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I am interested in learning about the fundamentals of on-line change point detection. I am specifically not interested in the Bayesian methods.

The only solid resource / review / survey I could find for on-line methods was the book Sequential Analysis: Hypothesis Testing and Changepoint Detection by Tartakovsky, Nikiforov, and Basseville but it is very advanced. Are there any other resources out there for someone getting into this line of research at an early grad level?

An example for what I am looking for, this paper that surveys offline methods is amazingly clear and beginner friendly.

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I found Chapter 2 of Dean Bodenham's PhD Thesis to be a good introduction to the subject.

One of the measures defined therein is the CUSUM process, which gives a sequence $S_0, S_1, \dots$ that becomes very large when the sequence $x_1, x_{2}, \dots$ is consistently exceeding the mean $\mu$ (taking into account the variance of the sequence $\sigma^2$). There is a different definition for the CUSUM that is more useful than the one given in Section 2.1.4 (Bodenham uses this definition in a different paper): $$S_0 = 0,$$ $$S_j = \max(0, S_{j-1} + (x_j - \mu) / \sigma - k), \ \ \ \ j = \{1,2,\dots\}.$$ You would declare that a change has occurred once the process $S_t$ exceeds some threshold $h$. In the paper I mentioned, Bodenham sets $S_0 = \mu$, which I think is a mistake: if $\mu > h$ then we would trigger the end of the process immediately.

In addition to the CUSUM that checks for positive drift in the process $x_1, x_2, \dots$, you can also run a simultaneous CUSUM process $T_0, T_1, \dots$ given by $$T_0 = 0,$$ $$T_j = \max(0, T_{j-1} - (x_j - \mu) / \sigma - k), \ \ \ \ j = \{1,2,\dots\},$$ which gets large when the process $x_1, x_2, \dots$ is consistently below the mean.

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  • $\begingroup$ Thanks for the references. I hadn't come across those and they do seem well-written. I'll accept your answer but if you ever come across more / different references that are as helpful. Please add them or notify me. Cheers. $\endgroup$ – guy May 26 at 0:58

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