Sequential Probability-ratio Test

Perceptual decision-making frequently requires accumulating noisy sensory inputs as evidence in order to execute rapid, reliable choices. Neural recordings from the lateral intra-parietal area in humans and primates performing perceptual decision-making tasks highlighted evidence accumulation mechanisms, often modeled as drifted diffusions. In those experiments, participants were exposed to computer-generated randomly fluctuating stimuli whose motion is not linked to any physical phenomenon. To better characterize the statistical processes underlying human decision-making, we performed experiments where human participants visualized fluctuations of physical nonequilibrium stationary states, and we analyzed responses in the context of stochastic thermodynamics. A total of forty fiveparticipants viewed hundreds of movies of a particle endowed with drifted Brownian dynamics and were tasked with judging the motion as leftward or rightward in a quick and reliable manner. Overall, the results uncover fundamental performance limits, consistent with recently established thermodynamic trade-offs (uncertainty relations, TURs) involving speed, accuracy, and dissipation; specifically, lower rates of entropy production lead to longer decision times. Moreover, to achieve a given level of observed accuracy, participants require more time than predicted by Wald's optimal sequential probability ratio test, indicating suboptimal integration of available information. In view of such suboptimality, we develop an alternative account equipped with non-Markovian evidence integration with a memory time constant, and find tight fits. Our results suggest that humans adapt their memory relaxation time to the rate of dissipation of the observed phenomenon, favouring memory over momentary evidence for effective decisions in scenarios where stimuli are far from equilibrium. Furthermore, we identify the effects of the environmental stability on decisionmaking performance and memory by comparing the results of the two sets of experiments: blocked (stationary) versus intermixed (non-stationary) conditions. Our study illustrates that perceptual psychophysics using stimuli rooted in nonequilibrium physical processes provides a robust platform for understanding how the human brain makes decisions on stochastic information inputs.

We present a Neyman-Pearson composite hypothesis test (NPCHT) and a Wald's sequential probability ratio test (WSPRT) to detect primary user emulation attacks (PUEA) in cognitive radio networks. Most approaches in the literature on PUEA assume the presence of underlying sensor networks for localization of the malicious nodes. There are no analytical studies available in the literature to study PUEA in the presence of multiple malicious users in fading wireless environments. We present an NPCHT and WSPRT based analysis to detect PUEA in fading wireless channels in the presence of multiple randomly located malicious users. We show that there is a range of network radii in which PUEA are most successful. Results also show that for the same desired threshold on the probability of missing the primary, WSPRT can achieve a probability of successful PUEA 50% less than that obtained by NPCHT.

The data or software is getting increased in the internet day by day, and a vibrant research is going on towards the software reliability. In this regard, there is a need for the people to have the tools/mechanism to detect whether the software is reliable or not. Several methods came into existence to assess the software reliability. In Classical Hypothesis testing, it takes more time to come to a decision because the conclusions can be drawn only after collecting the large amounts of data. But by adopting Sequential Analysis of Statistical science it can be decided very quickly whether the software which is developed is reliable or unreliable. To implement this, Sequential Probability Ratio Test (SPRT) is applied for Burr Type XII model.

Rapid growth of software usage enforces us to access the software reliability, a critical task in the development of a software system. Various models are adopted to assess the software reliability. In this paper a well known test procedure of statistical science called as Sequential Probability Ratio Test (SPRT) is adopted for Pareto Type IV model in assessing the reliability of developed software. It requires considerably less number of observations when compared with the other existing testing procedures. In Classical Hypothesis first of all testing volumes of data is to be collected and later the conclusions are to be drawn which may take more time. Hence Sequential Analysis of Statistical Science could be adopted to decide upon the reliable / unreliable of the developed software very quickly. Besides the present paper proposes the performance of SPRT on Interval domain data using Pareto type IV model and analyzed the results by applying on 6 data sets. The Maximum Likelihood Es...

In this paper an attempt has been made to construct CSCC under inspection error for Binomial Parameters when underlying distribution is Poisson. We have investigated distance d and angle ф along with ARL of CUSUM chart under inspection error.

