Determining Frequentist Confidence Limits Using a Directed Parameter
  Space Search
  We consider the problem of inferring constraints on a high-dimensional
parameter space with a computationally expensive likelihood function. We
propose a machine learning algorithm that maps out the Frequentist confidence
limit on parameter space 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 Bayesian credible
limits derived by the well-tested Markov Chain Monte Carlo (MCMC) algorithm
using both multi-modal toy likelihood functions and the 7-year WMAP cosmic
microwave background likelihood function. We find that our algorithm correctly
identifies the location, general size, and general shape of high-likelihood
regions in parameter space while being more robust against multi-modality than
MCMC.
