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Publication . Article . Preprint . 2016

Gaussianization for fast and accurate inference from cosmological data

Robert L. Schuhmann; Benjamin Joachimi; Hiranya V. Peiris;
Open Access  
Published: 01 Jun 2016 Journal: Monthly Notices of the Royal Astronomical Society, volume 459, pages 1,916-1,928 (issn: 0035-8711, eissn: 1365-2966, Copyright policy )
Publisher: Oxford University Press (OUP)
Country: United Kingdom
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 generalisations 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 MCMC 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 Gaussianising 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 Gaussianise the joint distribution of data from weak lensing and baryon acoustic oscillations (BAO), for different cosmological models, and find a preference for flat $\Lambda$CDM. 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.
Comment: 14 pages, 9 figures
Subjects by Vocabulary

Microsoft Academic Graph classification: Physics Gaussian symbols.namesake symbols Statistical physics Weak gravitational lensing Markov chain Kernel density estimation Joint probability distribution Marginal likelihood Posterior probability Markov chain Monte Carlo

Subjects

Space and Planetary Science, Astronomy and Astrophysics, Astrophysics - Cosmology and Nongalactic Astrophysics, Astrophysics - Instrumentation and Methods for Astrophysics

Planck Collaboration (Ade P.A.R. et al.), 2014, A&A, 571, A16 (arXiv:1311.1657) Planck Collaboration (Ade P.A.R. et al.), 2015, A&A, in press (arXiv:1502.01589) Sandvik H., Tegmark M., Wang X., Zaldarriaga M., 2004, Phys. Rev. D, 69, 063005 (arXiv:astro-ph/0311544v2) Silverman B.W., 1998, Density Estimation for Statistics and Data Analysis, London, Chapman & Hall/CRC Skilling J., 2006, Bayesian Analysis 1 no.4, 833-860 Velilla S., 1993, Statistics & Probability Letters 17, 259 Verde L., Feeney S.M., Mortlock D.J., Peiris H.V., 2013, JCAP09(2013)013 (arXiv:1307.2904)

Funded by
NSF| Programs on Critical Problems in Physics, Astrophysics and Biophysics at the Aspen Center for Physics
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1066293
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Physics
,
EC| COSMICDAWN
Project
COSMICDAWN
Understanding the Origin of Cosmic Structure
  • Funder: European Commission (EC)
  • Project Code: 306478
  • Funding stream: FP7 | SP2 | ERC
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Article . 2016
Providers: UCL Discovery