Evolution Strategies for Cosmology: A Comparison of Nested Sampling Methods

TL;DR

This paper introduces ESNested, a new nested sampling algorithm using Evolution Strategies for cosmological likelihood analysis, demonstrating improved maximum likelihood detection and evidence estimation compared to existing methods.

Contribution

The paper presents a novel nested sampling algorithm, ESNested, that employs Evolution Strategies, offering advantages in finding maxima and estimating Bayesian evidence without prior shape assumptions.

Findings

ESNested finds higher maximum likelihood than other methods.

Performance varies among algorithms for different tasks.

Multiple methods are recommended for comprehensive analysis.

Abstract

Here we present an investigation into using nested sampling algorithms in cosmological likelihood analysis. We present a new nested sampling algorithm, ESNested, that uses Evolution Strategies for sample proposals. This quickly finds the maximum for complex likelihoods and provides an accurate measure of the Bayesian evidence, with no prior assumptions about the shape of the likelihood surface. We present the first cosmological constraints using Evolution Strategies, from WMAP 7, HST and SNIa data using likelihood and data provided with CosmoMC. We find a significantly higher maximum likelihood than that found with other methods. We compare the performance of ESNested with the publicly available MultiNest and CosmoNest algorithms, in i) finding the maximum likelihood ii) calculating confidence contours in projected parameter spaces and iii) calculating the Bayesian evidence. We find that none of the algorithms provide a single solution for all of these products in general. Our recommendation is that multiple sampling methods should be used in cosmological likelihood analysis and that algorithms should be tailored to perform optimally for each of these requirements. These results have a resonance with the well-known No Free Lunch theorem.