Showing papers on "Sequential probability ratio test published in 2001"

Sequential methods of analysis for genome scans.

Abstract: As the preceding chapters illustrate, now that whole-genome scan analyses are becoming more common, there is considerable disagreement about the best way to balance between false positives and false negatives (traditionally called type I and type II errors in the statistical parlance). Type I and type II errors can be simultaneously controlled, if we are willing to let the sample size of analysis vary. This is the secret that Wald 1947 discovered in the 1940s that led to the theory of sequential sampling and was the inspiration for Newton Morton in developing the lod score method. We can exploit this idea further and capitalize on an old, but nearly forgotten theory: sequential multiple decision procedures (SMDP) Bechhoffer, et al. 1968, which generalizes the standard “two-hypotheses” tests to consider multiple alternative hypotheses. Using this theory, we can develop a single, genome-wide test that simultaneously partitions all markers into “signal” and “noise” groups, with tight control over both type I and type II errors ( Province, 2000 ). Conceiving this approach as an analysis tool for fixed sample design (instead of a true sequential sampling scheme), we can let the data decide at which point we should move from the hypothesis generation phase of a genome scan (where multiple comparisons make the interpretation of p values and significance levels difficult and controversial), to a true hypothesis-testing phase (where the problem of multiple comparison of multiple comparison has been all but eliminated so that p values may be accepted at face value.

Sequential sampling for incidence of phomopsis leaf blight of strawberry.

Abstract: Sequential sampling models for estimation and classification were developed for the incidence of strawberry leaflets infected by Phomopsis obscurans. Sampling protocols were based on a binary power law analysis of the spatial heterogeneity of Phomopsis leaf blight in commercial fields in Ohio. For sequential estimation, samples were collected until mean disease incidence could be estimated with a preselected coefficient of variation of the mean (C). For sequential classification, samples were collected until there was sufficient evidence to classify mean incidence as being below or above a threshold (pt) based on the sequential probability ratio test. Monte-Carlo simulations were used to determine the theoretical average sample number (ASN) and probability of classifying mean incidence as less than pt (operating characteristic) for any true value of incidence. Estimation and classification sampling models were both tested with bootstrap simulations of randomly selected data sets and validated by ...

Hypothesis Testing for Resolving Integer Ambiguity in GPS

Abstract: This paper presents statistical techniques for validating integer ambiguities and detecting cycle slips. The multiple-hypothesis Wald sequential probability ratio test (SPRT) validates the choice of initial integer ambiguities by finding the conditional probability that each set of integer biases under consideration is the true bias condition. The multiple-hypothesis Shiryayev SPRT monitors for cycle slips by determining the conditional probability that the integer biases have jumped from the nominal bias condition to each member of a collection of other bias conditions. Both tests use a geometric combination of the carrier-phase measurements and the difference between the carrier-phase measurements and code measurements as measurement residuals. Because the SPRT calculations operate on the probability density functions of these measurement residuals, they can correctly compensate for non-Gaussian measurement errors, such as multipath. The efficacy of our techniques is demonstrated by results from simulations and field experiments.

Uniform Asymptotic Expansion of Likelihood Ratio for Markov Dependent Observations

Abstract: An asymptotic expansion of the logarithm of the likelihood ratio for Markov dependent observation is obtained. A functional limit theorem for the likelihood ratio is proved, which gives a way to study limiting distributions of the likelihood ratio based on stopping times, in particular, that of sequential probability ratio test.

Sequential detection of targets in distributed systems

Abstract: It is supposed that there is a multisensor system in which each sensor performs sequential detection of a target. Then the binary decisions on target presence and absence are transmitted to a fusion center, which combines them to improve the performance of the system. We assume that sensors represent multichannel systems with possibly each one having different number of channels. Sequential detection of a target in each sensor is done by implementing a generalized Wald's sequential probability ratio test which is based on the maximum likelihood ratio statistic and allows one to fix the false alarm rate and the mis-detection rate at specified levels. We first show that this sequential detection procedure is asymptotically optimal for general statistical models in the sense of minimizing the expected sample size when the probabilities of errors vanish. We then construct the optimal non-sequential fusion rule that waits until all the local decisions in all sensors are made and then fuses them. It is optimal in the sense of maximizing the probability of target detection for a fixed probability of a false alarm or minimizing the maximal probability of error (minimax criterion). An analysis shows that the final decision can be made substantially more reliable even for a small number of sensors (3-5). The performance of the system is illustrated by the example of detecting a deterministic signal in correlated (color) Gaussian noise. In this example, we provide both the results of theoretical analysis and the results of Monte Carlo experiment. These results allow us to conclude that the use of the sequential detection algorithm substantially reduces the required resources of the system compared to the best non-sequential algorithm.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Simultaneous monitoring of mean and variance through optimally designed sprt charts

Abstract: Four essential properties that a control chart must have are applicability, high sensitivity for detecting shifts, cost-optimality, and the capability of jointly controlling all the important parameters that characterize a process. This paper introduces a quality monitoring system design for jointly monitoring the mean and the variance of a Gaussian process. The design of this monitoring system, the Economic Mean and Variance —Sequential Probability Ratio Tests (EMV-SPRT) charts, possesses all of the desired properties mentioned above. The applicability of the design comes from the utilization of assumptions that fit many actual processes. The sensitivity is a consequence of the use of SPRT. The determination of the design parameters through an economic model ensures cost optimality.

Robustness of likelihood ratio tests: hypothesis testing under incorrect models

Abstract: This paper formulates the trade-off between the sample size and the reliability of decisions in a multihypothesis test with possible model errors. We introduce a measure of the model uncertainty and derive the best error exponent for the decision error probabilities for the allowed levels of model uncertainty. For small deviations from the correct model, the error exponent for sequential probability ratio tests is quantified.

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.

Simple real time data fusion

Abstract: We are developing new simple algorithms to provide automatic methods for fusing data from multiple passive sensors and multiple targets in real time. Initially, we have developed algorithms to fuse data from multiple passive collocated sensors measuring the same quantities (bearing and bearing rate) from multiple targets. MATLAB results with simulated data have been very encouraging. We present results for the probability of correct data association (P A ) and the probability of false data association (P FA ) as a function of target angular separation, random noise, and the number of data updates used in the sequential probability ratio test (SPRT).

Ultrasensitive surveillance of sensors and processes

Abstract: A method and apparatus for monitoring a source of data for determining an operating state of a working system. The method includes determining a sensor (or source of data) arrangement associated with monitoring the source of data for a system, activating a method for performing a sequential probability ratio test if the data source includes a single data (sensor) source, activating a second method for performing a regression sequential possibility ratio testing procedure if the arrangement includes a pair of sensors (data sources) with signals which are linearly or non-linearly related; activating a third method for performing a bounded angle ratio test procedure if the sensor arrangement includes multiple sensors and utilizing at least one of the first, second and third methods to accumulate sensor signals and determining the operating state of the system.