Bayesian framework for curve alignment and change point detection applied to marine sediment core data

Abstract

Paleoclimate proxy records such as marine sediment cores are crucial for understanding past climate conditions. The deposition rate for these archives may vary dramatically both within individual cores and between them, obfuscating the temporal expression of events. Accurate alignment of cores is therefore critical for determining extent and rate of past climate change. Current methods are performed manually and rely on expert judgment of shared characteristics between cores. This approach is time intensive, subjective and lack former uncertainty quantification. This thesis presents a novel probabilistic framework that aligns time series data and detects key points of interest using state-of-the-art change point detection methods, while propagating the uncertainty to the results. The developed pipeline aligns the curves using Bayesian curve registration, capturing the distribution of possible alignments, and then applies Bayesian change point detection to identify significant features within the distribution. This approach was tested on magnetic susceptibility records from marine sediment cores. The results demonstrated the method's ability to reflect uncertainty in both alignment and feature detection. However, sensitivity to noise and additional model limitations reduce the reliability of the curve registration component. Overall, the findings demonstrate the potential of this probabilistic method to improve transparency in time series analysis, though further development is needed before it can be applied in real-world scenarios.