Bayesian inference on change point problems

Abstract

Change point problems are referred to detect heterogeneity in temporal or spatial data. They have applications in many areas like DNA sequences, financial time series, signal processing, etc. A large number of techniques have been proposed to tackle the problems. One of the most difficult issues is estimating the number of the change points. As in other examples of model selection, the Bayesian approach is particularly appealing, since it automatically captures a trade off between model complexity (the number of change points) and model fit. It also allows one to express uncertainty about the number and location of change points. In a series of papers [13, 14, 16], Fearnhead developed efficient dynamic programming algorithms for exactly computing the posterior over the number and location of change points in one dimensional series. This improved upon earlier approaches, such as [12], which relied on reversible jump MCMC. We extend Fearnhead's algorithms to the case of multiple dimensional series. This allows us to detect changes on correlation structures, as well as changes on mean, variance, etc. We also model the correlation structures using Gaussian graphical models. This allow us to estimate the changing topology of dependencies among series, in addition to detecting change points. This is particularly useful in high dimensional cases because of sparsity.