Göttingen 2025 – scientific programme
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GR: Fachverband Gravitation und Relativitätstheorie
GR 10: Cosmo II
GR 10.4: Talk
Thursday, April 3, 2025, 14:55–15:15, ZHG008
Simulation-based inference has its own Dodelson-Schneider effect (but it knows that it does) — •Jed Homer1, 2, Oliver Friedrich1,2,3, and Daniel Gruen1,2,3 — 1University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81677 Munich, Germany — 2Munich Center for Machine Learning (MCML) — 3Excellence Cluster ORIGINS, Boltzmannstr. 2, 85748 Garching, Deutschland.
Making inferences about physical properties of the Universe requires knowledge of the data likelihood. A Gaussian distribution is commonly assumed with a covariance matrix estimated from a set of simulations. The noise in such estimates causes two problems: it distorts the parameter contours, and it adds scatter to the location of those contours. For non-Gaussian likelihoods, an approximation may be derived via Simulation-Based Inference (SBI). It is often implicitly assumed that parameter constraints from SBI analyses are not affected by the same problems as parameter estimation, with a covariance matrix estimated from simulations. We investigate whether SBI suffers from effects similar to those of covariance estimation in Gaussian likelihoods. SBI suffers an inflation of posterior variance that is equal or greater than the analytical result in covariance estimation for Gaussian likelihoods for the same number of simulations. The assumption that SBI requires a smaller number of simulations than covariance estimation for a Gaussian likelihood analysis is inaccurate. Despite these issues, we show that SBI correctly draws the true posterior contour given enough simulations.
Keywords: Machine learning; Simulation-based inference; Astrostatistics; Likelihood-free inference