Showing papers on "Sequential probability ratio test published in 1998"

System for surveillance of spectral signals

Abstract: A method and system for monitoring at least one of a system, a process and a data source. A method and system have been developed for carrying out surveillance, testing and modification of an ongoing process or other source of data, such as a spectroscopic examination. A signal from the system under surveillance is collected and compared with a reference signal, a frequency domain transformation carried out for the system signal and reference signal, a frequency domain difference function established. The process is then repeated until a full range of data is accumulated over the time domain and a Sequential Probability Ratio Test (“SPRT”) methodology applied to determine a three-dimensional surface plot characteristic of the operating state of the system under surveillance.

Asymptotically optimal sequential tests for nonhomogeneous processes

Abstract: It is shown that under certain conditions the matrix sequential probability ratio test (SPRT) and the combinations of "rejecting" SPRTs minimize all moments of the stopping time distribution in the problem of sequential testing of several simple hypotheses for nonhomogeneous processes when probabilities of errors tend to zero. We consider the general case of observation process with discrete or continuous time parameter and asymmetric (relative to probabilities of errors) classes of tests.

A generalized sequential sign detector for binary hypothesis testing

Abstract: It is known that for fixed error probabilities sequential signal detection based on the sequential probability ratio test (SPRT) is optimum in terms of the average number of signal samples for detection. But, often suboptimal detectors like the sequential sign detector are preferred over the optimal SPRT. When the additive noise statistic is independent and identically distributed (i.i.d.), the sign detector is preferred for its simplicity and nonparametric properties. However, in many practical applications such as the usage of high speed sampling devices the noise is correlated. A generalized sequential sign detector for detecting binary signals in stationary, first-order Markov dependent noise is studied. Under the i.i.d. assumptions, this reduces to the usual sequential sign detector. The optimal decision thresholds and the average sample number for the test to terminate are derived. Numerical results are given to show that the proposed detector exploits the correlation in the noise and hence results in quicker detection. The method can also be extended to Mth order Markov dependence by converting it to a first-order dependence in an extended state space.

Sequential Hypothesis Testing

Abstract: Sequential sampling is a fast efficient tool for many sampling problems. Sequential sampling may be used (1) to obtain precise estimate(s) of the parameters), or (2) to test hypotheses concerning the parameters. Sequential estimation is used when the purpose of sampling is to obtain precise parameter estimates. Several sequential estimation procedures are discussed in Chapter 4. The focus of this chapter is sequential hypothesis testing. This approach is appropriate when we are interested in determining whether the population density is above or below a stated threshold. As in sequential estimation, sequential hypothesis testing requires taking observations sequentially until some stopping criterion is satisfied. The observations are taken at random over the sampling area. Generally, the accumulated total of the observations relative to the number of observations taken determines when sampling is stopped. The sequential hypothesis testing we consider requires some prior knowledge of the population distribution. This permits most computations to be completed in advance of sampling and to be stored in handheld calculators, laptop computers, or printed on cards or sheets. Wald’s sequential probability ratio test was the earliest sequential test and is described first. Lorden’s 2-SPRT is a more recent development that has some exciting possibilities for tests of hypotheses concerning population density and is discussed in the latter parts of this chapter.

Poisson Sequential Sampling Modified Towards Maximal Safety in Adverse Event Monitoring

Abstract: For applying Poisson sequential sampling in safety monitoring concerning new medical conditions (as well as in general control of safety) the one-sample Poisson sequential probability ratio test (SPRT) is modified. The modification results in an adaptive procedure with respect to the smallest detectable relative risk at any time point in the course of the monitoring process. Although this quality would imply maximal safety, the result must be seen as a modification towards maximal safety since the Wald constants of the Poisson SPRT, basic for the derivation of the proposed procedure, are approximate only. The procedure may detect high relative risks even by one observed event right after start of monitoring. The alternative hypothesis must not be specified and the chosen error probabilities α and β completely specify the sampling scheme which can be used with any value of the null hypothesis. The power function and run lengths are established by Monte Carlo runs for an exemplifying choice of α = 10% and β = 5%. Three specified SPRTs are evaluated, by Monte Carlo runs also, to compare their results with those of the modified procedure.

