Online Bayesian Model Selection Using the Extended Kalman

Bayesian model selection involves solving for an intractable integral, which is often approximated using Laplace’s asymptotic approximation. However, this can result in inaccurate and biased results when the sample size is small. In this work, we propose an alternative method for model selection that bypasses this integral by using the probability density functions of the prior, likelihood, and posterior distributions. The effectiveness of the proposed approach is demonstrated through a spring-mass-damper example, where the Extended Kalman Filter is used for parameter estimation and the proposed model selection algorithm is used for online model selection. Our approach has the potential to improve the performance of control systems by providing a more accurate and parsimonious model for design and prediction.