1205.2708 (Scott F. Daniel et al.)

An Efficient Parameter Space Search as an Alternative to Markov Chain Monte Carlo    [PDF]

Scott F. Daniel, Andrew J. Connolly, Jeff Schneider

We consider the problem of inferring constraints on a high-dimensional parameter space with a computationally expensive likelihood function. Markov chain Monte Carlo (MCMC) methods offer significant improvements in efficiency over grid-based searches and are easy to implement in a wide range of cases. However, MCMCs offer few guarantees that all of the interesting regions of parameter space are explored. We propose a machine learning algorithm that improves upon the performance of MCMC by intelligently targeting likelihood evaluations so as to quickly and accurately characterize the likelihood surface in both low- and high-likelihood regions. We compare our algorithm to MCMC on toy examples and the 7-year WMAP cosmic microwave background data release. Our algorithm finds comparable parameter constraints to MCMC in fewer calls to the likelihood function and with greater certainty that all of the interesting regions of parameter space have been explored.

View original: http://arxiv.org/abs/1205.2708