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 Estimation of the Mean of a Multinormal Population

Abstract: This article is a multivariate generalization of the sequential sampling procedure developed by Robbins (1959) and extended by Starr (1966b) for estimating the mean of a normal population when the scale parameter is unknown. The exact distribution of the stopping time is derived for the sequential procedure, and a recursive method for computing the distribution of the stopping time is proposed that can be easily programmed for mechanical calculation. It is shown that the “risk efficiency” of the sequential procedure is a function of the dimension of the population.

Method of detecting compromised computers in a network

Abstract: A method of detecting a compromised machine on a network. The method receives an email message from a machine on the network and classifies it as either spam or non-spam. A probability ratio is then updated, according to whether the message was spam or non-spam, by applying a sequential probability ratio test. If the probability ratio is greater than or equal to a first threshold, then the machine is compromised. If the probability ratio is less than or equal to a second threshold, then the machine is normal. The operations of receiving a message, classifying the message, updating the probability ratio, and indicating the machine is normal or compromised until the probability ratio is greater than or equal to the first threshold are repeated for a plurality of messages. Such repeated operations are performed on each of the messages one at a time, as each of the messages is received.

Sequential Hypothesis Testing

Abstract: Sequential sampling is a fast efficient tool for many sampling problems. Sequential sampling may be used (1) to obtain precise estimate(s) of the parameters), or (2) to test hypotheses concerning the parameters. Sequential estimation is used when the purpose of sampling is to obtain precise parameter estimates. Several sequential estimation procedures are discussed in Chapter 4. The focus of this chapter is sequential hypothesis testing. This approach is appropriate when we are interested in determining whether the population density is above or below a stated threshold. As in sequential estimation, sequential hypothesis testing requires taking observations sequentially until some stopping criterion is satisfied. The observations are taken at random over the sampling area. Generally, the accumulated total of the observations relative to the number of observations taken determines when sampling is stopped. The sequential hypothesis testing we consider requires some prior knowledge of the population distribution. This permits most computations to be completed in advance of sampling and to be stored in handheld calculators, laptop computers, or printed on cards or sheets. Wald’s sequential probability ratio test was the earliest sequential test and is described first. Lorden’s 2-SPRT is a more recent development that has some exciting possibilities for tests of hypotheses concerning population density and is discussed in the latter parts of this chapter.

Distributed Sequential Detection: Dependent Observations and Imperfect Communication

Abstract: In this paper, we consider the problem of distributed sequential detection using wireless sensor networks in the presence of imperfect communication channels between the sensors and the fusion center. Sensor observations are assumed to be spatially dependent. Moreover, the channel noise can be dependent and non-Gaussian. We propose a copula-based distributed sequential detection scheme that takes the spatial dependence into account. More specifically, each local sensor runs a memory-less truncated sequential test repeatedly and sends its binary decisions to the fusion center synchronously. The fusion center fuses the received messages using a copula-based sequential test. To this end, we first propose a centralized copula-based sequential test and show its asymptotic optimality and time efficiency. We then show the asymptotic optimality and time efficiency of the proposed distributed scheme. We also show that by suitably designing the local thresholds and the truncation window, the local probabilities of false alarm and miss detection of the proposed memory-less truncated local sequential tests satisfy the pre-specified error probabilities. Numerical experiments are conducted to demonstrate the effectiveness of our approach.

A sequential approximation to a permutation test

Abstract: A sequential method for approximating a general permutation test (SAPT) is proposed and evaluated. Permutations are randomly generated from some set G, and a sequential probability ratio test (SPRT) is used to determine whether an observed test statistic falls sufficiently far in the tail of the permutation distribution to warrant rejecting some hypothesis. An estimate and bounds on the power function of the SPRT are used to find bounds on the effective significance level of the SAPT. Guidelines are developed for choosing parameters in order to obtain a desired significance level and minimize the number of permutations needed to reach a decision. A theoretical estimate of the average number of permutations under the null hypothesis is given along with simulation results demonstrating the power and average number of permutations for various alternatives. The sequential approximation retains the generality of the permutation test,- while avoiding the computational complexities that arise in attempting to co...