This chapter overviews some of the work on detecting and estimating the location of a single change. We first consider the most common change-point problem, namely that of detecting a change in mean, before looking at extensions to detecting other types of change. The intuition from the problem of detecting a single change-point is helpful for understanding the variety of methods for detecting multiple changes.
This is a draft chapter from the forthcoming book "Change-Point Detection and Data Segmentation" by Paul Fearnhead and Piotr Fryzlewicz. Comments, particularly regarding the history of work in this area, are welcome