# Accelerated Parameter Estimation with DALE$\chi$

## TL;DR

DALEχ is a novel method for efficiently estimating confidence contours in high-dimensional, computationally expensive likelihood problems, outperforming nested sampling in evaluation efficiency.

## Contribution

Introduces DALEχ, a new algorithm that accelerates confidence contour estimation by targeting points on the confidence limit far from previous samples.

## Key findings

- DALEχ finds the same confidence limits as MultiNest with fewer likelihood evaluations.
- DALEχ is effective in high-dimensional, non-Gaussian, and non-linear likelihood scenarios.
- The method is open-source and publicly available.

## 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.