A Bayesian approach to change point analysis of discrete time series
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In this work we consider time series with a finite number of discrete point changes. We assume that the data in each segment follows a different probability density functions (pdf). We focus on the case where the data in all segments are modeled by Gaussian probability density functions with different means, variances and correlation lengths. We put a prior law on the change point instances (Poisson process) as well as on these different parameters(conjugate priors) and give the expression of the posterior probality distributions of these change points. The computations are done by using an appropriate Markov Chain Monte Carlo (MCMC) technique.
The problem as we stated can also be considered as an unsupervised classification and/or segmentation of the time serie. This analogy gives us the possibility to propose alternative modeling and computation of change points, which are more appropriate for multivariate signals, for example in image processing.