Showing papers on "Sequential probability ratio test published in 2004"

Fault-tolerant system, apparatus and method

Abstract: A method, apparatus and system are described having a minimum variance estimator of state estimates typically in navigation embodiments where a sensor and/or effecter fault detecting module is adapted to execute residual testing steps using the Multiple Hypothesis Wald Sequential Probability Ratio test, the Multiple Hypothesis Shiryayev Sequential Probability Ratio test, the Chi-Square test and combinations thereof to determine the likelihood of sensor and/or actuator fault occurrences and thereafter isolate the effects of the one or more identified fault from the state estimates.

An overview of risk-adjusted charts

Abstract: Summary The paper provides an overview of risk-adjusted charts, with examples based on two data sets: the first consisting of outcomes following cardiac surgery and patient factors contributing to the Parsonnet score; the second being age–sex-adjusted death-rates per year under a single general practitioner Charts presented include the cumulative sum (CUSUM), resetting sequential probability ratio test, the sets method and Shewhart chart Comparisons between the charts are made Estimation of the process parameter and two-sided charts are also discussed The CUSUM is found to be the least efficient, under the average run length (ARL) criterion, of the resetting sequential probability ratio test class of charts, but the ARL criterion is thought not to be sensible for comparisons within that class An empirical comparison of the sets method and CUSUM, for binary data, shows that the sets method is more efficient when the in-control ARL is small and more efficient for a slightly larger range of in-control ARLs when the change in parameter being tested for is larger The Shewart p-chart is found to be less efficient than the CUSUM even when the change in parameter being tested for is large

An efficient multiple hypothesis filter for bearing-only SLAM

Abstract: This paper presents a multiple hypothesis approach to solve the simultaneous localisation and mapping (SLAM) problem with a bearing-only sensor. The main contribution of the paper is to provide a remedy for the landmark initialisation problem that occurs due to the absence of range information, in a computationally efficient manner. Each landmark is initialised in the form of multiple hypotheses distributed along the direction of the bearing measurement. Using subsequent measurements, the validity of the hypotheses is evaluated based on the sequential probability ratio test (SPRT). Consequently, the best approximation to the landmark location is maintained. This approach enables an extended Kalman filler (EKF) to be used for bearing-only SLAM providing a computational efficient solution. Simulation and experimental results, from using a camera as the bearing-only sensor mounted on a Pioneer robot are included to demonstrate the effectiveness of the proposed technique.

Numerical vs. Statistical Probabilistic Model Checking: An Empirical Study ?

Abstract: Numerical analysis based on uniformisation and statistical techniques based on sampling and simulation are two distinct approaches for transient analysis of stochastic systems. We compare the two solution techniques when applied to the verification of time-bounded until formulae in the temporal stochastic logic CSL. This study differs from most previous comparisons of numerical and statistical approaches in that CSL model checking is a hypothesis testing problem rather than a parameter estimation problem. We can therefore rely on highly efficient sequential acceptance sampling tests, which enables statistical solution techniques to quickly return a result with some uncertainty. This suggests that statistical techniques can be useful as a first resort during system prototyping, rather than as a last resort as often suggested. We also propose a novel combination of the two solution techniques for verifying CSL queries with nested probabilistic operators.

Comparing Social Groups: Wald Statistics for Testing Equality among Multiple Logit Models

Abstract: Social scientists often study the differential effects of explanatory variables among multiple social groups such as race, ethnic group, and nation.This paper examines the Wald test for testing equality of logit coefficients from models of multiple social groups. I propose a Wald statistic that can perform some joint tests of group comparisons that the usual likelihood ratio test cannot. Two examples apply the Wald statistic for testing various hypotheses, and show that the Wald test is flexible and straightforward for making comparisons across social groups, and that the proposed Wald test may find wide applications in the social sciences.

Sequential generalized likelihood ratios and adaptive treatment allocation for optimal sequential selection

Abstract: Given k ≥ 2 populations from an exponential family, we consider herein the problem of efficient sequential selection of the population with the largest mean subject to a correct selection probability constraint. The selection procedure consists of a sampling rule, a stopping rule, and a terminal decision rule. Efficiency at every parameter configuration is measured by the expected total sampling cost together with the correct selection probability. By using sequential generalized likelihood ratio tests of multiple hypotheses and an adaptive sampling rule based on a constrained optimization problem, we show that it is possible to achieve asymptotic efficiency at the true (but unknown) parameter configuration as the probability of incorrect selection approaches 0, thereby resolving a number of open problems in this area. Finite-sample efficiency of the proposed procedure is demonstrated in simulation studies that also compare the procedure with other sequential selection procedures in the literatur...

Asymptotic robust Neyman-Pearson hypothesis testing based on moment classes

Abstract: A robust hypothesis testing framework is introduced in which candidate hypotheses are characterized by moment classes. It is shown that there exists a test sequence that is asymptotically optimal in the min-max sense, and that it is expressed as a comparison of a log-linear combination of the constraint functions to a predetermined threshold.

