A sequential multiple hypotheses test for the unknown parameters of a Gaussian distribution (Corresp.)

A sequential multiple hypotheses test for the unknown parameters of a Gaussian distribution is developed. The case of a known variance but an unknown mean belonging to the set (00,01,\´\´\´ ,Om_l} is considered as well as that of a known mean but an unknown variance belonging to the set . Analytical expressions are developed for the algorithm performance, i.e., the average length of the test and the error probability. The results are compared with a Bayes algorithm and show that the new algorithm needs about half as many samples. As far as the authors are aware this is the first ary sequential algorithm for which the performance has been found analytically. Because of the performance of this algorithm and the fact that it is a natural generalization of the binary sequential test, it is felt that the algorithm may be optimum or close to optimum.