Query Efficient Posterior Estimation in Scientific Experiments via Bayesian Active Learning

A common problem in disciplines of applied Statistics research such as Astrostatistics is of estimating the posterior distribution of relevant parameters. Typically, the likelihoods for such models are computed via expensive experiments such as cosmological simulations of the universe. An urgent challenge in these research domains is to develop methods that can estimate the posterior with few likelihood evaluations. In this paper, we study active posterior estimation in a Bayesian setting when the likelihood is expensive to evaluate. Existing techniques for posterior estimation are based on generating samples representative of the posterior. Such methods do not consider efficiency in terms of likelihood evaluations. In order to be query efficient we treat posterior estimation in an active regression framework. We propose two myopic query strategies to choose where to evaluate the likelihood and implement them using Gaussian processes. Via experiments on a series of synthetic and real examples we demonstrate that our approach is significantly more query efficient than existing techniques and other heuristics for posterior estimation.