Application of Sequential Probability Ratio Test to Computerized Criterion-Referenced Testing

Abstract: The adaptive testing is an important testing method in the modern educational/psychological testings. In adaptive mastery testing, the items are selected adaptively according to the estimated information of the unknown latent ability levels, and given then to the test-takers, sequentially. Hence, the decision (master or non-master; pass or fail) for each test-taker is made sequentially based on each test-taker's responses to a particular sequence of items administered to him/her. Thus, statistically speaking, by the natural character of the adaptive mastery testing, it is a sequential problem with dependent observations. The Wald's [Wald, A. Sequential Analysis; Wiley: New York, 1947] SPRT (sequential probability ratio test) has been applied to this kind of mental testing problem by many researchers in the field of educational/psychological measurement theory; for example, Reckase [Reckase, M. A procedure for decision making using tailored testing. In New Horizons in Testing – Latent Trait Test T...

Multi-dimensional sequential probability ratio test for detecting failure conditions in computer systems

Abstract: One embodiment of the present invention provides a monitoring system that detects anomalies in data gathered from sensors in a computer system. During operation, the monitoring system samples data from a plurality of sensors located at various sampling points throughout the computer system. Next, the monitoring system interpolates the data from the sampling points to produce a real-time digitized surface. The monitoring system then subtracts a reference digitized surface from the real-time digitized surface to produce a residual digitized surface. Finally, the monitoring system applies a multi-dimensional sequential probability ratio test (SPRT) to the residual digitized surface to detect anomalies in the residual digitized surface which indicate an impending failure of the computer system.

Classifying Acoustic Signatures Using the Sequential Probability Ratio Test

Abstract: Acoustic sensors can provide real time information about moving targets. The acoustic information is typically processed sequentially, allowing the sequential probability ratio test (SPRT) to be used as the basis to solve the target identification problem. The SPRT keeps gathering observations only as long as the statistical test has a value between the upper stopping boundary and the lower stopping boundary. When the test goes above the upper boundary or below the lower boundary, the system can make a decision. The desired false alarm error rate and the desired missed detection error rate determine the upper and lower stopping boundaries. We present extensions to the sequential probability ratio test to handle problems of dependence, contamination, and the unknown class. We also present results for using the SPRT for target identification using acoustic information.

Connections, Context, and Community: Abraham Wald and the Sequential Probability Ratio Test

Abstract: This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community” is the broadest. We include “schools” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.

On Sequential Data-Driven Density Estimation

Abstract: The theory and methods of minimax and sequential inferences, pioneered by Abraham Wald in 1940's, shaped the way statisticians see the statistics today. This article employs the Wald approaches together with the modern oracle analysis to develop the theory and methods of a sharp minimax adaptive sequential density estimation. In particular, it proves a long-standing conjecture about a sufficient condition for a sharp adaptive sequential estimation with an assigned mean integrated squared error. It also suggests, and then studies via intensive Monte-Carlo simulations, a data-driven sequential density estimator that can be recommended for practical applications.

Sequential detection with limited memory

Abstract: Sequential tests outperform fixed sample size tests by requiring fewer samples on average to achieve the same level of error performance The sequential probability ratio test (SPRT) has been suggested by Wald (1947) for sequential binary hypothesis testing problems SPRT recursively calculates the likelihood of an observed data stream and requires this likelihood to be stored in memory between samples In this paper we study the design of sequential detection tests under memory constraints We derive the optimal sequential test in the case where only a quantized version of the likelihood can be stored in memory An application of the proposed techniques is large scale sensor networks where price and communication constraints dictate limited complexity devices, which store and transmit concise representations of the state of nature

Double window acceptance sampling

Abstract: We introduce the concept of a sequential double window procedure and compare the resulting acceptance test with both a fixed sample size method as well as with the Wald sequential probability ratio test. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Statistical issues in computerized adaptive testing

Abstract: Computerized adaptive testing (CAT) serves as a more efficient alternative to traditional pencil-and-paper tests by (i) adaptively selecting questions that are appropriate for the examinee being tested; and (ii) ending the examination once enough information has accumulated. An important use of CAT is so-called “proficiency testing”, where the goal is a pass/fail classification of each examinee rather than accurate estimation of that examinee's ability. The main goal of this thesis is to critique and improve the efficiency of proficiency testing by finding optimal statistical designs for CAT procedures. Attention focuses on the problem of deciding when to cease testing in order to make the classification decision. Because questions are not interchangeable with one another, item response theory (IRT) is used to account for the fact that different test takers have not necessarily received questions with similar measurement properties. Statistical theory is developed without the common sequential analysis assumption of iid variables. A traditional method in sequential analysis, the truncated sequential probability ratio test (Wald, 1947), is shown not to be supported by theoretical results. More modern sequential analysis procedures are suggested, including those based on stochastic curtailment (Lan, Simon, & Halperin, 1982) and self-tuning methods (Lai & Shih, 2003). Different methods of ending the examination, referred to as “stopping rules” in sequential analysis, are compared in simulation, the results of which indicate that the traditional method can be shortened without compromising error rates. Practical challenges of implementing CAT, such as a possible lack of test security, are also incorporated into analysis of the methods' properties so that the different statistical approaches can be compared in a realistic setting. Theory and simulation both suggest considerable practical gain from stochastic curtailment and self-tuning methods in relation to the traditional method. Another section of the thesis introduces sequential confidence intervals as a way to make inferences about an examinee's ability once the test is over. Finally, the link between CAT methods and other applications of sequential analysis, such as clinical studies and psychological diagnosis, is explored.