We consider the problem of sensor selection for time-optimal detection of a hypothesis. We consider a group of sensors transmitting their observations to a fusion center. The fusion center considers the output of only one randomly chosen sensor at the time, and performs a sequential hypothesis test. We study sequential probability ratio test with randomized sensor selection strategy. We present optimal open loop sensor selection policies for three distinct cost functions. We utilize these policies to develop an adaptive sensor selection policy. We rigorously characterize the performance of the adaptive policy and show that it asymptotically achieves the performance of the globally optimal policy.

One of the most significant problems in the area of 3D range image processing is that of segmentation and classification from 3D laser range data, especially in real-time. In this work we introduce a novel multi-layer approach to the classification of 3D laser scan data. In particular, we build a hierarchical framework of online detection and identification procedures drawn from sequential analysis namely the CUSUM (Cumulative Sum) and SPRT (Sequential Probability Ratio Test), both of which are low complexity algorithms. Each layer of algorithms builds upon the decisions made at the previous stage thus providing a robust framework of online decision making. In our new framework we are not only able to classify in coarse classes such as vertical, horizontal and/or vegetation but to also identify objects characterized by more subtle or gradual changes such as curbs or steps. Moreover, our new multi-layer approach combines information across scanlines and results in more accurate decision making. We perform experiments in complex urban scenes and provide quantitative results.

One of the most significant problems in the area of 3D range image processing is that of segmentation and classification from 3D laser range data, especially in real-time. In this work we introduce a novel multi-layer approach to the classification of 3D laser scan data. In particular, we build a hierarchical framework of online detection and identification procedures drawn from sequential analysis namely the CUSUM (Cumulative Sum) and SPRT (Sequential Probability Ratio Test), both of which are low complexity algorithms. Each layer of algorithms builds upon the decisions made at the previous stage thus providing a robust framework of online decision making. In our new framework we are not only able to classify in coarse classes such as vertical, horizontal and/or vegetation but to also identify objects characterized by more subtle or gradual changes such as curbs or steps. Moreover, our new multi-layer approach combines information across scanlines and results in more accurate decision making. We perform experiments in complex urban scenes and provide quantitative results.

Laser range scanners have now the ability to acquire millions of 3D points of highly detailed and geometrically complex urban sites, opening new avenues of exploration in modeling urban environments. In the traditional modeling pipeline, range scans are processed off-line after acquisition. The slow sequential acquisition though is a bottleneck. The goal of our work is to alleviate this bottleneck, by exploiting the sequential nature of the data acquisition process. We have developed novel online algorithms, never before used in laser range scanning, that perform data classification on-the-fly as data is being acquired. These algorithms are extremely efficient, and can be potentially integrated with the scanner's hardware, rendering a sensor that not only acquires but also intelligently processes and classifies the scene points. This sensor, armed with the proposed algorithms, can classify 3D points in real-time as being in vegetation vs. non-vegetation regions, or in horizontal vs. vertical regions. The former classification is possible by the implementation of sequential algorithms through a hidden Markov model (HMM) formulation, and the latter through the use of a combination of cleverly designed sequential detection algorithms. We envision an arsenal of algorithms of this type to be developed in the future.

A general problem of testing two simple hypotheses about the distribution of a discrete-time stochastic process is considered. The main goal is to minimize an average sample number over all sequential tests whose error probabilities do not exceed some prescribed levels. As a criterion of minimization, the average sample number under a third hypothesis is used (modified Kiefer-Weiss problem). For a class of sequential testing problems, the structure of optimal sequential tests is characterized. An application to the Kiefer-Weiss problem for discrete-time stochastic processes is proposed. As another application, the structure of Bayes sequential tests for two composite hypotheses, with a fixed cost per observation, is given. The results are also applied for finding optimal sequential tests for discrete-time Markov processes. In a particular case of testing two simple hypotheses about a location parameter of an autoregressive process of order 1, it is shown that the sequential probability ratio test has the Wald-Wolfowitz optimality property.

