State Space Modeling & Bayesian Inference with Computational Intelligence

Abstract

Recursive Bayesian estimation using sequential Monte Carlos methods is a powerful numerical technique to understand latent dynamics of nonlinear non-Gaussian dynamical systems. It enables us to reason under uncertainty and addresses shortcomings underlying deterministic systems and control theories which do not provide sufficient means of performing analysis and design. In addition, parametric techniques such as the Kalman filter and its extensions, though they are computationally efficient, do not reliably compute states and cannot be used to learn stochastic problems. We review recursive Bayesian estimation using sequential Monte Carlo methods highlighting open problems. Primary of these is the weight degeneracy and sample impoverishment problem. We proceed to detail synergistic computational intelligence sequential Monte Carlo methods which address this. We find that imbuing sequential Monte Carlos with computational intelligence has many advantages when applied to many application and problem domains.