Boost-Phase Identification of Theater Ballistic Missiles Using Radar Measurements

Abstract: This paper addresses the problem of identification of theater ballistic missiles during boost phase using radar measurements. Based on the use of the Wald sequential probability ratio test (SPRT), three identification algorithms are presented, corresponding to scenarios of increasing uncertainty. The use of the SPRT allows meeting specified false-alarm and missed-detection probabilities, while minimizing identification time. When the missiles' dynamic models and launch initial conditions (location and time) are completely and accurately known, the SPRT works directly with the raw radar measurements. In other scenarios, including a case where the launch location and launch time are unknown, two extended Kalman filters are used to generate the innovations sequences driving the SPRT. An extensive Monte Carlo simulation study is used to demonstrate the performance of the proposed procedures. Although the identification times and actual error probabilities depend, to some degree, on proper filter tuning, it is shown that reasonable mean identification times can be attained, corresponding to acceptable false-alarm and missed-detection rates, even in the presence of model uncertainties. This performance renders the proposed algorithms viable for the difficult problem considered.

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.

A nonsymmetric sequential test

Abstract: A one-sided testing problem based on an i.i.d. sample of observations is considered. The usual one-sided sequential probability ratio test would be based on a random walk derived from these observations. Here we propose a sequential test where the random walk is replaced by Lindley’s random walk which starts anew at zero as soon as it becomes negative. We derive the asymptotics of the expected sample size and the error probabilities of this sequential test. We discuss the advantages of this test for certain nonsymmetric situations.

Sequential probability ratio tests based on improper priors

Abstract: One way of handling composite hypotheses by SPRT's is to integrate out nuisance parameters under both the null and alternative hypotheses and then form an SPRT. If the prior is improper, Wald inequalities will not hold in general. We provide sufficient conditions and then verify that the usual sequential |t|-test satisfies these conditions but Wald's |t|-test does not satisfy these conditions and in fact cannot satisfy a strengthened form of these inequalities in general. Nonetheless, simulations show Wald's inequalities for A, B, corresponding to usual small α, β, will usually hold.

Sequential Probability Ratio Test for the detection of a single electron spin in the OSCAR setup

Abstract: The MRFM device is a powerful setup for manipulating single electron spin in resonance in a magnetic field. However, the real time observation of a resonating spin is still an issue because of the very low SNR of the output signal. This paper investigates the usability and the efficiency of sequential detection schemes (the Sequential Probability Ratio Test) to decrease the required integration time, in comparison to standard fixed time detection schemes.

Tracking initiation and data association of multi-target passive tracking based on information fusion

Abstract: Tracking initiation and data association are key techniques of multi-target passive tracking by a single observer A new adaptive passive tracking initiation algorithm based on information fusion is proposed In this work First, according to multiple features of the target, a multidimensional dynamically variable tracking gate is built for adaptive detection Further, the sequential probability ratio test (SPRT) rule is used to confirm the track And also, a new data association algorithm based on information fusion is proposed Based on the information fusion of multiple features of a single valid observation, the decision of synthetic data association of all the targets is made With the help of computer simulations, the tracking initiation algorithm is proven to be correct and effective, and the data association algorithm is proven to be superior to the NN method

The Multiple-Hypothesis Wald Sequential Probability Ratio Test for GPS Integer Ambiguity Resolution

Abstract: An algorithm for resolving the GPS integer ambiguity is introduced. This algorithm is based on a log formulation of the Multiple-Hypothesis Wald Sequential Probability Test (MHWSPT) and is called the Multiple-Hypothesis Wald Sequential Probability Ratio Test (MHWSPRT). Given a set of integer hypotheses, the computational time of the MHWSPT is reduced, and convergence to the correct integer vector is achieved within a given probability in minimal time. The convergence characteristics of the proposed method allow independent testing of the various integer candidates hypothesized and therefore permit eliminating the hypotheses that are proven wrong, with high probability in the sequential processing of obtaining the true integer ambiguity. The proposed method is seen as a generalization of the classic two-hypothesis sequential probability ratio test (THSPRT). The method's relationship to the THSPRT is also derived.

Sampling Inspection Plans for Defect

Abstract: The sequential sampling inspection method is an extension of the multiple-sampling methods, and its theory is based on the sequential probability ratio test (SPRT) of Wald. In this paper, the characteristics of SPRT for testing the number of defects are approximated by using the estimated excess over the boundaries. The use of the estimated excess shows good performances in estimating the operating characteristic function and the average sample number of SPRT compared to the method by neglecting the excess. It also makes it possible to determine the boundary values which satisfy the desired error probabilities.