2017/05/02 by Scott F. Daniel, Daniel, Scott F., Eric V. Linder +1
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1705.02007
openalex publication_date 2017/05/02 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
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 DALEχ (Direct Analysis of Limits via the Exterior of χ2) 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 DALEχ finds the same confidence limit as MultiNest using roughly an order of magnitude fewer evaluations of the likelihood function. DALEχ is open-source and available at https://github.com/danielsf/Dalex.git.