Neyman-Pearson Test Research Articles

An application of the generalized Neyman-Pearson fuzzy test to stochastic-signal detection

In the article an application of the fuzzy testing of hypothesis to the stochastic-signal detection problem is considered when the signal-to-noise ratio approaches zero. We first obtain the general relationship between the test statistic of the locally optimum fuzzy detector and that of the locally optimum detector. Based on this result, the test statistic and structures of the locally optimum fuzzy detector for stochastic signals are obtained. Several aspects of the locally optimum fuzzy nonlinearity for stochastic signals are also described. Finally, performance characteristics of the locally optimum fuzzy detector are briefly discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Distributed decision fusion in the presence of networking delays and channel errors

The effects of transmission delay and channel errors on the performance of a distributed sensor system are studied. In a network of distributed sensors at a given time instant, the decisions from some sensors may not be available at the fusion center owing to networking and transmission delays. Assuming that the fusion center has to make a decision on the basis of the data from the rest of the sensors, provided that at least one peripheral decision has been received, it is shown that the optimal decision rule that maximizes the probability of detection for fixed probability of false alarm at the fusion center is the Neyman-Pearson test at the fusion center and the sensors as well. Furthermore, it is shown that, in the case of noisy channels, the decision made by each sensor depends on the reliability of the corresponding transmission channel. Moreover, the probability of false alarm at the fusion is restricted by the channel errors. For a given decision rule, the probability of any channel being in error must be kept at a certain level to achieve a desired probability of false alarm at the fusion. A suboptimal but computationally efficient algorithm is developed to solve for the sensor and fusion thresholds sequentially. Numerical results are provided to demonstrate the closeness of the solutions obtained by the suboptimal algorithm to the optimal solutions.

Rate-constrained target detection

Given little or no a priori information, a real world detection system has the task of allocating limited resources. Often these resources are themselves detection systems that operate at a slower rate, for example a tracker following a radar. Detection systems that are described by serial multiple decision points with each decision device assumed to be more reliable but slower than the device preceding it are considered. It is shown that because of the rate constraint the Neyman-Pearson criterion is suboptimum. An optimum rate-constraint test is developed which has the same likelihood ratio form as the Neyman-Pearson test. A strategy for controlling multiple-point detection sequences is developed that depends only on local information and is shown to be optimum under fairly broad conditions. The strategy can be implemented in practical systems, since it depends on the hit rate which is both controllable and observable. This approach to decision-making has applications in many fields and shows a promise as both an analysis and design tool.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Mathematical statistics and metastatistical analysis

This paper deals with meta-statistical questions concerning frequentist statistics. In Sections 2 to 4 I analyse the dispute between Fisher and Neyman on the so called logic of statistical inference, a polemic that has been concomitant of the development of mathematical statistics. My conclusion is that, whenever mathematical statistics makes it possible to draw inferences, it only uses deductive reasoning. Therefore I reject Fisher's inductive approach to the statistical estimation theory and adhere to Neyman's deductive one. On the other hand, I assert that Neyman-Pearson's testing theory, as well as Fisher's tests of significance, properly belong to decision theory, not to logic, neither deductive nor inductive. I then also disagree with Costantini's view of Fisher's testing model as a theory of hypothetico-deductive inferences.

The optimality of the censored mean-level detector

It is shown that the CMLD (censored mean-level detector) is optimal in that the probability of detection is maximized for a given probability of false alarm when no contaminating signals are present in the reference cells. Since the probability of detection in this case is the same as the probability of detection for the MLD (mean-level detector) when k reference cells are used, and since the probability of detection of the MLD converges to the probability of detection of a fixed-threshold Neyman-Pearson test as the number of reference cells becomes large, then this is also true of the CMLD as k becomes large. >

Hypothesis versus significance testing for controlled clinical trials: A dialogue

The mathematical formulations of Neyman-Pearson hypothesis testing and the Fisherian concept of significance tests are examined as alternative ways of applying statistical models to data from clinical trials.

Design considerations for neyman-pearson and wald hypothesis testing

The Neyman-Pearson Lemma describes a test for two simple hypotheses that, for a given sample size, is most powerful for its level. It is usually implemented by choosing the smallest sample size that achieves a prespecified power for a fixed level. The Lemma does not describe how to select either the level or the power of the test. In the usual Wald decision-theoretic structure there exists a sampling cost function, an initial prior over the hypothesis space and various payoffs to right/wrong hypothesis selections. The optimal Wald test is a Bayes decision rule that maximizes the expected payoff net of sampling costs. This paper shows that the Wald-optimal test and the Neyman-Pearson test can be the same and how the Neyman-Pearson test, with fixed level and power, can be viewed as a Wald test subject to restrictions on the payoff vector, cost function and prior distribution.

