Journal Article

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

B. Joachimi and A. N. Taylor

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 416, issue 2, pages 1010-1022
Published in print September 2011 | ISSN: 0035-8711
Published online September 2011 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.19107.x
Forecasts of non-Gaussian parameter spaces using Box–Cox transformations

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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 normalization 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 Gaussianized parameter space.

Keywords: gravitational lensing: weak; methods: analytical; methods: data analysis; methods: statistical; cosmological parameters

Journal Article.  8688 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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