Computational solutions for Bayesian inference in dynamical systems

This thesis proposes Bayesian inference as a feasible and possibly, under some circumstances, preferable alternative to mainstream approaches in dynamic system identification such as prediction error and maximum likelihood methods. The advantages of the Bayesian approach are demonstrated through empirical study of linear time invariant system identification with short and noisy data record. Empirical evidence for the minimum mean square error property of the Bayesian estimator under practical finite data length scenarios is presented. Multiple methods for approximating the high dimensional integration associated with Bayesian inference are also thoroughly analysed. Specifically, the state–of–the–art in computational design is reviewed through the analysis of two families of Markov Chain Monte Carlo algorithms, among other Monte Carlo and conventional numerical integration methods. Many practical combinations and adaptations of these well researched Markov Chain Monte Carlo algorithms are also presented. Empirical evidence of geometric convergence rate O(1/M) of the square error in Markov Chain Monte Carlo integration is also given for dynamic system with up to 12 parameters