor mixing if it is too computationally intensive to obtain high-precision likelihood estimates. The MCWM algorithm has better mixing properties, but less theoretical support. In this paper we propose to use Gaussian processes (GP) to accelerate the GIMH method, whilst using a short pilot run of MCWM to train the GP. Our new method, GP-GIMH, is illustrated on simulated data from a stochastic volatility and a gene network model.

Low-impact Use: A New Standard

Once the ugly duckling of the lighting world, the fluorescent bulb recently has become something of an eco-darling thanks to its energy efficiency. Whereas a standard off-the-shelf incandescent bulb devotes only about five percent of its total electrical consumption to produce visible light (the remainder is released in heat), fluorescent lighting employs an entirely different process (it radiates rather than burns) that is four to six times more efficient. Fluorescents are indisputably superior in ­performance, but up to 5 milligrams of mercury, a hazardous trace metal, is included in the manufacture of each lamp