Three approaches to sequential analysis and one to hidden Markov processes

Three approaches to sequential analysis are reviewed: Chernoff's development of the Wald approach, the dynamic programming analysis developed by the author some years ago and a 'path-averaging' approach which exploits the random-walk properties of the log-posterior under a given hypothesis. These last two approaches led to explicit determinations of the optimal decision boundary and its associated costs in the limit of a small sampling cost, for a general number of hypotheses. However, the particular interest of the path-averaging approach is that it applies also to state-estimation for a hidden Markov model, where it leads to Eq. (39), which gives an immediate indication of the effectiveness with which the different states are estimated.