Sequential tests for integrated-circuit failures

Abstract: We propose a sequential probability ratio test (SPRT) based on a 2-parameter Weibull distribution for integrated-circuit (IC) failure analysis. The shape parameter of the Weibull distribution characterizes the decreasing, constant, or increasing failure rate regions in the bath tub model for IC. The algorithm (SD) detects the operating region of the IC based on the observed failure times. Unlike the fixed-length tests, the SD, due to its sequential nature, uses the minimum average number of devices for the test for fixed error tolerances in the detection procedure. We find that SD is, on average, 96% more statistically efficient than the fixed-length test. SD is highly robust to the variations in the model parameters, unlike other existing sequential tests. Since the accuracy of the tests and the test length are conflicting requirements, we also propose a truncated SD which allows a better control of this tradeoff. It has both the sequential nature of examining measurements and the fixed-length property of guaranteeing that the tolerances be met approximately with a specified number of available measurements.

Improvements in the Theory of Identification of Burst-Shaped Events for Fault Diagnosis

Abstract: A method is discussed that enables detection of burstlike deviances in normal stochastical signals using autoregressive modeling combined with the sequential probability ratio test. Corrections are made to better estimate the beginning of the event, and Student distribution is used taking into account the actual amplitude distribution.

Exact computation for some sequential tests

Abstract: Assume that the probability density function for the lifetime of a newly designed product has the form: , for some known H(·). The Exponential e(θ), Rayleigh, and Pareto Pdf's are special cases. A class of continuous-time sequential tests based on the transformed total time on test and the total number of failures is proposed. The use of Steck's (1971) recursions for rectangle probabilities of uniform order statistics simplifies the exact computation for the operating characteristic, the average sample number, and the average failure number. Applications are given to Epstein and Sobel's (1955) continuous-time sequential probability ratio tests (SPRT), Anderson (1960) type of modification to the SPRT, a Bayesian sequential reliability demonstration test (BSRDT) and a predictive sequentila reliability demonstration test (PSRDT). Jeffreys’ prior appears inappropriate for both BSRDT's and PSRDT's. An ad hoc noninformative prior is used for BSRDT's and PSRDT's. Relationship between BSRDT's and PSRDT's is discu...

Approximately optimal designs for phase II clinical studies

Abstract: There is no consensus on determination of sample size in phase II clinical trials. The use of Bayesian decision theory has been proposed by Stallard (1), among others. In this article, optimal three-stage designs are obtained using decision theory. These are compared with procedures proposed by Schoenfeld (2), Ensign et al. (3), and Chen et al. (4) and the sequential probability ratio test of Wald (5) and Barnard (6). The three-stage procedures are shown to be close to the true optimal test; the sequential probability ratio test is easier to obtain and only marginally inferior. Because optimality of the decision-theory approach depends on accurate specification of costs and profits, an assessment is made of the sensitivity of the proposed procedures to a range of gain function parameter values.

Hybrid sequential acquisition schemes for noncoherent chip-asynchronous DS/SS systems

Abstract: This paper investigates the design and performance of hybrid sequential and nonsequential acquisition schemes for direct-sequence spread-spectrum (DS/SS) systems in the presence of multiple-access interference. Carrier phase and chip boundary information are not available at the time of acquisition. Simulation results show that the sequential scheme significantly outperforms the nonsequential scheme. For a DS/SS system using the sequential acquisition scheme, the acquisition-based capacity is evaluated and compared with the post acquisition-based capacity. Results show that for certain values of processing gain the system capacity is limited by the acquisition-based capacity.

Noncoherent SPRT-based acquisition scheme for DSSS

Abstract: A noncoherent sequential PN code acquisition scheme is proposed. The out-of-phase and on-phase sequences are properly modelled to avoid significantly high error probabilities occurring with the conventional SPRT-based acquisition. In addition, data modulation and frequency offset can be effectively overcome using this technique.

On Sequential Inference

Abstract: The idea of sequential inference is probably as old as that of induction itself. All traditional accounts of induction by simple enumeration say roughly this : elements of a class A are examined, one by one, for a property B; the process is continued until either (1) an element of A turns out to be not-B (in which case the hypothesis ‘all A are B’ is rejected), or (2) the inference maker is satisfied that he has accumulated enough evidence to accept the hypothesis ‘all A are B’. In spite of its crude form (no criterion of sufficient evidence is provided), the above procedure has certain properties characteristic of sequential inference. The accumulation of evidence on which the conclusion is to be based proceeds in consecutive steps ; their number is not determined in advance.