Sequential analysis is now commonly used for post-market drug and vaccine safety surveillance, and a Poisson stochastic process is typically used for rare adverse events. The conditional maximized sequential probability ratio test, CMaxSPRT, is a powerful tool when there is uncertainty in the estimated expected counts under the null hypothesis. This paper derives exact critical values for CMaxSPRT, as well as statistical power and expected time to signal. This is done for both continuous and group sequential analysis, and for different rejection boundaries. It is also shown how to adjust for covariates in the sequential design. A table of critical values is provided for selected parameters and rejection boundaries, while new functions in the R Sequential package can be used for other calculations. In addition, the method is illustrated for monitoring adverse events after pediarix vaccination data.

Summary For sequential analysis hypothesis testing, various alpha spending functions have been proposed. Given a prespecified overall alpha level and power, we derive the optimal alpha spending function that minimizes the expected time to signal for continuous as well as group sequential analysis. If there is also a restriction on the maximum sample size or on the expected sample size, we do the same. Alternatively, for fixed overall alpha, power and expected time to signal, we derive the optimal alpha spending function that minimizes the expected sample size. The method constructs alpha spending functions that are uniformly better than any other method, such as the classical Wald, Pocock or O’Brien–Fleming methods. The results are based on exact calculations using linear programming. All numerical examples were run by using the R Sequential package.

Sequential analysis is now commonly used for post-market drug and vaccine safety surveillance, and a Poisson stochastic process is typically used for rare adverse events. The conditional maximized sequential probability ratio test, CMaxSPRT, is a powerful tool when there is uncertainty in the estimated expected counts under the null hypothesis. This paper derives exact critical values for CMaxSPRT, as well as statistical power and expected time to signal. This is done for both continuous and group sequential analysis, and for different rejection boundaries. It is also shown how to adjust for covariates in the sequential design. A table of critical values is provided for selected parameters and rejection boundaries, while new functions in the R Sequential package can be used for other calculations. In addition, the method is illustrated for monitoring adverse events after pediarix vaccination data.

MANETs must be adaptive. In this work, we propose detection schemes that are suitable to detect in-band wormhole attacks. The first detection scheme uses the Sequential Probability Ratio Test (SPRT). The SPRT has been proven to be an optimal detection test when the probability distributions of both normal and abnormal behaviors are given. Furthermore, we introduce non-parametric methods, which require no training and are more adaptive to mobile scenarios. The proposed detection schemes are implemented and evaluated using a 48-node testbed and a mobile adhoc network emulator at the Army Research Lab. The performance and detection accuracy of various schemes are compared, especially in the presence of congestion. We provide tradeoffs analyses among detection latency and probabilities of false alarms and missed detection.

Sequential likelihood ratio testing is found to be most powerful in sequential studies with early stopping rules when grouped data come from the one-parameter exponential family. First, to obtain this elusive result, the probability measure of a group sequential design is constructed with support for all possible outcome events, as is useful for designing an experiment prior to having data. This construction identifies impossible events that are not part of the support. The overall probability distribution is dissected into stage specific components. These components are sub-densities of interim test statistics first described by Armitage, that are commonly used to create stopping boundaries given an α-spending function and a set of interim analysis times. Likelihood expressions conditional on reaching a stage are given to connect pieces of the probability anatomy together. The reduction of the support caused by the adoption of an early stopping rule induces sequential truncation (not nesting) in the probability distributions of possible events. Multiple testing induces mixtures on the adapted support. Even asymptotic distributions of inferential statistics are mixtures of truncated distributions. In contrast to the classical result on local asymptotic normality , statistics that are asymptotically normal without stopping options have asymptotic distributions that are mixtures of truncated normal distributions under local alternatives with stopping options; under fixed alternatives, asymptotic distributions of test statistics are degenerate. Keywords Adaptive designs • adapted support • group sequential designs • local asymptotics • interim hypothesis testing • likelihood ratio tests

Nations strive to avoid losing revenue and human lives through long traffic snarl ups and frequent accidents on the roads. For this reason Considerations must be made to increase the number of lanes or even better to change from a single carriage to more robust dual carriages. However number of lanes and dual carriage alone serve no purpose for the accidents frequencies and traffic snarl ups that appear to defy even the most modern and sophisticated highway designs. Service time for traffic using such roads would need to be improved. Clearly therefore a numerical model is necessary for the road designers and developers to help understand road improvement demands. In this paper we establish the queue model for the Nakuru – Salgaa road Stretch and test the model with real data from the Case Study. Data is collected between the Soil- junction and the Total junction. We derive the arrival rate, service rate, utilization rate and the probability of Bulking using the M/M/1 queuing model. ...

