Exact posterior distributions over the segmentation space and model selection for multiple change-point detection problems

TL;DR

This paper develops exact Bayesian formulas for change-point detection and model selection in segmentation problems, enabling precise inference over the entire segmentation space with practical applications demonstrated on simulated and genomic data.

Contribution

It introduces explicit, non-asymptotic Bayesian posterior formulas for change-point inference and a new model selection criterion, improving accuracy and reliability in segmentation analysis.

Findings

Exact posterior distributions derived for change-point models

A new criterion for model selection that assesses result reliability

Method demonstrated effectively on simulated and genomic data

Abstract

In segmentation problems, inference on change-point position and model selection are two difficult issues due to the discrete nature of change-points. In a Bayesian context, we derive exact, non-asymptotic, explicit and tractable formulae for the posterior distribution of variables such as the number of change-points or their positions. We also derive a new selection criterion that accounts for the reliability of the results. All these results are based on an efficient strategy to explore the whole segmentation space, which is very large. We illustrate our methodology on both simulated data and a comparative genomic hybridisation profile.