Bayesian system identification of dynamical systems using large sets of training data: A MCMC solution. (October 2015) - Green, P.L.
Abstract: In the last 20 years the applicability of Bayesian inference to the system identification of structurally dynamical systems has been helped considerably by the emergence of Markov chain Monte Carlo (MCMC) algorithms – stochastic simulation methods which alleviate the need to evaluate the intractable integrals which often arise during Bayesian analysis. In this paper specific attention is given to the situation where, with the aim of performing Bayesian system identification, one is presented with very large sets of training data. Building on previous work by the author, an MCMC algorithm is presented which, through combing Data Annealing with the concept of 'highly informative training data', can be used to analyse large sets of data in a computationally cheap manner. The new algorithm is called Smooth Data Annealing. Highlights: This paper is motivated by the situation where, with the aim of performing Bayesian system identification, one is presented with a large set of training data. A novel Markov chain Monte Carlo algorithm called Smooth Data Annealing (SDA) is proposed. SDA is able to 'absorb' training data in a smooth and continuous manner until certain criteria, such as the mean of the posterior parameter estimates, are judged to have converged. SDA saves time by quickly absorbing data which has little effect on the information content of the posterior parameter distribution (allowing it to focus on 'information rich' subsets of the training data).