We present the explicit solution of the Bayesian problem of
sequential testing of two simple hypotheses about the intensity of an observed
Poisson process. The method of proof consists of reducing the initial problem
to a free-boundary differential-difference Stephan problem and solving the
latter by use of the principles of smooth and continuous fit. A rigorous proof
of the optimality of the Wald’s sequential probability ratio test in the
variational formulation of the problem is obtained as a consequence of the
solution of the Bayesian problem.
Publié le : 2000-05-14
Classification:
Sequential testing,
Bayes decision rule,
Poisson process,
SPRT (sequential probability ratio test),
optimal stopping,
free-boundary differential-difference Stephan
problem,
principles of continuous and smooth fit,
point (counting)(Cox) process,
measure of jumps and its compensator,
Itô's formula,
62C10,
60G40,
62L10,
62L15,
34K10,
60J75
@article{1015952000,
author = {Peskir, G. and Shiryaev, A. N.},
title = {Sequential testing problems for Poisson processes},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 837-859},
language = {en},
url = {http://dml.mathdoc.fr/item/1015952000}
}
Peskir, G.; Shiryaev, A. N. Sequential testing problems for Poisson processes. Ann. Statist., Tome 28 (2000) no. 3, pp. 837-859. http://gdmltest.u-ga.fr/item/1015952000/