A1055
Title: Statistical properties of initial sequence type variance estimators for reversible Markov chains
Authors: Hyebin Song - The Pennsylvania State University (United States) [presenting]
Abstract: Initial sequence estimators, originally introduced by a prior study, are commonly used to estimate Monte Carlo standard errors in reversible Markov chain Monte Carlo chains. In particular, the initial positive sequence estimator utilizes the property that the sums of adjacent autocovariances are non-negative, summing autocovariances up to the point where this non-negativity condition is violated. While this estimator has been widely used and adapted to different settings, only its asymptotic conservativeness has been shown, while consistency remains an open question. This gap is addressed by investigating the statistical properties of the initial positive sequence estimator. The convergence behavior of its random truncation point is first studied. An alternative initial sequence-type estimator is also proposed based on a modified truncation rule. For both estimators, consistency is established, and bounds are derived on rates of convergence. Finally, through empirical studies using both simulated and real-world data, the theoretical findings are validated, and the empirical performance of the two initial sequence-type estimators is compared with the standard overlapping batch mean estimator.