Manutenções preventivas de sensores asseguram o seu funcionamento correto durante um certo período de tempo, mas não garantem que eles permaneçam sem defeito por outros períodos, além de eventualmente serem desnecessárias. Em plantas industriais, a análise dos sinais fornecidos pelos sensores que monitoram os processos de produção é uma tarefa difícil em virtude da grande dimensão dos dados. Portanto uma estratégia de monitoramento e correção on-line para múltiplos sensores é necessária. Este trabalho propõe a utilização de Redes Neurais Auto-Associativas com Treinamento Robusto Modificado e do Teste Seqüencial da Razão de Probabilidade (SPRT) em um sistema de monitoramento para auto-correção on-line e detecção de anomalias nas medidas geradas por um grande número de sensores. Diferentemente de modelos existentes, o sistema proposto visa a utilizar somente uma RNAAM para reconstruir os sinais dos sensores com falha. O modelo é avaliado com uma base dados que contém as medidas de sen...

An improvement of IEC-61124 in the field of a sequential probability ratio test (SPRT) is proposed. The current standard does not provide a proper solution for modern industry's needs, and the test plans are not up-to-date with the knowledge in the area of sequential tests. The advantages of the proposed version are reflected by the efficacy and accuracy of the tests, the wider range of the ready to use test's parameters, and available data regarding the test's characteristics. The proposed version is a significant improvement over the existing one. The changes will extend the use of SPRT and this standard. The proposal for updating the standard has been accepted to the work-plan of TC56 of IEC.

The present study deals with the planning methodology of tests in which the parameters of two exponentially-distributed random variables are compared. The largest application field of such tests is reliability checking of electronics equipment. They are highly cost-intensive, and the requirements as to their resolution capability become stricter all the time. Hence the topicality and importance of an optimal plan permitting decisions at a given risk level on the basis of a minimal sample size. Such comparison tests are required for example in assessing the desirability of replacing a "basic" object whose reliability is unknown, by a "new" one; or when the influence of test conditions on the results has to be eliminated. This is the case when an electronics manufacturing process is transferred to another site and the product undergoes accelerated testing. Recently, equipment and methods were developed for accelerated product testing through continuous observation of a population of copies and replacement of failed objects without interrupting the test. For such a procedure, the sequential approach is a feasible and efficacious solution with substantial shortening -on the average -of the test duration (see e.g. . In these circumstances there is high uncertainty in the acceleration factor, with the same effect on the estimated reliability parameters of the product. This drawback can be remedied by recourse to comparison testing. The latter serves also for reliability matching in objects of the same design and different origins, or a redesigned product versus its earlier counterpart, or different products with the same function (see e.g. Kececioglu, 2002). The exponential nature of the Time Between Failures (TBF) of repairable objects, or the time to failure of non-repairable ones -is noted in the extensive literature on the reliability of electronic equipment (Kececioglu

The sequential hypothesis testing problem is a class of statistical analyses where the sample size is not fixed in advance. Instead, the decision-process takes in new observations sequentially to make real-time decisions for testing an alternative hypothesis against a null hypothesis until some stopping criterion is satisfied. In many common applications of sequential hypothesis testing, the data can be highly sensitive and may require privacy protection; for example, sequential hypothesis testing is used in clinical trials, where doctors sequentially collect data from patients and must determine when to stop recruiting patients and whether the treatment is effective. The field of differential privacy has been developed to offer data analysis tools with strong privacy guarantees, and has been commonly applied to machine learning and statistical tasks. In this work, we study the sequential hypothesis testing problem under a slight variant of differential privacy, known as Renyi differential privacy. We present a new private algorithm based on Wald's Sequential Probability Ratio Test (SPRT) that also gives strong theoretical privacy guarantees. We provide theoretical analysis on statistical performance measured by Type I and Type II error as well as the expected sample size. We also empirically validate our theoretical results on several synthetic databases, showing that our algorithms also perform well in practice. Unlike previous work in private hypothesis testing that focused only on the classical fixed sample setting, our results in the sequential setting allow a conclusion to be reached much earlier, and thus saving the cost of collecting additional samples.

