Optimal detection of changes in the properties of random sequences. II. Successive detection

The paper is concerned with a Bayesian problem of truncated successive detection of «differences» in random sequences on the assumption that the «difference» occurs gradually and with a probability below 1. With independent observations the likelihood relation averaged over the distribution of the «difference» time is proved to supply sufficient statistics. Expressions are provided for the least a posteriori risk function which lead to optimal stoppage rules. An example is provided.