Determine the preferable convergence criterion for hierarchical likelihood inference

Determine which convergence criterion—effective sample size thresholds or log-likelihood variance thresholds—is preferable for reliable hierarchical Bayesian population inference when Monte Carlo estimators of the likelihood are noisy.

Background

The paper compares two approaches for controlling Monte Carlo uncertainty in hierarchical population inference: the authors’ effective-sample-size criterion, which penalizes regions with poorly sampled event or selection-function integrals, and the LVK analysis’s threshold on the variance of the log-likelihood estimator. Both methods are intended to prevent numerical inaccuracies from biasing posterior and evidence estimates, but their effects can differ for strongly parameterized population models.

The authors find that their independent implementation agrees closely with publicly released LVK results and that their posteriors lie between results obtained under two LVK variance thresholds. However, they do not establish which criterion is generally preferable, leaving unresolved the methodological question of how Monte Carlo convergence should be assessed in future population analyses.