Accelerated Parameter Estimation with DALE X

Abstract

We consider methods for improving the estimation of constraints on a high-dimensional parameter space with a computationally expensive likelihood function. In such cases Markov chain Monte Carlo (MCMC) can take a long time to converge and concentrates on finding the maxima rather than the often-desired confidence con-tours for accurate error estimation. We employ DALEχ(Direct Analysis of Limits via the Exterior ofχ2) for determining confidence contours by minimizing a cost function parametrized to incentivize points in parameter space which are both on the confidence limit and far from previously sampled points. We compare DALEχ to the nested sampling algorithm implemented in MultiNest on a toy likelihood function that is highly non-Gaussian and non-linear in the mapping between parameter values and χ2. We find that in high-dimensional cases DALEχfinds the same confidence limit as Multi-Nest using roughly an order of magnitude fewer evaluations of the likelihood function.DALE χ is open-source and available athttps://github.com/danielsf/Dalex.git.