Showing papers on "Sequential probability ratio test published in 1987"

Nonlinear Renewal Theory in Sequential Analysis

Abstract: Randomly Stopped Sequences Random Walks The Sequential Probability Ratio Test Nonlinear Renewal Theory Local Limit Theorems Open-Ended Tests Repeated Significance Tests Multiparameter Problems Estimation Following Sequential Testing Sequential Estimation.

Sequential Analysis and Optimal Design

Abstract: Preliminaries on probability Generalities about the conventional theory of design of experiments Optimal sample size Preliminaries on regression Design for linear regression: Elfving's method Maximum-likelihood estimation Locally optimal designs for estimation More design in regression experiments Testing hypotheses Optimal sample size in testing Sequential probability-ratio test Optimality of sequential probability-ratio test Motivation for an approach to sequential design of experiments in testing hypotheses Asymptotic optimality of procedure A in sequential design Extensions and open questions in sequential design The problem of adjacent hypotheses Testing for the sign of a normal mean: no indifference zone Bandit problems Sequential estimation of a normal mean sequential estimation of the common mean of two normal populations.

Sampling Plans in Insect Pest Management Based on Wald's Sequential Probability Ratio Test

Abstract: Equations for the stopping boundaries, and operating characteristic (OC) and average sample number (ASN) functions, of Wald's sequential probability ratio test (SPRT) are presented for the binomial, negative binomial, normal, and Poisson distributions. The effects of errors in Wald's OC and ASN equations due to overshooting the decision boundaries, and errors due to truncating, postponing decisions beyond the first stage, and taking more than one observation at each stage of the decision process are discussed. Monte Carlo procedures are used to show that Wald's equations overestimate the true error probabilities and underestimate the true ASN for a two-decision sampling plan based on the negative binomial distribution. A Monte Carlo procedure for modifying the decision boundaries to yield actual OC and ASN functions approximately equal to the desired ones is presented. Monte Carlo procedures are also used to examine the errors in Wald's OC and ASN functions when used to describe the OC and ASN functions of a composite three-decision sampling plan based on two single SPRT's using the negative binomial distribution. Wald's equations, in general, overestimate the true error probabilities and underestimate the true ASN even more for the three-decision case compared with the two-decision case. Recommendations are given as to the seriousness of the errors inherent in Wald's equations in relation to all of the other errors that are associated with the sampling process, and the choice between Wald's and Monte Carlo OC and ASN functions to describe the properties of a sampling plan.

Understanding Wald's Test for Exponential Families

Abstract: Anomalous behavior of Ward's test for exponential families is explained on the basis of the use of parameter estimates rather than null values in the variance part of the Wald expression. Illustration of the difficulty is made through use of single-parameter situations, albeit multiparameter situations were first cited to bring out the difficulty. Situations had been claimed in which statistical significance disappeared as data became more inconsistent with the null hypothesis. It is shown here that with use of the Wald test, according to the parameterization employed, the same data can be both consistent with all possible null values for the parameter and inconsistent with all possible values.

The Effect of Item Parameter Estimation Error on Decisions Made Using the Sequential Probability Ratio Test

Abstract: : A series of computer simulations were performed in order to observe the effects of item response theory(IRT)item parameter estimation error on decisions made using an IRT-based sequential probability ratio test. Specifically, the effects of such error on misclassification rates and the average number of items required for either a mastery(pass)or nonmastery(fail) decision were observed under varied SPRT conditions. These conditions include the a priori or nominal type I(alpha)and typeII(beta)error rates, the simple hypotheses tested by the SPRT procedure, and the composition of the item pool(specifically the a, b, and c parameters which characterized the items according to a three-parameter logistic model)used to administer the SPRT. The results of these simulations showed that these SPRT decisions are not greatly affected by this particular level of error in parameter estimates modeled in this study. Misclassification error rates were slightly greater when estimation error in the item parameters was present, but such differences appear to be negligible. Keywords: Adaptive testing.

