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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.
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TL;DR: The Sequential Probability Ratio Test (SPRT) based on the number of arrivals during the service period provides a saving of up to fifty per cent in the sample size according to traditional methods.
Abstract: The objective of the control technique is to detect changes in traffic intensity of a queueing system as quickly as possible, then take appropriate corrective actions, and determine how much of a sample size is needed in the applications. Thus, the sequential probability ratio test provides a saving of up to fifty per cent in the sample size according to traditional methods. Furthermore, the use of SPRT is easy for observing only the number of customers in the system at successive departure periods, which are embedded Markov points. This paper gives a method on the control of traffic intensity of Hypoexponential and Coxian queueing systems. This method uses The Sequential Probability Ratio Test (SPRT) based on the number of arrivals during the service period. Two theorems are given on the subject and these theorems are proved. Numerical illustrations for each model are graphically given by using Matlab software.
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26 Jul 2005TL;DR: This paper describes the proposed change-detection test based on the Doob's Maximal Inequality and shows that it is an approximation of the sequential probability ratio test (SPRT).
Abstract: A martingale framework for concept change detection based on testing data exchangeability was recently proposed (Ho, 2005). In this paper, we describe the proposed change-detection test based on the Doob's Maximal Inequality and show that it is an approximation of the sequential probability ratio test (SPRT). The relationship between the threshold value used in the proposed test and its size and power is deduced from the approximation. The mean delay time before a change is detected is estimated using the average sample number of a SPRT. The performance of the test using various threshold values is examined on five different data stream scenarios simulated using two synthetic data sets. Finally, experimental results show that the test is effective in detecting changes in time-varying data streams simulated using three benchmark data sets.
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TL;DR: To remedy the defect of test delay in SPRT, a modifed SPRT method is prescnted in which means and variants are all changed.
Abstract: In this paper,the failure detection system based on the sequential probability ratio test (SPRT) is in-troduced.To remedy the defect of test delay in SPRT,a modifed SPRT method is prescnted in whichmeans and variants are all changed.Some analyses are also given.
1 citations
01 Jan 2010
TL;DR: Simple principles of neural computation are sufficient to approximate this form of optimality quite closely in a class of N-choice tasks involving response-terminated stimuli, while simultaneously accounting for the fundamental role of tuning curves in the neural repre- sentation of sensory stimuli.
Abstract: Hebbian learning for deciding optimally among many alternatives (almost) Patrick Simen (psimen@mathprincetonedu) Princeton Neuroscience Institute, Princeton University, Green Hall, Washington Rd, Princeton, NJ 08544 Tyler McMillen (tmcmillen@fullertonedu) Department of Mathematics, California State University at Fullerton, Fullerton, CA 92834 Sam Behseta (sbehseta@fullertonedu) Department of Mathematics, California State University at Fullerton, Fullerton, CA 92834 Abstract Reward-maximizing performance and neurally plausible mechanisms for achieving it have been completely character- ized for a general class of two-alternative decision making tasks, and data suggest that humans can implement the optimal procedure A greater number of alternatives complicates the analysis, but here too, analytical approximations to optimal- ity that are physically and psychologically plausible have been analyzed All of these analyses, however, leave critical open questions, two of which are the following: 1) How are near- optimal model parameterizations learned from experience? 2) How can sensory neurons’ broad tuning curves be incorporated into the aforementioned optimal performance theory, which as- sumes decisions are based only on the most informative neu- rons? We present a possible answer to all of these questions in the form of an extremely simple, reward-modulated Hebbian learning rule for weight updates in a neural network that learns to approximate the multi-hypothesis sequential probability ra- tio test Keywords: Hebbian learning; diffusion model; neural net- work; multi-hypothesis sequential test; sequential probability ratio test; speed-accuracy tradeoff; response time Introduction We examine the problem of maximizing earnings from a se- quence of N-alternative decisions about the identity of noisy stimuli, with N > 2 Our goal is to parameterize a simple neural circuit model whose behavior approximates optimal performance in such tasks, while simultaneously accounting for the fundamental role of tuning curves in the neural repre- sentation of sensory stimuli Throughout, we take ‘optimal’ to mean reward maximizing, and we assume that correct de- cisions earn rewards for the decider As we show, simple principles of neural computation are sufficient to approximate this form of optimality quite closely in a class of N-choice tasks involving response-terminated stimuli: that is, stimuli that provide information continuously until the time (the response time) at which participants decide for themselves when to stop observing and make a response This is somewhat surprising, given that a general decision policy that guarantees truly optimal performance cannot even be explicitly formulated for such tasks, as we discuss below N-choice, response-terminated decision tasks We assume that participants earn rewards for correct re- sponses, and earn less for errors (for simplicity, we assume errors earn nothing) In the simple tasks we consider, each stimulus type has a fixed prior probability within a block of trials, and the average signal-to-noise ratio of each stimulus is fixed The duration, rather than the number of trials, is also held fixed, and the distribution of response-to-stimulus inter- vals (RSIs) that delay the onset of the next stimulus after a response is stationary In this case, maximizing the rate of reward also maximizes the total reward Maximizing gains in this and a variety of similar tasks requires probabilistic inference While the importance of a principled inference process is widely understood in psy- chology and neuroscience, the complexity of optimal deci- sion policies in tasks with response-terminated stimuli (also known as ‘free response’ or ‘response time’ tasks) and N > 2 choices appears to be less well appreciated For 2-choice tasks of the type just described, reward- maximizing performance has been completely characterized (Bogacz et al, 2006): a sequential probability ratio test (SPRT) should be carried out in which the current likelihood ratio of the two hypotheses is multiplied by the probability of a given data sample under one hypothesis and divided by the probability of that data sample under the other hypothe- sis (equivalently, the logs of these probabilities can be added and subtracted, respectively — from now on, we will cast our discussion in terms of log-likelihoods) A response should be made when the resulting log-likelihood exceeds a fixed threshold (Wald & Wolfowitz, 1948) There exists an optimal starting point of the log-likelihood ratio (eg, 0, for equally likely stimuli) and an optimal separation between the two re- sponse thresholds (one greater and one less than zero) that de- pends on the signal-to-noise ratio (SNR) and the RSI (Bogacz et al, 2006) Gold and Shadlen (2001) have demonstrated that for systems consisting of a neuron/anti-neuron pair, each of which is tuned for one of the two stimulus types in a 2- choice task, the log-likelihood ratio is approximately propor- tional simply to the difference between the activations of the two neurons, suggesting an extremely simple neural imple- mentation of the SPRT In contrast, if the number of choices is greater than 2, the optimal policy for deciding based on accumulated informa- tion is nontrivial In particular, a natural (but definitely sub- optimal) approach to N-choice decision making is to com- pute the posterior probability of each of the N hypotheses, and then select whichever one first exceeds a fixed threshold In fact, the best decision is made when the entire set of pos- terior probabilities meets conditions that are nontrivial func-
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