Posterior odds ratios for selected regression hypotheses

Zellner, Arnold; Siow, Aloysius

doi:10.1007/bf02888369

Cited by 379 publications

(410 citation statements)

References 6 publications

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“…In both the null and the alternative hypotheses, the prior on the precision 1/ 2 is assumed to be a gamma distribution with shape and rate parameters set to 0.5 (equivalent to a chi-square distribution with 1 degree of freedom), and the prior on is assumed to be an improper uniform distribution of infinite width. These assumptions for the prior distributions follow precedents of Jeffreys (1961) and Zellner and Siow (1980), and the approach is therefore called the JZS prior by Rouder et al (2009). Dienes (2008Dienes ( , 2011 provided another analytical solution, with a corresponding online calculator.…”

Section: Analytical Approach To Bayes Factormentioning

confidence: 99%

Bayesian Estimation Supersedes the t Test

Kruschke¹

2012

PsycEXTRA Dataset

315

412

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Bayesian estimation for 2 groups provides complete distributions of credible values for the effect size, group means and their difference, standard deviations and their difference, and the normality of the data. The method handles outliers. The decision rule can accept the null value (unlike traditional t tests) when certainty in the estimate is high (unlike Bayesian model comparison using Bayes factors). The method also yields precise estimates of statistical power for various research goals. The software and programs are free and run on Macintosh, Windows, and Linux platforms.Keywords: Bayesian statistics, effect size, robust estimation, Bayes factor, confidence interval One of the most frequently encountered scientific procedures is a comparison of two groups (e.g., du Prel, Röhrig, Hommel, & Blettner, 2010;Fritz, Morris, & Richler, 2012;Wetzels et al., 2011). Given data from two groups, researchers ask various comparative questions: How much is one group different from another? Can we be reasonably sure that the difference is non-zero? How certain are we about the magnitude of difference? These questions are difficult to answer because data are contaminated by random variability despite researchers' efforts to minimize extraneous influences on the data. Because of "noise" in the data, researchers rely on statistical methods of probabilistic inference to interpret the data. When data are interpreted in terms of meaningful parameters in a mathematical description, such as the difference of mean parameters in two groups, it is Bayesian analysis that provides complete information about the credible parameter values. Bayesian analysis is also more intuitive than traditional methods of null hypothesis significance testing (e.g., Dienes, 2011).This article introduces an intuitive Bayesian approach to the analysis of data from two groups. The method yields complete distributional information about the means and standard deviations of the groups. In particular, the analysis reveals the relative credibility of every possible difference of means, every possible difference of standard deviations, and all possible effect sizes. From this explicit distribution of credible parameter values, inferences about null values can be made without ever referring to p values as in null hypothesis significance testing (NHST). Unlike NHST, the Bayesian method can accept the null value, not only reject it, when certainty in the estimate is high. The new method handles outliers by describing the data as heavy tailed distributions instead of normal distributions, to the extent implied by the data. The new method also implements power analysis in both retrospective and prospective forms.The analysis is implemented in the widely used and free programming languages R and JAGS and can be run on Macintosh, Linux, and Windows operating systems. Complete installation instructions are provided, along with working examples. The programs can also be flexibly extended to other types of data and analyses. Thus, the software can be used by virtually ...

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Section: Analytical Approach To Bayes Factormentioning

confidence: 99%

Bayesian Estimation Supersedes the t Test

Kruschke¹

2012

PsycEXTRA Dataset

315

412

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“…Zellner and Siow (1980) provide the seminal advance here. They showed that the g-prior specification used here allowed researchers to symbolically integrate all the parameter except g!…”

Section: Model Comparisonmentioning

confidence: 99%

Developing constraint in bayesian mixed models.

Haaf¹,

Rouder²

2017

Psychological Methods

117

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Model comparison in Bayesian mixed models is becoming popular in psychological science. Here we develop a set of nested models that account for order restrictions across individuals in psychological tasks. An order-restricted model addresses the question "Does everybody," as in "Does everybody show the usual Stroop effect," or "Does everybody respond more quickly to intense noises than subtle ones?" The crux of the modeling is the instantiation of 10s or 100s of order restrictions simultaneously, one for each participant. To our knowledge, the problem is intractable in frequentist contexts but relatively straightforward in Bayesian ones. We develop a Bayes factor model-comparison strategy using Zellner and Siow's default g-priors appropriate for assessing whether effects obey equality and order restrictions. We apply the methodology to seven data sets from Stroop, Simon, and Eriksen interference tasks. Not too surprisingly, we find that everybody Stroops-that is, for all people congruent colors are truly named more quickly than incongruent ones. But, perhaps surprisingly, we find these order constraints are violated for some people in the Simon task, that is, for these people spatially incongruent responses occur truly more quickly than congruent ones! Implications of the modeling and conjectures about the task-related differences are discussed.

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“…We need only define mixtures of g-priors on the precision matrix of b, or equivalently on h 0 . Zellner and Siow (1980) proposed a Cauchy prior on g which is not as popular as the g-prior since closed form expressions for the marginal likelihoods are not available. More recently, and as an alternative to the Zellner-Siow's prior, (see also Cui and George (2008)) have proposed a Pareto type II hyper-g prior whose pdf is defined as:…”

Section: The Second Step Of the Robust Bayesian Estimatormentioning

confidence: 99%

Robust linear static panel data models usingε-contamination

Baltagi¹,

Bresson²,

Chaturvedi³

et al. 2018

Journal of Econometrics

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show abstract

Posterior odds ratios for selected regression hypotheses

Cited by 379 publications

References 6 publications

Bayesian Estimation Supersedes the t Test

Bayesian Estimation Supersedes the t Test

Developing constraint in bayesian mixed models.

Robust linear static panel data models usingε-contamination

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