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.

Unified Solutions of Integral Equations of SPRT for Exponential Random Variables

Abstract: The main characteristics of the sequential probability ratio test (SPRT) are described by acceptance probability (AP) and average sample number (ASN). The properties of the cumulative sum control procedure, CUSUM in short, which is a variant of the SPRT, are mainly determined by the average run length (ARL). The characteristics are obtained by solving Fredholm type integral equations. For the sake of mathematical simplicity, the models for the exponential random variables and the sum of the exponential random variables have been considered to test the effects of the design parameters of the SPRT and CUSUM. The solution of the integral equation for each case obtained by various methods in previous studies. In this article, we show that all the integral equations related to the characteristics of AP, ASN and ARL for the models of the exponential random variable and the sum of exponential random variables are defined in a framework, and their solutions are obtained precisely in a unified method. The...

Terrain Classification by Sequential Algorithms

Abstract: This paper presents several strategies developed for classification of terrain regions, based on the SPRT algorithm (Sequential Probability Ratio Test [1]). The SPRT algorithm is considered to be appropriate to two-class-classification and will be extended by the introduced strategies for resolution of multi-class-classification problems. A comparison between the classifiers is made and the classification scores are shown for statistic synthetic patterns as well as for remote sensing data taken from an aerial view over cultivated regions.

A sequential test procedure for monitoring a singular safety and efficacy outcome

Abstract: In this note we describe a modification of the sequential probability ratio test (SPRT) developed for the purpose of “flagging” a significant increase in the mortality rate of a treatment relative to a control while ensuring that double-blinding and the Type I error for the primary test of efficacy, also based on mortality rates, is not compromised. Key words: Interim analysis; safety monitoring; sequential testing. Trop J Pharm Res , December 2003; 2(2): 197-206

Practical Applications of Sequential Pattern Recognition Techniques

Abstract: Experiments involving sequential recognition tech­ niques and feature ordering schemes were performed on 23 feature samples of vowel spectra and 12 fea­ ture samples of remotely sensed agricultural crop data. Since each experiment dealt with two pattern classes, Wald's sequential probability ratio test was used. The test was implemented with both fixed and time-varying stopping boundaries. Feature ordering was accomplished by both dispersion analy­ sis and the divergence criterion. p(x|«,.)=[(2.)N/2 |K.| 1/2 ]-1 axp [-| (X M.)^1 (X It}] , i = 1,2 (2) then the above discriminant function yields D^X) log P( BI ) i log | K4 | |(X Mjf INTRODUCTION A pattern recognition system consists of a feature extractor and a classifier (see Figure l). The feature extractor makes measurements of salient characteristics of the input patterns. These are called feature measurements and based on them, the classifier assigns each input pattern to one of the possible pattern classes. We are concerned with those classifiers that are sequential in nature. That is, those that utilize the feature measurements one at a time in performing the classification. The advantages of sequential techniques are realized when the cost of taking feature measurements is high or the speed of classification is important. TECHNIQUES The problem of classifying patterns from two classes is formulated here as a statistical decision pro­ blem. N feature measurements, denoted by X^X^,*-*, Xjj, are given for each pattern. The two pattern classes are called u>j_ and u£. For each pattern class u>j, j = 1,2, it is assumed that the probabili­ ty density function of this feature vector X,p(XJ u>.)> is known* A /^•? *J A discriminant function, Di (X) = log 1,2 (1) is now defined which can easily be implemented by a Bayes classifyer. When DI(X) >Dj(X), i,j = 1,2, then X is said to be in class o^. When p(X | u^) i a 1,2, is a nmltivariate Gaussian density function with mean vector % and covariance matrix B, i.e., (5) This is the discriminant function used as the samples to be classified are assumed to be Gaussian in nature. In all recognition schemes used in this paper, the training procedure has: been to compute M^ and K. from the first 75 sannleB of each clsss. x For each sample to be classified, B^ and Bg were computed. If D^X) B2: (X) was positive, tte sample was placed in class. 1 and, if" negjative in class 2. In the above procedure it is necessaxy to me •' measurements from, each, pattern to be classified. Quite often this is inconvenient (because of «r time consumption) and it becomes desirable to a scheme using less feature measurements* Mien there are only two pattern classes to be recognised* Wald's sequential probability ratio "best (SRf) can be applied. Here the feature measurements can De taken one at a time* At the nth stageof the sequential process, that is, after the nth ftefcure measurement is taken, the classifier computes the sequential probability ratio