Bayesian Variance Change Point Detection With Credible Sets.

Area of Science:

• Statistics
• Bayesian inference
• Time series analysis

Background:

• Detecting changes in statistical properties of data sequences is crucial in many scientific fields.
• Existing methods for variance change detection often lack robust uncertainty quantification for change point locations.

Purpose of the Study:

• To introduce a novel Bayesian approach for detecting changes in variance within Gaussian sequence models.
• To quantify uncertainty in change point locations and provide a scalable inference algorithm.
• To frame the problem as a product of multiple scale parameter changes.

Main Methods:

• A Bayesian approach is proposed, framing variance change detection as a product of single scale changes.
• An iterative fitting procedure, analogous to additive models, is employed.
• Each iteration yields a probability distribution over time instances, capturing change point location uncertainty.
• The method is shown to be a variational approximation of the exact model posterior distribution.

Main Results:

• The proposed algorithm demonstrates convergence and provides a change point localization rate.
• Extensive simulations validate the method's performance.
• Successful application to biological data showcases practical utility.

Conclusions:

• The novel Bayesian approach effectively detects variance changes in Gaussian sequences.
• The method provides robust uncertainty quantification for change point locations.
• The scalable algorithm is suitable for both simulated and real-world data analysis, including biological applications.