Bayesian Parameter Estimation

Abstract

Taking the Bayesian approach in solving the discrete-time parameter estimation problem has two major results: the unknown parameters are legitimately included as additional system states, and the computational objective becomes calculation of the entire posterior density instead of just its first few moments. This viewpoint facilitates intuitive analysis, allowing increased qualitative understanding of the system behavior. With the actual posterior density in hand, the true optimal estimate for any given loss function may be calculated. While the computational burden may preclude on-line use, this provides a clearly justified baseline for comparison. These points are demonstrated by analyzing a scalar problem with a single unknown, and by comparing an established point estimator's performance to the true optimal estimate.