Bayesian inference of stochastic pursuit models from basketball tracking data

Abstract

We develop a Metropolis algorithm to perform Bayesian inference for models given by coupled stochastic differential equations. A key challenge in developing practical algorithms is the computation of the likelihood. We address this problem through the use of a fast method to track the probability density function of the stochastic differential equation. The method applies quadrature to the Chapman– Kolmogorov equation associated with a temporal discretization of the stochastic differential equation. The inference method can be adapted to scenarios in which we have multiple observations at one time, multiple time series, or observations with large and/or irregular temporal spacing. Computational tests show that the resulting Metropolis algorithm is capable of efficient inference for an electrical oscillator model.