Probability Integrals of Multivariate Normal and Multivariate $t^1$

Gupta, Shanti S.

doi:10.1214/aoms/1177704004

Cited by 383 publications

(142 citation statements)

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“…Nishisato and Torii (1969) the configuration to assess the probability. It appears as though direct integration of a multivariate normal over a certain region is in a general case nearly impossible (Gupta, 1963). Thus, some approximation method seems to be in order.…”

Section: Discussionmentioning

confidence: 99%

Structure and Probability Distribution of Dichotomous Response Patterns

Nishisato

1970

Jpn. Psychol. Res

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A view that dichotomous response patterns with negligible probabilities should be excluded from data analysis was pursued mainly to mitigate the difficulty in dealing with an enormous number of possible response patterns. Based on an assumption of latent structure, a geometric model of dichotomous response patterns was proposed. Monte Carlo computations revealed, among others, that the structural consideration of binary information can lead to an economical way of data analysis, and that the simplicity of interpretability of binary information degenerates rapidly as the structure of the information tends to become multidimensional.Only a deterministic model was discussed.

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Section: Discussionmentioning

confidence: 99%

Structure and Probability Distribution of Dichotomous Response Patterns

Nishisato

1970

Jpn. Psychol. Res

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“…(8a2.11), p. 522] th element of th element of (7) Now, the probability of error is given by (8) where (9) and denotes the standard Gaussian density. Because of equal correlation among any pair of variables from , the -fold integral embedded in the integrand of (8) can be reduced to a single integral involving a normal CDF and a normal density function [16]. Using this reduction, and using large , (8) can be approximated in a straightforward fashion to yield the asymptotic probability of error (10) where If necessary, a reader can consult [17] for more details on the derivation of (10).…”

Section: Asymptotic Performance Of Mrtmentioning

confidence: 99%

Two rank order tests for M-ary detection

Annampedu

Roganov

Viswanathan

2000

IEEE Trans. Inform. Theory

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Abstract-We consider a general -ary detection problem where, given groups of samples each, the problem is to identify which unique group of samples have come from the signal hypothesis. The optimal likelihood ratio test is unrealizable, when the joint distribution of samples is not completely known. In this paper we consider two rank order types of tests termed as the modified rank test (MRT) and the modified rank test with row sort (MRTRS). We examine through simulation, the small sample probability of error performances of MRT and MRTRS for detecting a signal among contaminants. Numerically computable closed -form error expressions are derived for some special cases. Asymptotic (large sample) error rate of MRT is also derived. The results indicate that MRTRS provides improved performance over other previously known rank tests.

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“…When xi's are Gaussian random variables with a zero mean and correlation matrix C, P (x 1 < t; 11 1; x N0k+j < t) can be expressed as in [17] P (x 1 < t; x 2 < t; 11 1; x N0k+j < t)…”

Section: Performance In Gaussian Noisementioning

confidence: 99%

Adaptive fusion of correlated local decisions

Chen

Ansari

1998

IEEE Trans. Syst., Man, Cybern. C

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Abstract-In this paper, an adaptive fusion algorithm is proposed for an environment where the observations and local decisions are dependent from one sensor to another. An optimal decision rule, based on the maximum posterior probability (MAP) detection criterion for such an environment, is derived and compared to the adaptive approach. In the algorithm, the log-likelihood ratio function can be expressed as a linear combination of ratios of conditional probabilities and local decisions. The estimations of the conditional probabilities are adapted by reinforcement learning. The error probability at steady state is analyzed theoretically and, in some cases, found to be equal to the error probability obtained by the optimal fusion rule. The effect of the number of sensors and correlation coefficients on error probability in Gaussian noise is also investigated. Simulation results that conform to the theoretical analysis are presented at the end of the paper.Index Terms-Correlated decisions, distributed detection, probability of detection, probability of false alarm, reinforcement learning.

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Probability Integrals of Multivariate Normal and Multivariate $t^1$

Cited by 383 publications

References 0 publications

Structure and Probability Distribution of Dichotomous Response Patterns

Structure and Probability Distribution of Dichotomous Response Patterns

Two rank order tests for M-ary detection

Adaptive fusion of correlated local decisions

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