Sequential Testing Problems for Poisson Processes

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 b...

Full description

Saved in:
Bibliographic Details
Published in:The Annals of statistics 2000-06, Vol.28 (3), p.837-859
Main Authors: Peskir, G., Shiryaev, A. N.
Format: Article
Language:English
Subjects:
34K10
60G40
60J75
62C10
62L10
62L15
A priori knowledge
Bayes decision rule
free-boundary differential-difference Stephan problem
Inference for Stochastic Processes
Infinitesimals
Itô's formula
Markov processes
Martingales
measure of jumps and its compensator
optimal stopping
point (counting)(Cox) process
Poisson process
principles of continuous and smooth fit
Probabilities
Ratio test
Sequential analysis
Sequential testing
SPRT (sequential probability ratio test)
Stopping distances
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1015952000