ABSTRACT
In this chapter, we discuss in detail changepoint detection by using multichart procedures for iid and general non-iid models, which are outlined in Chapter 6, Section 6.3.
9.1 Motivation for Applying Multichart Detection Procedures
As follows from Section 8.3, there are no recursive or other computationally feasible implementations of the weighted CUSUM and GLR algorithms in general. An obvious disadvantage of such schemes is that the number of maximizations grows to infinity with n. For example, if sampling is performed with the rate of a given ARL to false alarm γ (which is too optimistic and usually even not realistic since the rate is expected to be much higher), then the mean number of maximizations of the LR over θ1 ∈ Θ1 that should be performed at time n ∈ [1,γ] is O(γ). In the case of weighted CUSUM, the mean number of WLR calculations (related to the integration over possible values of the parameter θ ) also grows to infinity with n with the same rate.
