Bayesian multiple changing-points detection

• Published in: AIMS mathematics Vol. 10; no. 3; pp. 4662 - 4708
• Main Authors: Kang, Sang Gil, Lee, Woo Dong, Kim, Yongku
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.03.2025
• Subjects: binary segmentation; change-points detection; model selection; piecewise polynomial signals
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2025216

This study investigated the application of Bayesian multiple change-point detection techniques in the context of piecewise polynomial signals. Given the limited number of existing methodologies for identifying change-points in such signals, we proposed an objective Bayesian change-point detection approach that accommodated heterogeneous error distributions. Our methodology was grounded in a piecewise polynomial regression framework and employed binary segmentation. Initially, we identified change-points across various signals using Bayesian binary segmentation. Subsequently, we applied Bayesian model selection to ascertain the most suitable polynomial order for the identified segments. This approach facilitated a change-point detection method that minimized reliance on subjective inputs. We incorporated intrinsic priors that allowed for the formulation of Bayes factors and model selection probabilities. To evaluate the efficacy of the proposed change-point detection techniques, we conducted a simulation study alongside two empirical case studies: one involving the Goddard Institute for space studies surface temperature analysis and the other concerning the daily closing stock prices of Samsung Electronics Co.