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Simulation-based inference has its own Dodelson-Schneider effect (but it knows that it does)

J Homer, O Friedrich, D Gruen - arXiv preprint arXiv:2412.02311, 2024 - arxiv.org
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… For non-Gaussian likelihoods, an approximation may be derived via Simulation-Based Inference (SBI). It is often implicitly assumed that parameter constraints from SBI …

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BibTeX

@article{2412.02311v1,
Author        = {Jed Homer and Oliver Friedrich and Daniel Gruen},
Title         = {Simulation-based inference has its own Dodelson-Schneider effect (but it
  knows that it does)},
Eprint        = {2412.02311v1},
DOI           = {10.1051/0004-6361/202453339},
ArchivePrefix = {arXiv},
PrimaryClass  = {astro-ph.CO},
Abstract      = {Making inferences about physical properties of the Universe requires
knowledge of the data likelihood. A Gaussian distribution is commonly assumed
for the uncertainties with a covariance matrix estimated from a set of
simulations. The noise in such covariance estimates causes two problems: it
distorts the width of the parameter contours, and it adds scatter to the
location of those contours which is not captured by the widths themselves. 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, which do not use covariance matrices, 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. We use Neural Posterior and
Likelihood Estimation with continuous and masked autoregressive normalizing
flows for density estimation. We fit our approximate posterior models to
simulations drawn from a Gaussian linear model, so that the SBI result can be
compared to the true posterior. We test linear and neural network based
compression, demonstrating that neither methods circumvent the issues of
covariance estimation. 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. The limitations of traditional
likelihood analysis with simulation-based covariance remain for SBI with a
finite simulation budget. Despite these issues, we show that SBI correctly
draws the true posterior contour given enough simulations.},
Year          = {2024},
Month         = {Dec},
Note          = {A&A 699, A213 (2025)},
Url           = {http://arxiv.org/abs/2412.02311v1},
File          = {2412.02311v1.pdf}
}

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