Bibliography of Sequential Sampling Plans in Insect Pest Management Based on Wald's Sequential Probability Ratio Test

Abstract: This paper contains 65 references dealing with the development f sequential sampling plans in i ect pest management based on Wald's Sequential Probability Ratio Test (SPRT), 25 in forest entomology and 40 i agriculture entomology. The insect(s) sampled, whether the decision procedure was based on one or two SPRTs, and the mathematical distribution and probabilities of Type I (0'.) and Type II (/3) errors used to develop the SPRTs are also given for each sequential sampling plan. Sequential analysis includes all of those statistical procedures in which the sample size is not fixed prior t sampling. In sequential hypothesis testing, the number of observations taken in a given sample depends on the conclusiveness of evidence collected, observation by observation, for or against the null hypothesis or standard being tested. In other words, the final pattern and number of observations are not determined prior to sampling. The problem is to test the simple null hypothesis against some simple alternative hypothesis. The sample size is a random variable and is based on some stopping rule. Test procedures based on sequential techniques require, on the average, a much smaller sample size, i.e., only 40-60% as many observations, than is required by equally reliable procedures based on fixed sample size techniques. When observations are expensive, time consuming, r destructive, sequential procedures seem to have a distinct advantage. Sequential hypothesis testing can be used to classify popUlations or to accept or reject a specific standard. They are especially useful in surveys. Much of the theoretical literature in sequential hypothesis testing deals with Wald's Sequential Probability Ratio Test (SPRT) (Ghosh 1970; Wald 1943, 1945, 1947; Wetherill 1975). For literature reviews of the early work in sequential analysis, see Jackson (1960) and Johnson (1961). SPRT sampling plans have been used in insect pest management to aid in monitoring insect popUlations or their damage since Stark (1952) developed the procedure for sampling the lodgepole needleminer, R curvaria milleri Busck. To develop the decision boundaries of the SPRT, critical population levels for classification or decision-making (simple null and alternative hypotheses), probabilities (risk levels) for making Type I (0'.) and Type II (/3) errors, and underlying distribution of the variable or characteristic of interest are predetennined. Almost all SPRT insect sampling plans are based on the binomial, negative binomial, normal, and Poisson distributions. In this paper, we review agriculture and forest entomology applications of the SPRT. 'School of Natural Resources, The University of Michigan, Ann Arbor, MI48109-1115. 2School of Renewable Resources, The University of Arizona, Tucson, AZ 84721. 1 Fowler and Lynch: Bibliography of Sequential Sampling Plans in Insect Pest Manageme Published by ValpoScholar, 1987 166 THE GREAT LAKES ENTOMOLOGIST Vol. 20, NO.3 Table L Sequential probability ratio sampling plans for monitoring forest insect populations or their damage. Inseet No. of SPRTs cr, ~ values\" Binomial Distribution Larch sawfly (lves 1954) 2 d Larch sawfly (Ives and Prentice 1958) 2 d Hemlock sawfly (Hard 1971) I a,d,e Pine leaf adelgid (Dimond 1974) 2 d Nantucket pine tip moth (Waters 1974) I a,d Negative Binomial Distribution Spruce budworm (Morris 1954) 2 d Spruce budworm (Waters 1955) 2 d Forest tent caterpillar (Connola et at 1957) I c Red pine sawfly (Connola et aL 1959) I d Spruce budworm (Cole 1960) 2 d Spruce beetle (Knight 1960a) 1,2 d Mountain pine beetle (Knight 1960b) 2 d,e Cone and seed insects (Kozak 1964) 2 ? White grubs (lves and Warren 1965) 1,2 d Mountain pine beetle (Knight 1967) 2 c,d,e Douglas-fir tussock moth (Mason 1969) I a,d Spruce budworm (McKnight et aL 1970) 3 d,e,g Roundheaded borers (Safranyik and Raske 1970) 2 d Forest tent caterpillar (Shepherd and Brown 1971) 2 d Jack pine sawfly (Tostowaryk and McLeod 1972) 2 d Pine leaf adelgid (Dimond 1974) 2 d,f Spruce budworm (Waters 1974) 2 d Normal Distribution Lodgepole needleminer (Stark 1952) 2 b,d Lodgepole needleminer (Stevens and Stark 1962) 3 d Pine leaf ade1gid (Dimond 1974) 2 d Poisson Distribution Winter moth (Reeks 1956) 2 d Spruce budworm (Cole 1960) 1 d Saddled prominent eggs (Grimble and Kasile 1974) 1 c

On Hypothesis Testing in Distributed Sensor Networks.

