Partition function approach to non-Gaussian likelihoods

• Verfasst von: Röver, Lennart [VerfasserIn]
• Verfasst von: Bartels, Lea Carlotta [VerfasserIn]
• Verfasst von: Schäfer, Björn Malte [VerfasserIn]
• Titel: Partition function approach to non-Gaussian likelihoods
• Titelzusatz: formalism and expansions for weakly non-Gaussian cosmological inference
• Verf.angabe: Lennart Röver, Lea Carlotta Bartels and Björn Malte Schäfer
• E-Jahr: 2023
• Jahr: 2023 May 16
• Umfang: 12 S.
• Fussnoten: Gesehen am 16.08.2023
• Titel Quelle: Enthalten in: Royal Astronomical SocietyMonthly notices of the Royal Astronomical Society
• Ort Quelle: Oxford : Oxford Univ. Press, 1827
• Jahr Quelle: 2023
• Band/Heft Quelle: 523(2023), 2 vom: Aug., Seite 2027-2038
• ISSN Quelle: 1365-2966
• DOI: doi:10.1093/mnras/stad1471
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1856312429

Abstract

Non-Gaussian likelihoods, ubiquitous throughout cosmology, are a direct consequence of non-linearities in the physical model. Their treatment requires Monte Carlo Markov chain (MCMC) or more advanced sampling methods for the determination of confidence contours. As an alternative, we construct canonical partition functions as Laplace transforms of the Bayesian evidence, from which MCMC methods would sample microstates. Cumulants of order n of the posterior distribution follow by direct n-fold differentiation of the logarithmic partition function, recovering the classic Fisher-matrix formalism at second order. We connect this approach for weakly non-Gaussianities to the DALI and Gram−Charlier expansions and demonstrate the validity with a supernova-likelihood on the cosmological parameters Ωm and w. We comment on extensions of the canonical partition function to include kinetic energies in order to bridge to Hamilton Monte Carlo sampling, and on ensemble Markov-chain methods, as they would result from transitioning to macrocanonical partition functions depending on a chemical potential. Lastly we demonstrate the relationship of the partition function approach to the Cramér−Rao boundary and to information entropies.