The sequential hypothesis testing problem is a class of statistical analyses where the sample size is not fixed in advance. Instead, the decision-process takes in new observations sequentially to make real-time decisions for testing an alternative hypothesis against a null hypothesis until some stopping criterion is satisfied. In many common applications of sequential hypothesis testing, the data can be highly sensitive and may require privacy protection; for example, sequential hypothesis testing is used in clinical trials, where doctors sequentially collect data from patients and must determine when to stop recruiting patients and whether the treatment is effective. The field of differential privacy has been developed to offer data analysis tools with strong privacy guarantees, and has been commonly applied to machine learning and statistical tasks. In this work, we study the sequential hypothesis testing problem under a slight variant of differential privacy, known as Renyi differential privacy. We present a new private algorithm based on Wald's Sequential Probability Ratio Test (SPRT) that also gives strong theoretical privacy guarantees. We provide theoretical analysis on statistical performance measured by Type I and Type II error as well as the expected sample size. We also empirically validate our theoretical results on several synthetic databases, showing that our algorithms also perform well in practice. Unlike previous work in private hypothesis testing that focused only on the classical fixed sample setting, our results in the sequential setting allow a conclusion to be reached much earlier, and thus saving the cost of collecting additional samples.

The change-point detection problem seeks to identify distributional changes in streams of data. Increasingly, tools for change-point detection are applied in settings where data may be highly sensitive and formal privacy guarantees are required, such as identifying disease outbreaks based on hospital records, or IoT devices detecting activity within a home. Differential privacy has emerged as a powerful technique for enabling data analysis while preventing information leakage about individuals. Much of the prior work on change-point detection---including the only private algorithms for this problem---requires complete knowledge of the pre-change and post-change distributions. However, this assumption is not realistic for many practical applications of interest. This work develops differentially private algorithms for solving the change-point problem when the data distributions are unknown. Additionally, the data may be sampled from distributions that change smoothly over time, rathe...

This paper has supplementary downloadable material available at . The supplemental material provides a generalization of the paper results to a general observation model and proofs to some of the mathematical statements. The total size of the files is 561 KB..

This paper has supplementary downloadable material available at . The supplemental material provides a generalization of the paper results to a general observation model and proofs to some of the mathematical statements. The total size of the files is 561 KB..

Wald's [A. Wald, Sequential Analysis, Wiley, New York, 1947] sequential probability ratio test (SPRT) and group sequential probability ratio test (GSPRT) remain relevant in addressing a wide range of practical problems. The area of clinical trials owes a great debt to the theory and methodologies of SPRT and GSPRT. In recent years, there has been a surge of practical applications of these methodologies in many areas including low frequency sonar detection, tracking of signals, early detection of abrupt changes in signals, computer simulations, agricultural sciences, pest management, educational testing, economics, and finance. But, obviously, there are circumstances where sampling one observation at a time may not be practical. In contexts of monitoring "inventory" or "queues", observations may appear sequentially but in groups where the group sizes may be ideally treated as random variables themselves. For example, one may sequentially record the number of stopped cars (M i ) and the number of cars ( M i j=1 X i j ) without "working brake lights" when a traffic signal changes from green to red, i = 1, 2, . . .. This can be easily accomplished since every "working brake light" must glow bright red when a driver applies brakes. In this example, one notes that (i) it may be reasonable to model M i 's as random, but (ii) it would appear impossible to record data sequentially on the status of brake lights (that is, X i j = 0 or 1) individually for car #1, and then for car #2, and so on when a group of cars rush to stop at an intersection! In order to address these kinds of situations, we start with an analog of the concept of a best "fixedsample-size" test based on data {M i , X i1 , . . . , X i M i , i = 1, . . . , k}. Then, a random sequential probability ratio test (RSPRT) is developed for deciding between a simple null hypothesis and a simple alternative hypothesis with preassigned Type I and II errors α, β. The RSPRT and the best "fixed-sample-size" test with k ≡ k min associated with the same errors α, β are compared. Illustrations of RSPRT include a oneparameter exponential family followed by substantive computer simulations that lead to a broad set of guidelines. Two real applications and data analysis are highlighted.