A statistical analysis of angular distribution of neutrino events observed in Kamiokande II and IMB detectors from supernova SN 1987 A

A detailed statistical analysis of angular distribution of neutrino events observed in Kamiokande II and IMB detectors on UT 07∶35, 2/23'87 is carried out. Distribution functions of the mean scattering angles in the reactions\(\bar \upsilon _e p \to e^ + n\) andve→ve are constructed with account taken of the multiple Coulomb scattering and the experimental angular errors. The Smirnov and Wald-Wolfowitz run tests are used to test the hypothesis that the angular distributions of events from the two detectors agree with each other. We test with the use of the Kolmogorov and Mises statistical criterions the hypothesis that the recorded events all represent\(\bar \upsilon _e p \to e^ + n\) inelastic scatterings. Then the Neyman-Pearson test is applied to each event in testing the hypothesis\(\bar \upsilon _e p \to e^ + n\) against the alternativeve→ve. The hypotheses that the number of elastic events equalss=0, 1, 2, ... against the alternativess≠0, 1, 2, ... are tested on the basis of the generalized likelihood ratio criterion. The confidence intervals for the number of elastic events are also constructed. The current supernova models fail to give a satisfactory account of the angular distribution data.

Optimal distributed decision fusion

The problem of decision fusion in distributed sensor systems is considered. Distributed sensors pass their decisions about the same hypothesis to a fusion center that combines them into a final decision. Assuming that the sensor decisions are independent of each other for each hypothesis, the authors provide a general proof that the optimal decision scheme that maximizes the probability of detection at the fusion for fixed false alarm probability consists of a Neyman-Pearson test (or a randomized N-P test) at the fusion and likelihood-ratio tests at the sensors. >

Optimal serial distributed decision fusion

The problem of distributed detection involving N sensors is considered. The configuration of sensors is serial in the sense that the Jth sensor decides using the decision it receives along with its own observation. When each sensor uses the Neyman-Pearson test, the probability of detection is maximized for a given probability of false alarm, at the Nth stage. With two sensors, the serial scheme has a performance better than or equal to the parallel fusion scheme analyzed in the literature. Numerical examples illustrate the global optimization by the selection of operating thresholds at the sensors. >

On the Asymptotic Behavior of Probabilities of Type I and Type II Errors in the Neyman–Pearson Test. (Case of Total Asymptotically Distinguishable Hypotheses)

On the Asymptotic Behavior of Probabilities of Type I and Type II Errors in the Neyman–Pearson Test. (Case of Total Asymptotically Distinguishable Hypotheses)

Policy research at the congress: A case study of a research unit at the U.S. senate

The Survey and Statistical Analysis section (SSA) of the U.S. Senate Computer Center is analyzed as a case study of a unit that provides information to the U.S. Congress. Most information processed by the SSA is either gathered or analyzed using sociological research methods. This article discusses the activities of the SSA, uses of SSA information by the Senate, certain special issues affecting policy research for the Senate (the adversarial nature of the Senate, the unsuitability of Neyman-Pearson hypothesis testing, and the ethics of participating in the misinterpretation of data), and the place of sociology in the activities of the SSA. Some attention is given to the skills that are utilized by the SSA in conducting its research.

Optimal Decision Fusion in Multiple Sensor Systems

The problem of optimal data fusion in the sense of the Neyman-pearson (N-P) test in a centralized fusion center is considered. The fusion center receives data from various distributed sensors. Each sensor implements a N-P test individually and independently of the other sensors. Due to limitations in channel capacity, the sensors transmit their decision instead of raw data. In addition to their decisions, the sensors may transmit one or more bits of quality information. The optimal, in the N-P sense, decision scheme at the fusion center is derived and it is seen that an improvement in the performance of the system beyond that of the most reliable sensor is feasible, even without quality information, for a system of three or more sensors. If quality information bits are also available at the fusion center, the performance of the distributed decision scheme is comparable to that of the centralized N-P test. Several examples are provided and an algorithm for adjusting the threshold level at the fusion center is provided.

