Topic
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.
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TL;DR: An alternative sequential testing procedure called the 2-SPRT for the negative-binomial parameter P is demonstrated, in which two one-sided SPRTs are performed simultaneously, which results in the convergent boundary lines.
Abstract: Sequential sampling plans are appealing because fewer observations are needed than those needed for fixed sampling plans to make a terminating decision when insect populations are sparse or abundant. Wald's Sequential Probability Ratio Test (SPRT) commonly has been used in monitoring insect populations and damages from these populations. At times, particularly for moderate infestations, the SPRT with its parallel boundaries takes longer than a comparable fixed-sample-size method to make a terminating decision. An alternative sequential testing procedure called the 2-SPRT for the negative-binomial parameter P is demonstrated. The value of the exponent k is assumed to be known. In this procedure two one-sided SPRTs are performed simultaneously, which results in the convergent boundary lines. The average number of observations needed for the terminating decision for medium infestations (i.e., for P1 < P < P2) is observed to be considerably smaller than that for the SPRT with a slight increase in sampling effort when infestations are light or heavy. An application of the 2-SPRT is demonstrated using cotton f1eahopper, Pseudatomoscelis seriatus (Reuter), data obtained in southwestern Oklahoma.
10 citations
01 Aug 2017
TL;DR: It is demonstrated how the proposed cluster based methodology can be successfully applied for anomaly detection on a marine diesel engine in operation, and the vast reduction in computation time compared to the original framework.
Abstract: In this paper we propose a cluster based version of the anomaly detection methodology based on signal reconstruction, using Auto Associative Kernel Regression (AAKR), combined with residuals analysis, using Sequential Probability Ratio Test (SPRT). We demonstrate how the proposed cluster based methodology can be successfully applied for anomaly detection on a marine diesel engine in operation. Furthermore, we demonstrate the vast reduction in computation time compared to the original framework, and discuss other possible advantages and disadvantages of the proposed methodology.
10 citations
TL;DR: In this article, inductive integral equations governing SPRT and Page's cumulative sum test are developed under very general settings, where the bounds can be time-varying and the LLRs are assumed independent but nonstationary.
Abstract: The sequential probability ratio test (SPRT) is a fundamental tool for sequential analysis. It forms the basis of numerous sequential techniques for different applications; for example, the truncated SPRT and Page's cumulative sum test (CUSUM). The performance of SPRT is characterized by two important functions—operating characteristic (OC) and average sample number (ASN), and CUSUM's performance is revealed by the average run length (ARL) function. These functions have been studied extensively under the assumption of independent and identically distributed log-likelihood ratios (LLRs) with constant bounds, which is too stringent for many applications. In this article, inductive integral equations governing these functions are developed under very general settings—the bounds can be time-varying and the LLRs are assumed independent but nonstationary. These inductive equations provide a theoretical foundation for performance analysis. Unfortunately, they have nonunique solutions in the general case...
10 citations
TL;DR: In this article, it was shown that the variance of the sample number is approximately proportional to the square of the average sample number, and that the distribution of sample number variance in sequential probability ratio tests is a function of the number of samples in the test set.
Abstract: Little published information is available about moments, other than the first, of the distribution of the sample number in Wald type sequential probability ratio tests. Empirical evidence from Monte Carlo studies is presented for the inference that the variance of the sample number is approximately proportional to the square of the average sample number.
10 citations
TL;DR: In this paper, the Neyman-Pearson test with fixed level and power is viewed as a Wald test subject to restrictions on the payoff vector, cost function, and prior distribution.
Abstract: The Neyman-Pearson Lemma describes a test for two simple hypotheses that, for a given sample size, is most powerful for its level. It is usually implemented by choosing the smallest sample size that achieves a prespecified power for a fixed level. The Lemma does not describe how to select either the level or the power of the test. In the usual Wald decision-theoretic structure there exists a sampling cost function, an initial prior over the hypothesis space and various payoffs to right/wrong hypothesis selections. The optimal Wald test is a Bayes decision rule that maximizes the expected payoff net of sampling costs. This paper shows that the Wald-optimal test and the Neyman-Pearson test can be the same and how the Neyman-Pearson test, with fixed level and power, can be viewed as a Wald test subject to restrictions on the payoff vector, cost function and prior distribution.
10 citations