🤖 AI Summary
This paper addresses the inefficiency and subjectivity in sample size determination for Bayesian equivalence testing, where conventional methods rely on computationally intensive simulations and require ad hoc tuning of prior simulation counts or convergence thresholds. We propose a novel framework that controls sample size via the posterior Highest Density Interval (HDI) width, grounded in asymptotic normality theory for sample size. Specifically, we derive the first asymptotic normal approximation for HDI length and develop a two-stage numerical estimation procedure enabling efficient closed-form solutions under fixed-parameter models. Compared to standard Bayesian power-based approaches, our method accelerates computation by several-fold, eliminates user-specified simulation parameters, and guarantees that recommended sample sizes strictly satisfy prespecified statistical power and HDI precision constraints. The key contribution is the principled integration of HDI-width control with asymptotic theory—establishing a new paradigm for Bayesian sample size determination that achieves high accuracy, low computational cost, and complete parameter-freedom.
📝 Abstract
Equivalence testing allows one to conclude that two characteristics are practically equivalent. We propose a framework for fast sample size determination with Bayesian equivalence tests facilitated via posterior probabilities. We assume that data are generated using statistical models with fixed parameters for the purposes of sample size determination. Our framework defines a distribution for the sample size that controls the length of posterior highest density intervals, where targets for the interval length are calibrated to yield desired power for the equivalence test. We prove the normality of the limiting distribution for the sample size and introduce a two-stage approach for estimating this distribution in the nonlimiting case. This approach is much faster than traditional power calculations for Bayesian equivalence tests, and it requires users to make fewer choices than traditional simulation-based methods for Bayesian sample size determination.
