Coverage is not enough: What SBI posteriors of f_NL are actually telling you

Abstract

Simulation-based inference (SBI) is increasingly used to extract cosmological information from complex observables, with reliability typically validated through coverage-based diagnostics such as simulation-based calibration (SBC) and the coverage test of accuracy with random points (TARP). These tests check whether posteriors contain the true parameter value with the expected frequency; a necessary condition for accuracy. However, coverage is insensitive to posterior shapes, so an estimator can pass such tests while exhibiting systematic tail biases or realization-level discrepancies that go undetected. In this talk I present our work where we systematically compare posteriors obtained through likelihood-based inference (LBI) and SBI with contrastive neural ratio estimation (CNRE) for constraining local primordial non-Gaussianity ($f_{\rm NL}^{\rm local}$) from dark matter halo statistics in the Quijote-PNG simulations. Using the power spectrum ($P$), bispectrum ($B$), and wavelet scattering transform (WST) coefficients, we compare posterior distributions across 1000 test realizations, examining higher-order moments, credible interval shapes, and tail behavior. We also use the Wasserstein-2 distance as a shape-sensitive diagnostic to capture discrepancies that aren't captured by other metrics. We show that the $P+B$ SBI posterior is systematically under-confident relative to that from LBI, a miscalibration invisible to standard diagnostics, demonstrating concretely that passing coverage tests does not guarantee posterior faithfulness. We also find that WST coefficients improve $f_{\rm NL}^{\rm local}$ constraints beyond $P+B$ even at large scales ($k_{\rm max} = 0.14\, h\, {\rm Mpc}^{-1}$), supporting field-level summaries as probes of primordial physics.