A new sequential detector for short-duration signals

Abstract: For quickest detection of a permanent change in distribution of otherwise i.i.d. observations Page's test provides the optimal processor. Page's test has also been applied to the detection of transient (i.e. temporary) changes in distribution: it is easy to implement and has reliable performance, but as applied to the transient problem its optimality is questionable. In this paper we offer an alternative to the Page procedure which we call the iterated generalized sequential probability ratio test, or IGSPRT. While Page's test is itself an IGSPRT, its form and performance are constrained by its reliance on constant thresholds and biases. We demonstrate that with these time-varying, markedly increased detection probabilities are possible. The IGSPRT is easiest to understand and motivate in the Gaussian shift-in-mean problem, and we discuss this in detail, but since that problem is of limited practical interest, we also examine the effect of the IGSPRT in a more realistic situation.

A context-dependent approach for speaker verification using sequential decision.

Abstract: This paper is concerned about speaker veri ca tion SV using the sequential probability ratio test SPRT In the SPRT input samples are usually as sumed to be i i d samples from a probability density function because an on line probability computation is required Feature vectors used in speech processing obviously do not satisfy the assumption and there fore the correlation between successive feature vectors has not been considered in conventional SV using the SPRT The correlation can be modeled by the hidden Markov model HMM but unfortunately the HMM can not be directly applied to the SPRT because of statistical dependence of input samples This paper proposes a method of HMM probability computation using the mean eld approximation to resolve this problem where the probability of whole input samples is nominally represented as the product of probability of each sample as if input samples were independent each other

Robust sequential detectors employing an order statistic prefilter

Abstract: The authors propose robust detection schemes for detecting signals corrupted by additive non-Gaussian noise by employing an order statistic filter (OSF) as a preprocessor. The OSF can effectively suppress non-Gaussian noise components, but its output characteristics are not easy for mathematical manipulation due to its nonlinear operation. To alleviate difficulty in the analytical design of the detector, the output variance of the OSF is approximated by a piecewise linear model. The sequential detectors are designed using the sequential probability ratio test (SPRT) and truncated SPRT (TSPRT) schemes. The performance of the proposed detectors is compared to that of other robust detectors in terms of the sample size required for given false alarm and miss detection probabilities. Finally, analytical results are verified by computer simulation.

SPRT for Weibull distributed integrated circuit failures

Abstract: In this paper, we propose a sequential probability ratio test based on a two parameter Weibull distribution for IC failures. The shape parameter of the Weibull distribution characterizes the decreasing, constant and the increasing failure rate regions in the bath tub model for ICs. The algorithm detects the operating region of the IC based on the observed failure times. Unlike the fixed-length test, the proposed algorithm due to its sequential nature uses the minimum average number of devices for the test for fixed error tolerances in the detection procedure. We find that the proposed test is on an average 96 percent more efficient than the fixed-length test. Our algorithm is shown to be highly robust to the variations in the model parameters unlike other existing sequential tests. Further, extensive simulations are used to validate the analytic results of the sequential test.

Achieving optimal detection through discrete diffusion equations

Abstract: It is known that sequential signal detection based on the sequential probability ratio test (SPRT) is the shortest on an average among other tests. Most of the work in sequential signal detection assumes independent, identically distributed noise. The decision thresholds are not exact. This is due to the complexity involved in doing an exact analysis of the sequential detector. In this paper, we propose a sequential sign detector for detecting constant signals in first order Markov noise. The distribution of the sufficient statistic is derived as a solution to the discrete diffusion equations. This leads to the derivation of the exact values of the decision thresholds and the average sample number.

Minimum-sample SPRT for sensor or operating point selection in a single- or multisensor environment

Abstract: This paper describes a technique for employing the sequential probability ratio test (SPRT) in a single or multisensor environment. The technique minimizes the number of sensor decisions required to declare the null or alternative hypothesis when there is a choice of different sensors or sensor operating points. Thus the technique will be dubbed the Minimum-Sample SPRT (MS-SPRT). The first step of the MS-SPRT requires an off-line optimization of the choice of sensors across all possible values of the alternative hypothesis probability. The second step of the technique involves the application of two Kalman filters to estimate the probability of the alternative hypothesis and to optimize a set of sensor probabilities. The sensor probabilities determine the optimal sensor choice that minimizes the expected number of samples before a decision is made. Three examples are given using simulated data. In the first example, it is shown that the MS-SPRT is not necessary. The second example shows the usefulness of the MS-SPRT when there is a step discontinuity in the null/alternative hypothesis probabilities. In the third example, the MS-SPRT facilitates the use of the proper sensor for a probabilistic variation in the hypothesis probabilities.

Time sequential testing with fixed study time

Abstract: We investigate sampling plans in time sequential testing af snrvival distributions, when the study time is fixed. We obtain the asymptotic value of optimal sampling plans as the error probabilities of the test approach zero.