SPRT and CUSUM in hidden Markov models
SPRT and CUSUM in hidden Markov models
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隐马尔可夫模型中的 SPRT 和 CUSUM
DOI：
10.1214/aos/1056562468
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发表时间：
2003
影响因子：
4.5
通讯作者：
C. Fuh
中科院分区：
文献类型：
--
作者：
C. Fuh
本文研究参数化隐马尔可夫模型的序贯概率比检验问题。我们调查的一些细节的测试性能，并得出错误概率和预期的样本大小校正布朗近似。建立了基于隐马尔可夫链数据的序贯概率比检验的渐近最优性。接下来，我们考虑在这个模型中的变化点检测的累积和（Cumulative Sum，简称CSUM）过程。基于停止规则的更新性质，可将该检验看作是一个重复的单侧序贯概率比检验。在Lorden（1971）的意义下证明了该方法的渐近最优性。受隐马尔可夫模型序列分析的启发，给出了马尔可夫随机矩阵乘积的Wald似然比恒等式和Wald方程。我们将这些结果应用到几种类型的隐马尔可夫模型：i.i.d.隐马尔可夫模型、开关高斯回归和开关高斯自回归，它们通常用于数字通信、语音识别、生物信息学和经济学。
In this paper, we study the problems of sequential probability ratio tests for parameterized hidden Markov models. We investigate in some detail the performance of the tests and derive corrected Brownian approximations for error probabilities and expected sample sizes. Asymptotic optimality of the sequential probability ratio test for testing simple hypotheses based on hidden Markov chain data is established. Next, we consider the cumulative sum (CUSUM) procedure for change point detection in this model. Based on the renewal property of the stopping rule, CUSUM can be regarded as a repeated one-sided sequential probability ratio test. Asymptotic optimality of the CUSUM procedure is proved in the sense of Lorden (1971). Motivated by the sequential analysis in hidden Markov models, Wald's likelihood ratio identity and Wald's equation for products of Markov random matrices are also given. We apply these results to several types of hidden Markov models: i.i.d. hidden Markov models, switch Gaussian regression and switch Gaussian autoregression, which are commonly used in digital communications, speech recognition, bioinformatics and economics.
影响因子：
5.6
作者：
KROGH, A;BROWN, M;HAUSSLER, D
通讯作者：
HAUSSLER, D