Efficient Bayesian analysis of multiple changepoint models with dependence across segments

TL;DR

This paper introduces an efficient Bayesian online algorithm for analyzing multiple changepoint models with dependent parameters, enabling accurate inference of changepoint locations and curve discontinuities.

Contribution

It presents a novel Markov dependence-based approach and an efficient algorithm for Bayesian changepoint analysis with dependent segment parameters.

Findings

Approximation error is negligible in simulations.

Method outperforms existing techniques in curve inference.

Allows for inference of curve discontinuities.

Abstract

We consider Bayesian analysis of a class of multiple changepoint models. While there are a variety of efficient ways to analyse these models if the parameters associated with each segment are independent, there are few general approaches for models where the parameters are dependent. Under the assumption that the dependence is Markov, we propose an efficient online algorithm for sampling from an approximation to the posterior distribution of the number and position of the changepoints. In a simulation study, we show that the approximation introduced is negligible. We illustrate the power of our approach through fitting piecewise polynomial models to data, under a model which allows for either continuity or discontinuity of the underlying curve at each changepoint. This method is competitive with, or out-performs, other methods for inferring curves from noisy data; and uniquely it allows for inference of the locations of discontinuities in the underlying curve.