Anytime-valid simulation-based hypothesis testing

תקציר מקורי באנגליתarXiv:2610.08210v1 Announce Type: cross Abstract: For a given data distribution $(X_t)_{t \in \mathbb{N}} \sim Q$ i.i.d., we investigate the hypothesis testing problem: $H_0: Q = P_0$ vs. $H_1: Q = P_1$, for two different model probability distributions $P_0$ and $P_1$. In contrast to the standard setting, where analytic densities $p_0$ and $p_1$ are given, here, we consider the density-free setting, where we only have access to i.i.d. simulations $(Z^0_t)_{t \in \mathbb{N}} \sim P_0$ and $(Z^1_t)_{t \in \mathbb{N}} \sim P_1$. For this simulation-based hypothesis testing setting, we construct an e-test martingale, resulting in a sequential test with anytime-valid type-I error guarantees, approximate growth optimality, geometrically decaying type-II error bounds, and asymptotic power one. M