Incomplete data is a common complication in applied research. This complication has been mostly ignored by researchers using sequential test methodology. In this article we bring together the theoretical and practical benefits of both fields by combining them together. This is a first attempt to develop methodology for the sequential probability ratio test when data are incomplete.

We consider a sequence of independent observations from a N distribution with 0 < c < . Here, remains unknown. Given independent observations X 1 X n from N , the statistic T = n i=1 X 2 i is complete and sufficient for and T has a noncentral 2 n with = n when is the true parameter value. The problem is one of testing H 0 : = 0 vs. H 1 : = 1 where 0 1 0 = 1 are specified positive numbers with target type-I and type-II error probabilities 0 < < 1 and 0 < < 1, respectively, + < 1. We first adapt Wald's sequential probability ratio test (SPRT) and describe some crucial characteristics. However, observations may instead arrive with random group sizes sequentially rather than one at a time. Thus, as a follow-up, next we implement Mukhopadhyay and de Silva's (2008) notion of a random SPRT (RSPRT). In the case of both SPRT and RSPRT, we address the issue of truncation. The proposed methodologies are illustrated with appropriate statistical data analysis. In the end, we briefly explore the problem of confidence interval estimation for the parameter after termination of the SPRT.

The Wiener diffusion model (WDM) for 2-alternative tasks assumes that sensory information is integrated over time. Recent neurophysiological studies have found neural correlates of this integration process in certain neuronal populations. This paper analyses the properties of the WDM with two different boundary conditions in decision making tasks in which the time of response is indicated by a cue. A dual reflecting boundary mechanism is proposed and its performance is compared with a well-established absorbing boundary in the cases of the WDM, the WDM with extensions, and the WDM with prior probability. The two types of boundary influence the dynamics of the model and introduce differential weighting of evidence. Comparisons with Ornstein-Uhlenbeck models are also done, and it is shown that the WDM with both types of boundaries achieves similar performance and produce similar fits to existing behavioural data. Further studies are proposed to distinguish which boundary mechanism is more consistent with experimental data.

The evaluation and learning of classifiers is of particular importance in several computer security applications such as intrusion detection systems (IDSs), spam filters, and watermarking of documents for fingerprinting or traitor tracing. There are however relevant considerations that are sometimes ignored by researchers that apply machine learning techniques for security related problems. In this work we identify and work on two problems that seem prevalent in security-related applications. The first problem is the usually large class imbalance between normal events and attack events. We address this problem with a unifying view of different proposed metrics, and with the introduction of Bayesian Receiver Operating Characteristic (B-ROC) curves. The second problem to consider is the fact that the classifier or learning rule will be deployed in an adversarial environment. This implies that good performance on average might not be a good performance measure, but rather we look for good performance under the worst type of adversarial attacks. We work on a general methodology that we apply for the design and evaluation of IDSs and Watermarking applications. 1 approaches p 0 . As g decreases, more mass of p * 1 concentrated towards the smaller backoff values.

