Predictive Distributions as a Data-Driven Indicator for Phase-Pick Confidence

ABSTRACT Reliable measures of phase-pick confidence are essential for using neural-network phase pickers in automated seismic monitoring and catalog construction. Using the Pacific Northwest Seismic Network data set, we show that the spread of predicted probability mass functions (PMFs) tracks relative picking difficulty even when models are trained only with one-hot arrival-time labels, which assign probability one to the catalog pick time and zero to all other times, and without explicit quality information. Controlled label-perturbation experiments indicate that the predictive distributions inherit both systematic bias and label variability from the training targets, allowing probabilistic structure to emerge under deterministic supervision. We also find that disagreement across separately trained models increases for more difficult samples but can be substantially reduced by training on ensemble-averaged soft labels. PMF interquartile range follows the expected ordering of analyst-assigned quality tiers more consistently than either signal-to-noise ratio or a simple magnitude–distance metric, whereas its modest correlations with these measures indicate that it provides complementary information about picking difficulty. Together, these results show that PMF-derived measures such as interquartile range provide data-driven, reproducible indicators of picking difficulty, with practical value for both seismic monitoring and retrospective catalog construction.