Showing papers on "Sequential probability ratio test published in 1986"

On the bias of maximum likelihood estimation following a sequential test

Abstract: SUMMARY Tlhe bias of maximum likelihood estimates calculated at the end of a sequential procedure is investigated For the two sequential designs considered in detail, the sequential probability ratio test and the triangular test, this bias is appreciable A method of calculating an adjusted estimate with reduced bias is described, and an approximation to the standard error of the new estimate is provided Examples of the implementation of the method are given, and its advantages and disadvantages relative to alternative approaches are discussed

Cusum quality control-multivariate approach

Abstract: A new multivariate approach to quality control is presented. On the basis of sequential probability ratio tests, a multivariate cumulative sum chart is derived. Using an approximation to the noncentral x2 distribution, a linear decision rule is obtained.

The VPRT: A Sequential Testing Procedure Dominating the SPRT

Abstract: Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed by Wald and Wolfowitz, it reduces to the one-observation-at-a-time sequential probability ratio test (SPRT). The ways in which the size and power of the VPRT depend upon the parameters of the decision problem are also examined.

An optimal property of the repeated significance test.

Abstract: We consider the problem of testing the sign of the drift θ of a Brownian motion. As in the preceding section we let the costs depend on the underlying parameter and choose it as “cθ2”, c>0. We show that a certain simple Bayes rule, which defines a repeated significance test, is optimal for the testing problem in a Bayes sense. The simple Bayes rules stop sampling when the posterior mass of the hypothesis or the alternative is too small.

Sequential Detection of a Positive Signal

Abstract: In this chapter we consider the problem of detecting a positive signal in additive noise. The observations are assumed to be discrete-time. Denote the observation random variables by Y1,Y2,…, the noise random variables by X1X2,…, and the signal by θ 1. We have to make a decision, based on the observations, whether the signal is absent or present.

A simulation study of three sequential methods for the comparison of two treatment groups when the response criterion is censored.

Abstract: Three recent sequential methods, group sequential analysis (GSA), the sequential probability ratio test (SPRT) and the triangular test (TT) are well suited to randomized clinical trials with a censored response criterion, as they do not require matched pairs of patients. We undertook a simulation study to investigate their statistical properties and to compare these three methods with the fixed-sample design. Our results suggest that (i) the three methods have the expected statistical properties for size and power; (ii) they allow an important reduction of the average number of events before stopping, except with GSA when there is no treatment difference; (iii) the triangular test (closed design) appears the optimal design, as the variance of the number of events is smaller than with the sequential probability ratio test (open design) and (iv) analysis after every twenty new events does not alter the statistical properties of these sequential methods and enhances their usefulness.

Sequential testing for exponential and pareto distributions

Abstract: This paper deals with the exact calculation of the decision boundaries for sequential probability ratio test for simple hypotheses and alternatives in the case of an exponential or a Pareto distribution. The calculations also enable one to give some idea of the mean sample size for the sequential test.

Detection of system failure by human operator (Part 2). The case of human controller.

Abstract: A model of failure detection behavior of human operator who is actively controlling a linear system or passively monitoring a display is proposed in this paper. Estimation and signal detection theory are applied to the development of the model. In this model, the failure detection mechanism is expressed by likelihood ratio function based on Wald's Sequential Probability Ratio Test; prediction of signals, visual cue and stick travel, recognized by operator is described by two autoregressive model each correspond to hypothesis H0 (system is normal) and to H1 (system is failed). The remarkable feature of this model is that proprioceptive infomlation generated by control manipulation is included in the model as available information for controller addition to visual display information. Detection time and detection accuracy predicted by the model are in good agreement with the experimental data over a wide range investigated for both case of controller and monitor.

Detection of system failure by human operator (Part 1) The case of monitor.

Abstract: Two types of model, which describes the human monitoring behabior in failure detection task are proposed in this paper. In the first model, detection behavior of human monitor is modeled by two linear optimal estimator (Kalman filter); the failure detection mechanism in the model is based on Wald's Sequential Probability Ratio Test (SPRT). The second model is composed of two fundamental function, that are, linear predictor using autoregressive model and Wald's SPRT. Digital simulations are carried out for checking on the accuracy of proposed models and illustrating the procedure to predict monitor's performance. The simulation results of detection time (the time needed for detecting the failure) and detection accuracy (frequency of miss and/or false alarm) are compared with data obtained from a set of failure detection experiments. From these comparison, it is found that the models can explain adequately the essential characteristics of human operator performing the monitoring task, and also important information for system failure detection by human monitor is rate of visual perception signal. The second model will be applied to a study of failure detection by human controller in a further paper.

Application of sequential methods in randomized clinical trials with censored response criteria

Abstract: In randomized clinical trials with a censored response criterion, it is common practice to perform interim analyses, especially for reasons of medical ethics. Sequential methods allow for repeated testing. Three sequential methods are well adapted to censored data: the group sequential analysis, the sequential probability ratio test and the triangular test. Among them, the triangular test has the best statistical properties. The influence of the frequency of the analyses on the statistical properties of sequential methods has been studied by simulation: sequential analyses need not be performed more frequently than interim analyses. Sequential methods have been applied to several randomized clinical trials. The results are briefly reported for two of them. The ability of the triangular test and of the sequential probability ratio test to reach conclusions early when there is no difference between two compared treatments is supported by these two examples. Moreover, careful patient follow-up must be planned in the protocol in order to reduce the time for data updating and to perform sequential analyses at the required frequency. It appears well-founded to propose the use of the triangular test in randomized clinical trials with a censored response criterion. Four types of analyses with different aims must be planned in the protocol.