Bayesian variance change point detection with credible sets

TL;DR

This paper presents a Bayesian method for detecting variance change points in Gaussian data, providing uncertainty quantification and scalable inference, with applications in medical and oceanographic data analysis.

Contribution

It introduces a novel Bayesian framework that models multiple variance change points as a product of single changes, with a variational approximation for the posterior distribution.

Findings

The method accurately detects change points in simulations.

It quantifies uncertainty in change point locations.

Demonstrated effectiveness on liver viability and oceanographic data.

Abstract

This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a measure of uncertainty is necessary when change point methods are deployed in sensitive applications, for example, when one is interested in determining whether an organ is viable for transplant. The key of our proposal is framing the problem as a product of multiple single changes in the scale parameter. We fit the model through an iterative procedure similar to what is done for additive models. The novelty is that each iteration returns a probability distribution on time instances, which captures the uncertainty in the change point location. Leveraging a recent result in the literature, we can show that our proposal is a variational approximation of the exact model posterior distribution. We study the algorithm's convergence and the change point localization rate. Extensive experiments in simulation studies illustrate the performance of our method and the possibility of generalizing it to more complex data-generating mechanisms. We apply the new model to an experiment involving a novel technique to assess the viability of a liver and oceanographic data.