Abstract

Prediction-powered inference (PPI) combines abundant machine predictions with scarce human labels to estimate population quantities. We study binary prevalence estimation using a thresholded autorater decision $A$ and human label $H$, with target $g=P(H=1)=P(A=1)P(H=1\mid A=1)+P(A=0)P(H=1\mid A=0)$. Under independent Beta priors and Bernoulli likelihoods, the chain-rule estimator (CRE) has a posterior that factorizes into three independent Beta distributions; uncertainty for $g$ is propagated by direct sampling without MCMC. This is a focused conjugate specialization of broader Bayesian PPI, providing an interpretable posterior for the binary audit table. We compare CRE with labeled-only Bayes, a binary difference estimator, continuous-score PPI, and a scalar PPI++-style power-tuned baseline. Experiments use subject-level out-of-fold predictions from ADNI MRI data. In the full cohort ($2116$ scans, $503$ subjects), Uniform-prior CRE has empirical 95\% coverage of $0.944$--$0.970$ across label budgets $n=10,20,40,80$; the age 65--70 subset ($291$ scans, $93$ subjects) is conservative, with coverage $0.978$--$0.986$. Jeffreys-prior sensitivity yields coverage $0.930$--$0.960$ and $0.936$--$0.988$, respectively, including mild empirical undercoverage in three configurations. CRE is competitive with the continuous-score baselines, without a claim of universal dominance. Threshold audits, age-stratified discrimination, exchangeability diagnostics, conjugate K-bin sensitivity, and simulation-based calibration delimit the method's scope. The repeated-labeling study targets the assembled scan population and does not provide a cluster-robust subject-level coverage guarantee.