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arXiv · 1705.02007

Accelerated Parameter Estimation with DALE$\chi$

Scott F. Daniel·Eric V. Linder
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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 contours for accurate error estimation. We employ DALE$\chi$ (Direct Analysis of Limits via the Exterior of $\chi^2$) 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 DALE$\chi$ 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 $\chi^2$. We find that in high-dimensional cases DALE$\chi$ finds the same confidence limit as MultiNest using roughly an order of magnitude fewer evaluations of the likelihood function. DALE$\chi$ is open-source and available at https://github.com/danielsf/Dalex.git.

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Scott F. Daniel, Eric V. Linder. 2017-05-02. Accelerated Parameter Estimation with DALE$\chi$. https://arxiv.org/abs/1705.02007

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