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Gaussianization for fast and accurate inference from cosmological data

Joachimi, B; Schuhmann, RL; Peiris, HV; (2016) Gaussianization for fast and accurate inference from cosmological data. Monthly Notices of the Royal Astronomical Society (MNRAS) , 459 (2) pp. 1916-1928. 10.1093/mnras/stw738. Green open access

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Abstract

We present a method to transform multivariate unimodal non-Gaussian posterior probability densities into approximately Gaussian ones via non-linear mappings, such as Box–Cox transformations and generalizations thereof. This permits an analytical reconstruction of the posterior from a point sample, like a Markov chain, and simplifies the subsequent joint analysis with other experiments. This way, a multivariate posterior density can be reported efficiently, by compressing the information contained in Markov Chain Monte Carlo samples. Further, the model evidence integral (i.e. the marginal likelihood) can be computed analytically. This method is analogous to the search for normal parameters in the cosmic microwave background, but is more general. The search for the optimally Gaussianizing transformation is performed computationally through a maximum-likelihood formalism; its quality can be judged by how well the credible regions of the posterior are reproduced. We demonstrate that our method outperforms kernel density estimates in this objective. Further, we select marginal posterior samples from Planck data with several distinct strongly non-Gaussian features, and verify the reproduction of the marginal contours. To demonstrate evidence computation, we Gaussianize the joint distribution of data from weak lensing and baryon acoustic oscillations, for different cosmological models, and find a preference for flat Λcold dark matter. Comparing to values computed with the Savage–Dickey density ratio, and Population Monte Carlo, we find good agreement of our method within the spread of the other two.

Type: Article
Title: Gaussianization for fast and accurate inference from cosmological data
Open access status: An open access version is available from UCL Discovery
DOI: 10.1093/mnras/stw738
Publisher version: http://dx.doi.org/10.1093/mnras/stw738
Additional information: This is a pre-copyedited, author-produced PDF of an article accepted for publication in Monthly Notices of the Royal Astronomical Society (MNRAS following peer review. The version of record Joachimi, B; Schuhmann, RL; Peiris, HV; (2016) Gaussianization for fast and accurate inference from cosmological data. Monthly Notices of the Royal Astronomical Society (MNRAS), 459 (2) pp. 1916-1928. 10.1093/mnras/stw738 is available online at: http://dx.doi.org/10.1093/mnras/stw738
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
URI: https://discovery-pp.ucl.ac.uk/id/eprint/1498778
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