The VTP test for transients of equal detectability

For detection of a permanent and precisely-modeled change in distribution of iid observations, Page\´s test is optimal. When employed to detect a transient change between known distributions, Page\´s test is a generalised likelihood ratio test (GLRT). However, the situation of interest here is of transient of unknown scale parameter: a fixed Page procedure tuned to a "short-and-loud" signal uses heavy biasing and low threshold, a combination ill-suited to a "long-but-quiet" signal. We offer an easy alternative to the standard Page: it uses a constant bias and a time-varying threshold. The idea is that the above short signals are detected quickly before post-termination data has a chance to refute them; and that evidence for a long signal is allowed to build, rather than being summarily discarded too early. Results show that the approach works quite well.