Integral estimation based on Markovian design

Abstract

AbstractSuppose that a mobile sensor describes a Markovian trajectory in the ambient space and at each time the sensor measures an attribute of interest, e.g. the temperature. Using only the location history of the sensor and the associated measurements, we estimate the average value of the attribute over the space. In contrast to classical probabilistic integration methods, e.g. Monte Carlo, the proposed approach does not require any knowledge of the distribution of the sensor trajectory. We establish probabilistic bounds on the convergence rates of the estimator. These rates are better than the traditional `rootn'-rate, wherenis the sample size, attached to other probabilistic integration methods. For finite sample sizes, we demonstrate the favorable behavior of the procedure through simulations and consider an application to the evaluation of the average temperature of oceans.