Abstract

Modern astronomical surveys increasingly rely on complex numerical simulators and machine-learning models to connect physical theories to observed data. Simulation-based inference methods, which often use neural networks to learn likelihoods, posteriors, or summary statistics directly from simulated and/or observed data, have made it possible to analyze problems whose likelihoods are intractable. However, the resulting uncertainty estimates are often poorly calibrated, particularly when the learned models are imperfect or when the simulations differ from real observations (domain shift).

In this talk, I will discuss recent work, in collaboration with Ann Lee's group at CMU, on constructing Bayesian-style inferences that retain frequentist guarantees even when the underlying machine-learning components are approximate. This will include a confidence-distribution-based framework that produces confidence sets with valid coverage from learned models, as well as extensions of conformal prediction that account for heteroscedastic uncertainties common in scientific data. I will try to illustrate these methods with applications to stellar and galaxy surveys, as well as with state-of-the-art tabular foundation models.

Work done in collaboration with: James Carzon, Joshua D. Ingram, Ann B. Lee, Leo Watson, Radu Craiu, Ricardo Baptista, and Biprateep Dey, along with Luca Masserano, Alex Shen, Antonio Carlos Herling Ribeiro Junior, Tommaso Dorigo, Michele Doro, and Rafael Izbicki.