This report describes a study comparing the classification results obtained from a one-parameter and three-parameter logistic based tailored testing procedure used in conjunction with Wald's sequential probability ratio test (SPEY). Eighty-eight college students were classified into four grade categories using achievement test results obtained from tailored testing pnacedures based on maximum information item selection and maximum likelihood ability estimation. Tests were terminated using the SPRT procedure. The results of the study showed that the three-parameter logistic based procedure had higher decision consistency than the one-parameter based procedure when classifications were repeated after one week. Both procedures required fewer items for classification into grade categories than a traditional test over the same materia.L. The three-parameter procedure required the fewest items of all, using -n average of 12 to 13 items to assign a grade. (Author)

proposed a widely used method of applying the sequential probability ratio test (SPRT; to computerized classification testing with item response theory. This method formulates the classification problem as a point hypothesis that an examinee's ability, θ, is equal to a point, θ 1, below the cutscore or a point, θ 2, above the cutscore. The current paper argues that the actual goal of classification testing is a composite hypothesis that an examinee's ability θ is in the region of θ either above or below the cutscore, rather than equal to an arbitrarily defined point. A formulation of the SPRT to reflect this testing paradigm is proposed.

Computer-based testing can be used to classify examinees into mutually exclusive groups. Currently, the predominant psychometric algorithm for designing computerized classification tests (CCTs) is the sequential probability ratio test (SPRT; based on item response theory (IRT). The SPRT has been shown to be more efficient than confidence intervals around θ estimates as a method for CCT delivery . More recently, it was demonstrated that the SPRT, which only uses fixed values, is less efficient than a generalized form which tests whether a given examinee's θ is below θ 1 or above θ 2 . This formulation allows the indifference region to vary based on observed data. Moreover, this composite hypothesis formulation better represents the conceptual purpose of the test, which is to test whether θ is above or below the cutscore. The purpose of this study was to explore the specifications of the new generalized likelihood ratio (GLR; . As with the SPRT, the efficiency of the procedure depends on the nominal error rates and the distance between θ 1 and θ 2 . This study utilized a monte-carlo approach, with 10,000 examinees simulated under each condition, to evaluate differences in efficiency and accuracy due to hypothesis structure, nominal error rate, and indifference region size. The GLR was always at least as efficient as the fixed-point SPRT while maintaining equivalent levels of accuracy.

Reckase (1983) proposed a widely used method,ofapplying the sequential probability ratio test (SPRT; Wald, 1947) to computerized classification testing withitem response theory. This method formulates the classification problem as a point hypothesis that an examinee’s ability, θ, is equal to a point, θ1,below the cutscore or a point, θ2,above the cutscore. The current paper argues that the actual goal

In this paper, we propose a sequential probability ratio test (SPRT) to overcome the problem of limited samples in studies related to complex genetic diseases. The results of this novel approach are compared with the ones obtained from the traditional transmission disequilibrium test (TDT) on simulated data. Although TDT classifies single-nucleotide polymorphisms (SNPs) to only two groups (SNPs associated with the disease and the others), SPRT has the flexibility of assigning SNPs to a third group, that is, those for which we do not have enough evidence and should keep sampling. It is shown that SPRT results in smaller ratios of false positives and negatives, as well as better accuracy and sensitivity values for classifying SNPs when compared with TDT. By using SPRT, data with small sample size become usable for an accurate association analysis.

Family-based designs are commonly used in genetic association studies to locate markers associated with diseases. It is a challenging task to collect a large enough sample size, perform a statistical test, and obtain the desired statistical power. The sequential probability ratio test (SPRT) was introduced to overcome the limited sample size problem. However, the drawback of SPRT is that, for the sake of accuracy, the test leaves many markers in a gray zone meaning "no decision". In this article, we propose a novel approach: a sequential probability ratio test 'plus' (SPRT +) to reduce the number of these gray zone markers. Using simulated data, the results of SPRT + are compared with the results of SPRT. SPRT + shows a promising overall performance in identifying highly and moderately associated markers in the correct association region without a loss of accuracy.

In this paper sequential detection problems are treated in the context of cognitive biases. We present a general bias model and we design a generalized sequential probability ratio test (GSPRT) to mitigate the bias impact following a composite hypothesis testing approach. We also derive an optimal ordering of the incoming observations for fast detection defined in terms of the average sample number (ASN) of observations. We verify through numerical analysis that the designed detector fulfills the time and accuracy requirements. Results show that its performance emulates that of a Bayesian detector optimized for fast sequential detection in absence of biases.

