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Nuisance hardened data compression for fast likelihood-free inference
Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC). Flatiron Institute, USA; Imperial College London, UK.
Number of Authors: 22019 (English)In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 488, no 4, p. 5093-5103Article in journal (Refereed) Published
Abstract [en]

We show how nuisance parameter marginalized posteriors can be inferred directly from simulations in a likelihood-free setting, without having to jointly infer the higher dimensional interesting and nuisance parameter posterior first and marginalize a posteriori. The result is that for an inference task with a given number of interesting parameters, the number of simulations required to perform likelihood-free inference can be kept (roughly) the same irrespective of the number of additional nuisances to be marginalized over. To achieve this, we introduce two extensions to the standard likelihood-free inference set-up. First, we show how nuisance parameters can be recast as latent variables and hence automatically marginalized over in the likelihood-free framework. Secondly, we derive an asymptotically optimal compression from N data to n summaries - one per interesting parameter - such that the Fisher information is (asymptotically) preserved, but the summaries are insensitive to the nuisance parameters. This means that the nuisance marginalized inference task involves learning n interesting parameters from n nuisance hardened' data summaries, regardless of the presence or number of additional nuisance parameters to be marginalized over. We validate our approach on two examples from cosmology: supernovae and weak-lensing data analyses with nuisance parametrized systematics. For the supernova problem, high-fidelity posterior inference of Omega(m) and w(0) (marginalized over systematics) can be obtained from just a few hundred data simulations. For the weak-lensing problem, six cosmological parameters can be inferred from just simulations, irrespective of whether 10 additional nuisance parameters are included in the problem or not.

Place, publisher, year, edition, pages
2019. Vol. 488, no 4, p. 5093-5103
Keywords [en]
methods: data analysis
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-175035DOI: 10.1093/mnras/stz1900ISI: 000484349700052OAI: oai:DiVA.org:su-175035DiVA, id: diva2:1366741
Available from: 2019-10-30 Created: 2019-10-30 Last updated: 2019-10-30Bibliographically approved

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