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Regression models, which typically model the relationship between variables or provide prediction, are very important tools in data science and machine learning! Regression with Multiple Change Points (or switch points, break points, broken) is often called segmented regression and has a wide application, in particular, when the independent variables cluster into different groups or exhibit different relationships between the variables in these regions. The boundaries between the segments are change points, which are often unknown in practice. Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.

This project aims to develop different algorithms, efficient algorithms under Bayesian inference for those regression problems, including unknown number of change-point estimation, prior selection, likelihood structure and posterior inference, high-dimensional data analysis and modern variable selection, model misspecification and robust inference and test, segment trees under Machine Learning.