A general group sequential statistical decision model is investigated. Using a Bayesian approach and Bayesian dynamic programming, we exanaine structural properties of the cost functions and of optimal sampling procedures. In particular, we consider variablesample-size-sequential probability ratio tests and show that the so-called onion-skins conjecture is false. 1.

There are several methods to combine and extend the continuous lifetime models to increase their flexibility and generality. Here we proposed a new lifetime distribution model with two parameters. Various lifetime distribution representations related to this model are derived and presented with their properties. Several Statistical measures and their properties are also studied. The method maximum likelihood estimator is discussed. Simulation studies are performed to assess the finite sample performance of the maximum likelihood estimators (MLEs) of the parameters. In the end, to show the flexibility of this distribution, an application using real data sets is presented

The goal of this study is the introduction and experimental assessment of a sequential probability ratio test framework for vibration-based structural health monitoring. This framework is based on a combination of binary and multihypothesis versions of the statistically optimal sequential probability ratio test and employs the residual sequences obtained through a single stochastic time series model of the healthy structure. The full list of properties and capabilities of the sequential probability ratio test is for the first time presented and explored in the context of vibration-based damage diagnosis. The approach postulated in this framework is shown to achieve early and robust damage detection, identification (classification), and quantification based on predetermined sampling plans, which are both analytically and experimentally compared and assessed. The framework’s performance is determined a priori via the use of the analytical expressions of the operating characteristic an...

Diagnostic classification models (DCMs) can provide multidimensional diagnostic feedback about students' mastery levels of knowledge components or attributes. One advantage of using DCMs is the ability to accurately and reliably classify students into mastery levels with a relatively small number of items per attribute. Combining DCMs with computerized adaptive testing can further shorten a test by strategically administering different items to different examinees. Current studies about item selection methods select the next item to increase the classification accuracy for the overall attribute profile and have been explored with item pools that have equal attribute information for all attributes on the assessment. In practice, the attribute information for diagnostic assessment is usually not balanced in the item pool. We propose a new attribute-level item selection method based on Cognitive Diagnostic Index at the Attribute Level (CDI_A; that helps balance classification accuracies among attributes on an assessment when item pools are not balanced across attributes. We conducted simulation studies to compare the performance of the CDI_A to other leading item selection methods; a pair of studies was theoretically based, and the last study was empirically based. Results showed that the new method can increase the classification accuracy and the reliability for attributes with weaker items in the item pool by administering more items to measure the attribute. Although using fewer items, the method retains reasonable accuracies for the attributes with stronger items in the pool. Thus, the CDI_A provides a trade-off to maintain an acceptable level of estimation accuracy for all attributes.

Nations strive to avoid losing revenue and human lives through long traffic snarl ups and frequent accidents on the roads. For this reason Considerations must be made to increase the number of lanes or even better to change from a single carriage to more robust dual carriages. However number of lanes and dual carriage alone serve no purpose for the accidents frequencies and traffic snarl ups that appear to defy even the most modern and sophisticated highway designs. Service time for traffic using such roads would need to be improved. Clearly therefore a numerical model is necessary for the road designers and developers to help understand road improvement demands. In this paper we establish the queue model for the Nakuru – Salgaa road Stretch and test the model with real data from the Case Study. Data is collected between the Soil- junction and the Total junction. We derive the arrival rate, service rate, utilization rate and the probability of Bulking using the M/M/1 queuing model. ...

Modified Sequential probability ratio test (MSPRT) technique helps to increase the reliability and speed of stabilization detection on the Non homogenous poison process (NHPP) with the maximum number of software faults to reduce error between the consumer risk and producer risk, with the time cumulative system of hours. Modified sequential probability ratio test can be used to reduce the average sample size required to perform statistical hypothesis tests at specified levels of significance and power. The proposed result suggests MSPRT along with maximum number of faults contained in software would be useful in speeding up decision making while dealings error in a software reliability weekly index, we show the graphical performance of the MSPRT and average sample number (ASN).