Discussion on "Is average run length to false alarm always an informative criterion?" by Yajun Mei

In his interesting paper Mei criticized the use of the expected run length as the mean for controlling the rate of false detection and proposed alternative measures. In this paper we join Mei's attack on the traditional constraint by claiming that the rate of detection is a local phenomena, and hence should be balanced against local constraints on false detection. We propose local probabilistic constraints on the rate of false detection and demonstrate their usefulness in the detection of a shift in a normal mean with an unknown baseline.