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 detection of targets in multichannel systems

Abstract: It is supposed that there is a multichannel sensor system which performs sequential detection of a target. Sequential detection is done by implementing a generalized Wald's sequential probability ratio test, which is based on the maximum-likelihood ratio statistic and allows one to fix the false-alarm rate and the rate of missed detections at specified levels. We present the asymptotic performance of this sequential detection procedure and show that it is asymptotically optimal in the sense of minimizing the expected sample size when the probabilities of erroneous decisions are small. We do not assume that the observations are independent and identically distributed (i.i.d.). The first-order asymptotic optimality result holds for general statistical models that are not confined to the restrictive i.i.d. assumption. However, for i.i.d. and quasi-i.i.d. cases, where the log-likelihood ratios can be represented in the form of sums of random walks and slowly changing sequences, we obtain much stronger results. Specifically, using the nonlinear renewal theory we are able to obtain both tight expressions for the error probabilities and higher order approximations for the average sample size up to a vanishing term. The performance of the multichannel sequential detection algorithm is illustrated by an example of detection of a deterministic signal in correlated (colored) Gaussian noise. In this example, we provide both the results of theoretical analysis and the results of a Monte Carlo experiment. These results allow us to conclude that the use of the sequential detection algorithm substantially reduces the required resources of the system compared to the best nonsequential algorithm.

Detection of hidden Markov model transient signals

Abstract: Addressed here is the quickest detection of transient signals which can be represented as hidden Markov models (HMMs), with the application of detection of transient signals. Relying on the fact that Page's test is equivalent to a repeated sequential probability ratio test (SPRT), we are able to devise a procedure analogous to Page's test for dependent observations. By using the so-called forward variable of an HMM, such a procedure is applied to the detection of a change in hidden Markov modeled observations, i.e., a switch from one HMM to another. Performance indices of Page's test, the average run length (ARL) under both hypotheses, are approximated and confirmed via simulation. Several important examples are investigated in depth to illustrate the advantages of the proposed scheme.

A Reminder of the Fallibility of the Wald Statistic

Abstract: Computer programs often produce a parameter estimate and estimated variance (). Thus it is easy to compute a Wald statistic (- θ0){()}−1/2 to test the null hypothesis θ = θ0. Hauck and Donner and Vaeth have identified situations in which the Wald statistic has poor power. We consider another example that is not in the classes discussed by those authors. We present data from a balanced one-way random effects analysis of variance (ANOVA) that illustrate the poor power of the Wald statistic compared to the usual F test. In this example the parameter of interest is the variance of the random effect. The power of the Wald test depends on the parameterization used, however, and a whole family of Wald statistics with p values ranging from 0 to 1 can be generated with power transformations of the random effect parameter.

Bayes Solutions of Sequential Decision Problems.

Abstract: The study of sequential decision functions was initiated by one of the authors in [1]. Making use of the ideas of this theory the authors succeeded in [4] in proving the optimum character of the sequential probability ratio test. In the present paper the authors continue the study of sequential decision functions, as follows: a) The proof of the optimum character of the sequential probability ratio test was based on a certain property of Bayes solutions for sequential decisions between two alternatives, the cost function being linear. This fundamental property, the convexity of certain important sets of a priori distributions, is proved in Theorem 3.9 in considerable generality. The number of possible decisions may be infinite. b) Theorem 3.10 and section 4 discuss tangents and boundary points of these sets of a priori distributions. (These results for finitely many alternatives were announced by one of us in an invited address at the Berkeley meeting of the Institute of Mathematical Statistics in June, 1948) c) Theorem 3.6 is an existence theorem for Bayes solutions. Theorem 3.7 gives a necessary and sufficient condition for a Bayes solution. These theorems generalize and follow the ideas of Lemma 1 of [4] d) Theorems 3.8 and 3.8.1 are continuity theorems for the average risk function. They generalize Lemma 3 in [4] e) Other theorems give recursion formulas and inequalities which govern Bayes solutions.

Chi-square and SPRT combined fault detection for multisensor navigation

Abstract: A fault-detection algorithm for a redundant multisensor navigation system for hypersonic cruise vehicles (HCVs) is proposed. The algorithm comprehensively diagnoses failures according to the failure level monitored by the sequential probability ratio test (SPRT) and chi-square test as well as the failure trend monitored by the SPRT. A test statistics feedback-reset loop is also added to shorten the recovery time after failure ceases. Simulations indicate improvements in both failure detection and recovery speed, contributing to improved accuracy and stability in HCV fault-tolerant navigation.