Sequential probability ratio test

About: Sequential probability ratio test is a research topic. Over the lifetime, 1248 publications have been published within this topic receiving 22355 citations.

Sequential Life Tests for the Exponential Distribution with Changing Parameter

Abstract: For life testing from the exponential distribution the sequential probability ratio test is used to test hypotheses in which the exponential parameter and its alternatives change value a finite number of times during the test. Applications to nonexponential life distributions are indicated.

Effects of Item-Selection Criteria on Classification Testing with the Sequential Probability Ratio Test. ACT Research Report Series.

Abstract: This paper presents comparisons among three item-selection criteria for the sequential probability ratio test. The criteria were compared in terms of their efficiency in selecting items, as indicated by average test length (ATL) and the percentage of correct decisions (PCD). The item-selection criteria applied in this study were the Fisher information function, the KullbackLeibler information function, and a weighted log-odds ratio. We also examined the effects of the cutoff scores, the width of the indifference region, the item pool size, and the item exposure rate under the different item-selection criteria. The results of the computer simulations showed that the three criteria yielded very small differences in the outcome measures, regardless of the conditions imposed.

Sequential Detection of Markov Targets With Trajectory Estimation

Abstract: The problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered. Assuming a Markov evolution of the system (in particular, the pair signal-observation forms a hidden Markov model (HMM)), a sequential procedure is proposed, wherein the detection part is a sequential probability ratio test (SPRT) and the estimation part relies upon a maximum a posteriori probability (MAP) criterion, gated by the detection stage (the parameter to be estimated is the trajectory of the state evolution of the system itself). A thorough analysis of the asymptotic behavior of the test in this new scenario is given, and sufficient conditions for its asymptotic optimality are stated, i.e., for almost sure minimization of the stopping time and for (first-order) minimization of any moment of its distribution. An application to radar surveillance problems is also examined.

Quickest detection of hidden Markov models

Abstract: Page's test is optimal in quickly detecting distributional changes among independent observations. In this paper we propose a similar procedure for the quickest detection of dependent signals which can be conveniently modeled as hidden Markov models. Considering Page's test as a repeated sequential probability ratio test, we use Wald's approximation, with modification regarding the threshold overshoot, to predict the performance of the test, namely the average run length (ARL), between false alarms T. Using the asymptotic convergence property of the test statistic, we are also able to predict the ARL to detection D. The analysis shows that T is asymptotically exponential in D, as in the i.i.d. case. The results are supported by numerical examples.