Forecasts of non-Gaussian parameter spaces using Box-Cox transformations

TL;DR

This paper introduces a novel method combining Fisher matrix forecasts with Box-Cox transformations to accurately predict complex, non-Gaussian posterior shapes in astrophysical parameter estimation, especially for cosmological surveys.

Contribution

The paper proposes a new approach that applies Box-Cox transformations to parameter space, enabling Fisher matrix forecasts to handle non-Gaussian posteriors more accurately.

Findings

Successfully predicts non-Gaussian posterior features.

Reproduces non-linear degeneracies in cosmological parameters.

Enhances forecasting accuracy for future weak lensing surveys.

Abstract

Forecasts of statistical constraints on model parameters using the Fisher matrix abound in many fields of astrophysics. The Fisher matrix formalism involves the assumption of Gaussianity in parameter space and hence fails to predict complex features of posterior probability distributions. Combining the standard Fisher matrix with Box-Cox transformations, we propose a novel method that accurately predicts arbitrary posterior shapes. The Box-Cox transformations are applied to parameter space to render it approximately multivariate Gaussian, performing the Fisher matrix calculation on the transformed parameters. We demonstrate that, after the Box-Cox parameters have been determined from an initial likelihood evaluation, the method correctly predicts changes in the posterior when varying various parameters of the experimental setup and the data analysis, with marginally higher computational cost than a standard Fisher matrix calculation. We apply the Box-Cox-Fisher formalism to forecast cosmological parameter constraints by future weak gravitational lensing surveys. The characteristic non-linear degeneracy between matter density parameter and normalisation of matter density fluctuations is reproduced for several cases, and the capabilities of breaking this degeneracy by weak lensing three-point statistics is investigated. Possible applications of Box-Cox transformations of posterior distributions are discussed, including the prospects for performing statistical data analysis steps in the transformed Gaussianised parameter space.