Change Point Detection Using Bayesian Adaptive LASSO Quantile Regression

Statistical inference can be adversely impacted by abrupt changes or ‘change points’ in data series, such as those found in climate change analysis. Therefore, recognizing these change points is crucial to ensure accurate and reliable analysis. In this paper, we propose a novel Bayesian adaptive LASSO quantile regression (QR) model to robustly detect and locate change points in univariate data series exhibiting a simple linear trend. The model incorporates an asymmetric Laplace distribution (ALD) for the model error and independent Laplace priors on the regression coefficients. The paper presents an efficient Markov chain Monte Carlo (MCMC) sampling algorithm that takes advantage of the mixture representations of the ALD and Laplace distributions to draw samples from the joint posterior distribution of the unknown parameters. Numerical studies demonstrate that our approach delivers robust and accurate detection for multiple change points, as evidenced by high true detection rates and low false discovery rates in scenarios of varying sample sizes, error distributions, and change points’ locations and jump sizes. The effectiveness of the proposed methodology is showcased through carefully designed simulation studies and two real-data applications, where our results exhibit favorable comparisons to those of an existing frequentist procedure. Thus, our proposed method offers a comprehensive solution for accurate change point analysis, further improving the reliability and applications of QR-based change point detection processes.