Optimal sequential procedures with Bayes decision rules

Andrey Novikov

Kybernetika (2010)

  • Volume: 46, Issue: 4, page 754-770
  • ISSN: 0023-5954

Abstract

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In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In particular, we have a characterization of the form of optimal sequential decision procedures when the Bayesian risk includes both the loss due to incorrect decision and the cost of observations.

How to cite

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Novikov, Andrey. "Optimal sequential procedures with Bayes decision rules." Kybernetika 46.4 (2010): 754-770. <http://eudml.org/doc/196417>.

@article{Novikov2010,
abstract = {In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In particular, we have a characterization of the form of optimal sequential decision procedures when the Bayesian risk includes both the loss due to incorrect decision and the cost of observations.},
author = {Novikov, Andrey},
journal = {Kybernetika},
keywords = {sequential analysis; discrete-time stochastic process; dependent observations; statistical decision problem; Bayes decision; randomized stopping time; optimal stopping rule; existence and uniqueness of optimal sequential decision procedure; sequential analysis; discrete-time stochastic process; dependent observations; statistical decision problem; Bayes decision; randomized stopping time; optimal stopping rule; existence and uniqueness of optimal sequential decision procedure},
language = {eng},
number = {4},
pages = {754-770},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Optimal sequential procedures with Bayes decision rules},
url = {http://eudml.org/doc/196417},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Novikov, Andrey
TI - Optimal sequential procedures with Bayes decision rules
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 4
SP - 754
EP - 770
AB - In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In particular, we have a characterization of the form of optimal sequential decision procedures when the Bayesian risk includes both the loss due to incorrect decision and the cost of observations.
LA - eng
KW - sequential analysis; discrete-time stochastic process; dependent observations; statistical decision problem; Bayes decision; randomized stopping time; optimal stopping rule; existence and uniqueness of optimal sequential decision procedure; sequential analysis; discrete-time stochastic process; dependent observations; statistical decision problem; Bayes decision; randomized stopping time; optimal stopping rule; existence and uniqueness of optimal sequential decision procedure
UR - http://eudml.org/doc/196417
ER -

References

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