Abstract: : In this report, some hypothesis testing problems in distributed sensor networks are considered. Optimum data fusion rules are obtained when the decision rules at the detectors are known. The distributed hypothesis testing problem with a distributed data fusion is solved using the Bayesian as well as the Neyman-Pearson approach. The decentralized Neyman-Pearson hypothesis testing problem and the sequential hypothesis testing problem for a tandem topology network are investigated. The distributed sequential probability ratio test problem is also studied. In all these problems, optimal strategies at each site and at each time stage are obtained. Keywords include: Fusion, Surveillance, Remote Receivers, Detection, and Estimation. (r.h.)

Minimax sequential tests of composite hypotheses on the drift of a Wiener process

Abstract: A Wiener process with unknown drift parameter μ is, beginning at O, observed continuously and one has to decide between the hypotheses μ≤0 and μ>0. For loss functions of the form sμr and linear cost functions one wants to determine a minimax sequential test. Generalizing the results of DeGroot (1960) a minimax test in the class of all symmetrical SPRT’s is given in an explicit form. On the other hand it is shown that this SPRT is, in general, no longer minimax in the class of all sequential tests.

Combined dynamic data analysis and process variable prediction approach for system fault detection

Abstract: A fault detection approach based on the combination of the Generalized Consistency Check and the Sequential Probability Ratio Test is developed and applied for validation of signals from process sensors. The basic methodology requires at least triple redundancy of a given measurement from like sensors and analytical measurements. The separate measurement of the signal mean value and the random fluctuation improves the reliability of fault identification and signal reconstruction. The diagnostics of the source of anomaly in a sub-system is performed by multivariate autoregressive modeling of the process signals and the analysis of resulting signatures.

Application of sequential probability ratio test to uranium enrichment verification

Abstract: The sequential probability ratio test is a statistical process capable of quickly and accurately verifying the uranium enrichment in the header pipes of uranium centrifuge enrichment facilities. The test minimizes the time required for a measurement, making a complete verification possible in 15–30 min.

Sequential Analysis for Diagnosing Diabetes

Abstract: The authors use a truncated sequential probability ratio test (SPRT) to diagnose diabetes. It is hypothesized that, for a given oral glucose tolerance test (OGTT), the differences between successive observations are more diagnostic than the observations alone. Using such differences in a SPRT, OGTT test data for 950 subjects are analyzed and thresholds for classifying diabetes and normal values are established. This sequential approach provides the same diagnosticity as that obtained by using the National Diabetic Data Group criteria, but it is more efficient. In particular, the procedure significantly reduces the sampling cost and average patient waiting time. Key words: sequential probability ratio test; diabetes; oral glucose tolerance test. (Med Decis Making 7:47-51, 1987)

Sequential testing on the rate of a counting process

Abstract: In this paper, optimality results are given for the problems of Bayesian and Wald sequential (simple, binary) hypothesis testing on the rate of a counting process. An explicit formula is given for the Bayes risk, and the system to solve for the exact optimal thresholds is also given.

The X2 process and its application to statistics

Abstract: One introduces central and noncentral chi-square processes and their descriptions in terms of finite-dimensional distributions. From this point of view one investigates a sequential test of the likelihood ratio.

A general inequality for the rejection probability of the sprt

Abstract: Let be i.i.d. random variables and SO that N is the stopping rule of Wald's SPRT, if the Zi are log-likelihood statistics. For the case that and an upper bound of order for is derived.