Control variates for multivariate truncated probability density functions with application in system identification

Monte Carlo methods are useful for computing numerical approximations of expected values, especially when these expectations cannot be computed analytically. Nevertheless, these methods depend on random sampling. The accuracy of the numerical approximation depends on the number of samples used and convergence to the true value can be slow. Control variates provide a way to use the samples more efficiently and reduce the variance of the sample mean estimator. This poster considers the computation of control variates for multivariate truncated probability density functions and its application in hyperparameter estimation for regularized impulse response identification of Lebesgue-sampled systems. The use of control variates in this application reduces the computational cost of an expensive step in each iteration of the expectation-maximization (EM) algorithm.