Identifying regime switches through Bayesian wavelet estimation: application to environmental and genetic data

Two-component mixture models have proved powerful tools for modeling heterogeneity in various clustering scenarios. However, traditional models often assume constant mixture weights, which can be unsuitable for some applications. In this paper, we relax this assumption and allow the mixture weights to vary dynamically with the data index, making the model adaptable to diverse data sets. We introduce an efficient Gibbs sampling algorithm that jointly estimates the mixture component parameters and dynamic weights. We propose a wavelet-based version of data augmentation to assess the dynamic behavior of the mixture weights, exploiting the advantageous properties of wavelet bases in curve estimation. We validate the method through Monte Carlo simulations and real-world applications, including flood detection in a river in southern Brazil and the identification of chromosomal anomalies in DNA samples. The results align with existing findings, demonstrating the robustness of our method.