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Теория вероятн. и ее примен., 2004, том 49, выпуск 3, страницы 538–582 (Mi tvp207)  

Эта публикация цитируется в 67 научных статьях (всего в 67 статьях)

General asymptotic Bayesian theory of quickest change detection

[General asymptotic Bayesian theory of quickest change detection]

A. G. Tartakovskiia, V. Veeravallib

a University of Southern California
b University of Illinois at Urbana-Champaign

Аннотация: Оптимальное правило обнаружения изменений свойств независимых и одинаково распределенных (н.о.р.) последовательностей в байeсовской постановке задачи получено А. Н. Ширяевым в 1960-е годы. Однако задача анализа характеристик этого правила — средней задержки обнаружения и вероятности ложной тревоги — оставалась открытой. В настоящей статье разрабатывается общая асимптотическая теория обнаружения изменений (разладки), которая не ограничена жестким н.о.р.-допущением. Характеристики правила Ширяева исследуются для общих статистических моделей в дискретном времени в асимптотической постановке задачи, когда вероятность ложной тревоги стремится к нулю. Показано, что правило Ширяева асимптотически оптимально в случае зависимых и неодинаково распределенных наблюдений при весьма слабых условиях. Показано также, что две популярные небайесовские процедуры обнаружения — процедура Пейджа и процедура Ширяева–Робертса–Поллака — вообще говоря, неоптимальны (даже асимптотически) для байесовского критерия. Результаты исследования являются особенно важными для изучения асимптотик в нецентрализованных распределенных системах обнаружения.

Ключевые слова: обнаружение изменений (разладки), последовательное обнаружение, асимптотическая оптимальность, нелинейная теория восстановления, правило Ширяева, процедура кумулятивных сумм.

DOI: https://doi.org/10.4213/tvp207

Полный текст: PDF файл (4321 kB)
Список литературы: PDF файл   HTML файл

Англоязычная версия:
Theory of Probability and its Applications, 2005, 49:3, 458–497

Реферативные базы данных:

Поступила в редакцию: 07.11.2003
Язык публикации: английский

Образец цитирования: A. G. Tartakovskii, V. Veeravalli, “General asymptotic Bayesian theory of quickest change detection”, Теория вероятн. и ее примен., 49:3 (2004), 538–582; Theory Probab. Appl., 49:3 (2005), 458–497

Цитирование в формате AMSBIB
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    Эта публикация цитируется в следующих статьяx:
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    46. Li D. Kar S. Cui Sh., “Distributed Bayesian Quickest Change Detection in Sensor Networks Via Large Deviation Analysis”, 2016 54Th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Annual Allerton Conference on Communication Control and Computing, IEEE, 2016, 1274–1281  isi
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