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 Multi-Hypothesis Testing in Multi-Armed Bandit Problems: An Approach for Asymptotic Optimality

Abstract: We consider a multi-hypothesis testing problem involving a $K$ -armed bandit. Each arm’s signal follows a distribution from a vector exponential family. The actual parameters of the arms are unknown to the decision maker. The decision maker incurs a delay cost for delay until a decision and a switching cost whenever he switches from one arm to another. His goal is to minimise the overall cost until a decision is reached on the true hypothesis. Of interest are policies that satisfy a given constraint on the probability of false detection. This is a sequential decision making problem where the decision maker gets only a limited view of the true state of nature at each stage, but can control his view by choosing the arm to observe at each stage. An information-theoretic lower bound on the total cost (expected time for a reliable decision plus total switching cost) is first identified, and a variation on a sequential policy based on the generalised likelihood ratio statistic is then studied. Due to the vector exponential family assumption, the signal processing at each stage is simple; the associated conjugate prior distribution on the unknown model parameters enables easy updates of the posterior distribution. The proposed policy, with a suitable threshold for stopping, is shown to satisfy the given constraint on the probability of false detection. Under a continuous selection assumption, the policy is also shown to be asymptotically optimal in terms of the total cost among all policies that satisfy the constraint on the probability of false detection.

Speeding up pattern localization and other tasks

Abstract: Detection of objects in images using statistical classifiers is a well studied and documented technique. Different applications of such detectors often require selection of the image position with the highest response of the detector—they perform non-maxima suppression. This article introduces the concept of early non-maxima sup- pression, which aims to reduce necessary computations by making the non-maxima suppression decision early based on incomplete information provided by a partially evalu- ated classifier. We show that the error of one such specu- lative decision with respect to a decision made based on response of the complete classifier can be estimated by collecting statistics on unlabeled data. The article then considers a sequential strategy of multiple early non- maxima suppression tests which follows the structure of soft-cascade detectors commonly used for object detection. We also show that an optimal (fastest for requested error rate) suppression strategy can be created by a novel variant of Wald's sequential probability ratio test (SPRT) which we call the conditioned SPRT (CSPRT). Experimental results show that the early non-maxima suppression sig- nificantly reduces amount of computation in the case of object localization while the error rates are limited to low predefined values. The proposed approach notably outper- forms the state-of-the-art detectors based on WaldBoost. The potential applications of the early non-maxima suppression approach are not limited to object localization and could be applied wherever the goal is to find the strongest response of a classifier among a set of classified samples.

A Modified Sequential Probability Ratio Test

Abstract: We describe a modified sequential probability ratio test that can be used to reduce the average sample size required to perform statistical hypothesis tests at specified levels of significance and power. Examples are provided for $z$ tests, $t$ tests, and tests of binomial success probabilities. A description of a software package to implement the test designs is provided. We compare the sample sizes required in fixed design tests conducted at 5$\%$ significance levels to the average sample sizes required in sequential tests conducted at 0.5$\%$ significance levels, and we find that the two sample sizes are approximately equal.

The Sequential Probability Ratio Test (SPRT) in Feature Extraction and Expert Systems in Nuclear Material Management

Abstract: The Y-12 National Security Complex in Oak Ridge, TN, maintains the nation's stockpile of highly enriched uranium (HEU) for use in nuclear weapons. A proposed system for monitoring the HEU is the Continuous Automated Vault Inventory System (CAVIS), which uses radiation and mass detectors. Radionuclides decay stochastically ( in a random manner that can be approximated by statistical analysis) and normal electronics and computer failures are inevitable. Therefore the system can and does experience spurious alarms arising from normal decay characteristics and system operation and not from material removal. To reduce the spurious alarms and their associated costs, CA VIS operators desire a system to monitor the monitoring system. This system will alert operators and security personnel in the event of an actual alarm and assist operators in diagnosing and correcting false alarms. The system of choice for this task is an expert system, using a knowledge base to diagnose and propose remedies for system malfunctions. The expert system requires information on which to base its decisions, and thus uses a feature extraction system to provide it the pertinent data. This feature extraction system uses the Sequential Probability Ratio Test (SPRT) to examine the radiation detector data and identify departures from the expected signal characteristics. The SPR T thus proves useful in the management of nuclear material. In addition to the SPRT, the feature extraction system uses several other analytical methods including statistical runs tests. iv This thesis outlines and explains the development and use of the SPRT and the other methods for the feature extraction and the use of the feature extraction system. Although the CAVIS uses radiation and mass detectors, this research uses only the radiation detector information as its basis for monitoring and feature extraction. This research shows that radiation detector signals, when collected conscientiously (without changing the statistical characteristics of the measured attribute), do meet the requirement of normality necessary for the correct SPRT operation. Further, this thesis applies the feature extraction system with simulated and real data as collected in a laboratory setting. These applications show that the feature extraction system is an excellent choice for use in a nuclear material management situation.