Asymptotic Properties of Neyman-Pearson Tests for Infinite Kullback-Leibler Information

In the present paper we will improve the results concerning the rate of convergence of the error of second kind of the Neyman-Pearson test if the Kullback-Leibler information $K(P_0,P_1)$ is infinite. It is pointed out that in certain cases the sequence $exp(-q_\infty,n)$ is the correct rate of convergence if $-q_\infty,n$ denotes the logarithm of the critical value of the Neyman-Pearson test of level and sample size n. Therefore we generalize the classical results of Stein, Chernoff, and Rao which deal with the error probability of second kind and state that $q_\infty,n\tilde nK(P_0,P_1)$ if the Kullback-Leibler information is finite. Moreover the relation between $q_\infty,n$ and the local behavior of the Laplace transform of the log-likelihood distribution with respect to the hypothesis is studied. The results can be applied to one-sided test problems for exponential families if the hypothesis consists of a single point. In this case it may happen that $q_\infty,n$ is of the order $n^{1/p}$ for some p, 0<p<1.

ENTROPY MINIMAX MULTIVARIATE STATISTICAL MODELING–I: THEORY

Abstract The theory of entropy mimmax, an information theoretic approach to predictive modeling, is reviewed. Comparisons are given to other methodologies, including: Neyman-Pearson hypothesis testing, James-Stein “empirical Bayes” estimation, maximum likelihood estimation, least-squares fitting, linear regression and logistic regression. Examples are provided showing how maximum entropy expectation probabilities are computed and how minimum entropy partitions are determined. The importance of the a priori weight normalization, in establishing the coarse-grain of the minimum entropy partition, is discussed. The trial crossvalidation procedure for determining the normalization is described. Generalizations utilizing Zadeh's fuzzy entropies are provided for variables involving indistinguishability, partial or total. Specific cases are discussed of maximum likelihood estimation, illustrating ils “data range irregularity” which is avoided by methods such as entropy minimization that account for residuals over...

Empirical test of scale type resulting from the Power Law for heaviness.

Stevens claims the ratio-scale level for the scale values resulting from direct scaling procedures and the Power Law, whereas according to Torgerson only a logarithmic transformation of these values leads to an interval scale. Both hypotheses are evaluated for the continuum of heaviness by testing empirically an axiom of a Finite, Equally-spaced Difference Structure, with the Neyman-Pearson test of significance as an error theory. The reported subjective differences in heaviness are represented by numerical differences between scale values resulting from the Power Law but not by differences between logarithmic transformed scale values. Subjective ratios, on the other hand, are not represented by ratios between the values resulting from the Power Law. The Power Law for heaviness leads to an interval scale, not to a ratio scale.

On maximum tests for normal distributions

Lety be a normally distributed random vector with known regular covariance matrix and letA, B be disjoint closed convex sets inR n . To be tested is the zero-hypothesisE(y)eA against the alternative hypothesisE(y) e B at a level of significanceα. Taking the set of admissible tests as one strategy set, the set of probability densities corresponding toB as the other strategy set and the power function of the test problem as the pay-off function this game has an equilibrium point. Thus there is a test, in particular a Neyman-Pearson test, which is simultaneously a maximin and a minimax test. The optimal test is uniquely determined, except on sets with measure zero. Finally the case of non-convexA, B is briefly considered.

On a Problem in Forensic Science

A Neyman-Pearson test of identification in forensic science is shown to reflect all the properties of a Bayes factor approach presented by D. V. Lindley in a previous volume of this journal.

On a problem in forensic science

A Neyman-Pearson test of identification in forensic science is shown to reflect all the properties of a Bayes factor approach presented by D. V. Lindley in a previous volume of this journal.

Comparison of the Optimal Properties of the Wald and Neyman-Pearson Criteria

Let $H_\theta $ be a hypothesis that the theoretical density of probability is $f(x,\theta )$, where $\theta = (\theta ^1 , \ldots ,\theta ^p )$ is an unknown parameter. The statistical problem of distinguishing between two hypotheses $H_0 $ and $H_\theta $ provided $\theta \to \theta _0 = 0$ is considered. The paper gives asymptotic formulas for the necessary number $n(\alpha ,\beta ;\theta )$ of observations when the Neyman-Pearson test is used (Theorem 1) and for the mean number of necessary observations for the Wald sequential test (Theorem 2). The limit of the ratio of these two numbers depends only on a and $\beta $ (probabilities of the errors of first and second kind) (Theorem 3). The variation of this limit with $\alpha $ and $\beta $ is illustrated by a table at the end of the paper.