Some Bayesian and non-Bayesian procedures for the analysis of comparative experiments and for small-area estimation: computational aspects, frequentist properties, and relationships

Hulting, Frederick L.

doi:10.31274/rtd-180813-12593

Cited by 7 publications

(12 citation statements)

References 38 publications

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“…But in parametric inference this problem is handled by a two-stage approach to obtain BLUPs (Best Linear Unbiased Predictors). See Hulting and Harville (1991) and Samuels et a/. (1991) for discussions about the BLUPs.…”

Section: Asymptotic Relative Efficiencymentioning

confidence: 99%

Inference based on ranks for two-way models with a grouping factor and a repeated measures factor

Rashid

1996

Journal of Nonparametric Statistics

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To cite this article: M. Mushfiqur rashid (1996) Inference based on ranks for two-way models with a grouping factor and a repeated measures factor, Journal of Nonparametric Statistics, 6:1, 27-42To link to this article: http://dx.4 unified r;cnh-haied a n ;~l~s i s is developed for two-way models with a grouping factor (unequal number of subjzch per group) anti a repeated measures factor hahed on a d~q x i -s~u~ I'u~litic)n assulning edxangcahility of the errors within each subject. This analysis produces asymptotically distribution-frce tests for general linear hypotheses, and multiple comparihan procedures based on R-estimators. A Monte Carh) Study is conducted to investigate the sm'tll sample behavior of a rank test for testing the hypothesis of no interaction between the repeated measures and the grouping factors.

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Section: Asymptotic Relative Efficiencymentioning

confidence: 99%

Inference based on ranks for two-way models with a grouping factor and a repeated measures factor

Rashid

1996

Journal of Nonparametric Statistics

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“…The marginal posterior "density" of the variance ratio a;/a: can be obtained in closed form (up to a normalizing constant), and the joint conditional posterior distribution of p and S given a : / o : is multivariate-t (e.g., Hulting and Harville 1991). Thus, the problem of computing various characteristics of the posterior distribution of the fixed and random effects (e.g., posterior means and variances of the effects or linear combinations of the effects) can be reduced to a problem of one-dimensional numerical integration, thereby providing an alternative to the use of the multivariate normal or multivariate-t approximation discussed in Section 4.…”

Section: Posterior Distributions In Linear Modelsmentioning

confidence: 99%

“…There has been much recent interest in a Bayesian approach to inferences about linear combinations of the fixed and random effects in mixed-effects models (e.g., Gianola, Im, and Macedo, 1990;Gelfand, Hills, Racine-Poon, and Smith, 1990;Hulting and Harville, 1991;Harville and Carriquiry, 1992;Carriquiry and Kliemann, 1992). When taking a Bayesian approach, it is convenient to reparameterize model (1.1) in terms of the precision components z, = l/a; and z, = l/a; or in terms of z, and the ratio p = zs/ze = a:/ai.…”

Section: Introductionmentioning

confidence: 99%

The posterior distribution of the fixed and random effects in a mixed-effects linear model

Harville

Zimmermann

1996

Journal of Statistical Computation and Simulation

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The subject of this paper is Bayesian inference about the fixed and random effects of a mixed-effects linear statistical model with two variance components. It is assumed that a priori the fixed effects have a noninformative distribution and that the reciprocals of the variance components are distributed independently (of each other and of the fixed effects) as gamma random variables. It is shown that techniques similar to those employed in a ridge analysis of a response surface can be used to construct a one-dimensional curve that contains all of the stationary points of the posterior density of the random effects. The "ridge analysis" (of the posterior density)can be useful (from a computational standpoint)in finding the number and the locations of the stationary points and can be very informative about various features of the posterior density. Depending on what is revealed by the ridge analysis, a multivariate normal or multivariate-t distribution that is centered at a posterior mode may provide a satisfactory approximation to the posterior distribution of the random effects (which is of the poly-t form).

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“…(For reviews, see Hulting and Harville [1991] and Ghosh and Rao [1994].) Empirical Bayes procedures do not account for the uncertainty in the estimated parameters, and therefore estimates of uncertainty tend to be biased low.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Bayes Estimation of Hunting Success Rates with Spatial Correlations

He¹,

Sun²

2000

Biometrics

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A Bayesian hierarchical generalized linear model is used to estimate hunting success rates at the subarea level for postseason harvest surveys. The model includes fixed week effects, random geographic effects, and spatial correlations between neighboring subareas. The computation is done by Gibbs sampling and adaptive rejection sampling techniques. The method is illustrated using data from the Missouri Turkey Hunting Survey in the spring of 1996. Bayesian model selection methods are used to demonstrate that there are significant week differences and spatial correlations of hunting success rates among counties. The Bayesian estimates are also shown to be quite robust in terms of changes of hyperparameters.

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Some Bayesian and non-Bayesian procedures for the analysis of comparative experiments and for small-area estimation: computational aspects, frequentist properties, and relationships

Abstract: 3.1.2 Posterior distributions: f{iu | y) and f{io \ y) 59 3.1.3 Characterizations of f{iu | 2/) 3.2 Computational Aspects iv 3.2.1 Computing /(tu | y), P{S | y), and up 63 3.

Cited by 7 publications

References 38 publications

Inference based on ranks for two-way models with a grouping factor and a repeated measures factor

Inference based on ranks for two-way models with a grouping factor and a repeated measures factor

The posterior distribution of the fixed and random effects in a mixed-effects linear model

Hierarchical Bayes Estimation of Hunting Success Rates with Spatial Correlations

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Some Bayesian and non-Bayesian procedures for the analysis of comparative experiments and for small-area estimation: computational aspects, frequentist properties, and relationships

Abstract: 3.1.2 Posterior distributions: f{iu | y) and f*{io \ y) 59 3.1.3 Characterizations of f*{iu | 2/) 3.2 Computational Aspects iv 3.2.1 Computing /*(tu | y), P*{S | y), and up 63 3.

Cited by 7 publications

References 38 publications

Inference based on ranks for two-way models with a grouping factor and a repeated measures factor

Inference based on ranks for two-way models with a grouping factor and a repeated measures factor

The posterior distribution of the fixed and random effects in a mixed-effects linear model

Hierarchical Bayes Estimation of Hunting Success Rates with Spatial Correlations

Contact Info

Product

Resources

About

Abstract: 3.1.2 Posterior distributions: f{iu | y) and f{io \ y) 59 3.1.3 Characterizations of f{iu | 2/) 3.2 Computational Aspects iv 3.2.1 Computing /(tu | y), P{S | y), and up 63 3.