Adaptive online variance estimation in particle filters: the ALVar estimator

Abstract We present a new approach—the estimator—to estimation of asymptotic variance in sequential Monte Carlo methods, or, particle filters. The method, which adjusts adaptively the lag estimator proposed Olsson and Douc (Bernoulli 25(2):1504–1535) applies to very general distribution flows filters, including auxiliary filters with adaptive resampling. algorithm operates entirely online, sense that it is able monitor filter real time with, on average, constant computational complexity memory requirements per iteration. Crucially, does not require calibration any algorithmic parameter. Estimating only basis genealogy propagated cloud, without additional simulations, routine requires minor code additions underlying algorithm. Finally, we prove consistent for true as number particles tends infinity illustrate numerically its superiority existing approaches.