A Joint Bayesian Model for Change-Points and Heteroskedasticity Applied to the Canadian Longitudinal Study on Aging

Maintaining homeostasis, the regulation of internal physiological parameters, is essential for health and well-being. Deviations from optimal levels, or 'sweet spots,' can lead to health deterioration and disease. Identifying biomarkers with sweet spots requires both change-point detection and variance effect analysis. Traditional approaches involve separate tests for change-points and heteroskedasticity, which can yield inaccurate results if model assumptions are violated. To address these challenges, we propose a unified approach: Bayesian Testing for Heteroskedasticity and Sweet Spots (BTHS). This framework integrates sampling-based parameter estimation and Bayes factor computation to enhance change-point detection, heteroskedasticity quantification, and testing in change-point regression settings, and extends previous Bayesian approaches. BTHS eliminates the need for separate analyses and provides detailed insights into both the magnitude and shape of heteroskedasticity, enabling robust identification of sweet spots without strong assumptions. We applied BTHS to blood elements from the Canadian Longitudinal Study on Aging identifying nine blood elements with significant sweet spot variance effects.