Bayesian Retrospective Multiple‐Changepoint Identification

Changepoint identification is important in many data analysis problems, such as industrial control and medical diagnosis–given a data sequence, we wish to make inference about the location of one or more points of the sequence at which there is a change in the model or parameters driving the system. For long data sequences, however, analysis (especially in the multiple‐changepoint case) can become computationally prohibitive, and for complex non‐linear models analytical and conventional numerical techniques are infeasible. We discuss the use of a sampling‐based technique, the Gibbs sampler, in multiple‐changepoint problems and demonstrate how it can be used to reduce the computational load involved considerably. Also, often it is reasonable to presume that the data model itself is continuous with respect to time, i.e. continuous at the changepoints. This necessitates a continuous parameter representation of the changepoint problem, which also leads to computational difficulties. We demonstrate how inferences can be made readily in such problems by using the Gibbs sampler. We study three examples: A simple discrete two‐changepoint problem based on a binomial data model; a continuous switching linear regression problem; a continuous, non‐linear, multiple‐changepoint problem.