Numerical Computation of Multivariate Normal Probabilities

Genz, Alan

doi:10.1080/10618600.1992.10477010

Cited by 637 publications

(366 citation statements)

References 7 publications

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“…It might be thought that this assumption would allow us to directly calculate the required probabilities when the tests are not independent. However, obtaining a solution to this type of problem by direct analytic means is remarkably difficult (Gentz, 1992;Ingraham & Aiken, 1996). This is because conditional distributions derived from a multivariate normal distribution do not, in general, have a closed form when the condition is an inequality (e.g., the score on Test X is abnormally low) rather than an equality (e.g., the score on Test X is 36).…”

mentioning

confidence: 99%

Estimating the percentage of the population with abnormally low scores (or abnormally large score differences) on standardized neuropsychological test batteries: A generic method with applications.

Crawford¹,

Garthwaite

Gault³

2007

Neuropsychology

134

142

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Information on the rarity or abnormality of an individual's test scores (or test score differences) is fundamental in interpreting the results of a neuropsychological assessment. If a standardized battery of tests is administered, the question arises as to what percentage of the healthy population would be expected to exhibit one or more abnormally low test scores (and, in general, j or more abnormally low scores). Similar issues arise when the concern is with the number of abnormal pairwise differences between an individual's scores on the battery, or when an individual's scores on each component of the battery are compared with the individual's mean score. A generic Monte Carlo simulation method for tackling such problems is described (it requires only that the matrix of correlations between tests be available) and is contrasted with the use of binomial probabilities. The method is then applied to Index scores for the Wechsler Adult Intelligence Scale-Third Edition (WAIS-III; D. Wechsler, 1997) and Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV;D. Wechsler, 2003). Three computer programs that implement the methods are made available.

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mentioning

confidence: 99%

Estimating the percentage of the population with abnormally low scores (or abnormally large score differences) on standardized neuropsychological test batteries: A generic method with applications.

Crawford¹,

Garthwaite

Gault³

2007

Neuropsychology

134

142

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“…all the individuals genotyped). So, the Monte-Carlo Quasi Monte-Carlo method of [6] and based on [16], is still suitable here.…”

Section: Asymptotic Test For Quantitative Trait Locus Detection In Prmentioning

confidence: 99%

“…critical value) in our study is exactly the same as the classical threshold used in the oracle situation. So, in order to obtain our threshold, the MonteCarlo Quasi Monte-Carlo methods of [6], based on [16] is still suitable here. This is an alternative to the permutation method proposed by [10].…”

Section: Introductionmentioning

confidence: 99%

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An asymptotic test for Quantitative Trait Locus detection in presence of missing genotypes

Rabier¹

2014

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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“…Furthermore, as reported by Zeger and Karim [1991], successive samples of random effects tend to be highly correlated, so convergence can be very slow. Pawitan et al [2004] used the marginal likelihood approach using Genz's [1993] for fast Monte Carlo integration of random effects. While this can handle each high-dimensional integration quite well, in large data sets it is difficult to handle general covariates.…”

Section: Introductionmentioning

confidence: 99%

Multicomponent variance estimation for binary traits in family‐based studies

Noh

Yip

Lee

et al. 2005

Genetic Epidemiology

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In biometrical genetic analyses of binary traits, the use of family data overcomes some limitations of twin studies, particularly in terms of sample size and types of genetic or environmental factors that can be estimated. However, because of computational problems, recent methods in the application of generalized linear mixed models for family data structure have limited the ability to handle large data sets with general covariates. In this paper, we investigate the use of the hierarchical likelihood approach to the analysis of binary traits from family data. In a simulation study, the method is shown to be highly accurate for the estimation of both the variance components and fixed regression parameters, even for small family sizes. For illustration, we analyze a real data set of familial aggregation of preeclampsia, a pregnancy-induced hypertension. When possible, the analysis is compared with the exact maximum likelihood approach. Genet. Epidemiol. 30: 37-47, 2006. r 2005 Wiley-Liss, Inc.

show abstract

Numerical Computation of Multivariate Normal Probabilities

Cited by 637 publications

References 7 publications

Estimating the percentage of the population with abnormally low scores (or abnormally large score differences) on standardized neuropsychological test batteries: A generic method with applications.

Estimating the percentage of the population with abnormally low scores (or abnormally large score differences) on standardized neuropsychological test batteries: A generic method with applications.

An asymptotic test for Quantitative Trait Locus detection in presence of missing genotypes

Multicomponent variance estimation for binary traits in family‐based studies

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