Mixtures of <i>g</i> Priors for Bayesian Variable Selection

Liang, Feng; Paulo, Rui; Molina, Germán; Clyde, Merlise A.; Berger, James O.

doi:10.1198/016214507000001337

Cited by 984 publications

(1,382 citation statements)

References 27 publications

Supporting

Mentioning

1,365

Contrasting

Unclassified

Order By: Relevance

“…It is clearly desirable to extend the Bayes factor hypothesis test to more general scenarios such as those that involve generalized linear models (Dey, Ghosh, & Mallick, 2000) and variable selection in regression (Liang, Paulo, Molina, Clyde, & Berger, 2008). The extension of the Bayesian hypothesis test to more general statistical models is ongoing, and it is likely that MCMC-based methods will be crucial for their flexible application (e.g., Ntzoufras, 2009, chap.…”

Section: Concluding Commentsmentioning

confidence: 99%

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

Wagenmakers

Lodewyckx

Kuriyal

et al. 2010

Cognitive Psychology

650

642

View full text Add to dashboard Cite

a b s t r a c tIn the field of cognitive psychology, the p-value hypothesis test has established a stranglehold on statistical reporting. This is unfortunate, as the p-value provides at best a rough estimate of the evidence that the data provide for the presence of an experimental effect. An alternative and arguably more appropriate measure of evidence is conveyed by a Bayesian hypothesis test, which prefers the model with the highest average likelihood. One of the main problems with this Bayesian hypothesis test, however, is that it often requires relatively sophisticated numerical methods for its computation. Here we draw attention to the Savage-Dickey density ratio method, a method that can be used to compute the result of a Bayesian hypothesis test for nested models and under certain plausible restrictions on the parameter priors. Practical examples demonstrate the method's validity, generality, and flexibility.

show abstract

Section: Concluding Commentsmentioning

confidence: 99%

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

Wagenmakers

Lodewyckx

Kuriyal

et al. 2010

Cognitive Psychology

650

642

View full text Add to dashboard Cite

show abstract

“…This specification is well studied and has been influential in linear modeling in statistics (e.g. Bayarri & Garcia-Donato, 2007;F. Liang, Paulo, Molina, Clyde, & Berger, 2008;Overstall & Forster, 2010).…”

Section: Additional Specificationsmentioning

confidence: 99%

“…They showed that the g-prior specification used here allowed researchers to symbolically integrate all the parameter except g! It is for this reason that the g-prior specification has been popular (see Bayarri & Garcia-Donato, 2007;F. Liang et al, 2008;Zellner, 1986).…”

Section: Model Comparisonmentioning

confidence: 99%

See 1 more Smart Citation

Developing constraint in bayesian mixed models.

Haaf¹,

Rouder²

2017

Psychological Methods

117

View full text Add to dashboard Cite

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.

show abstract

“…These priors form an integral part of the model, and they are informed by theoretical considerations and possibly also by available prior knowledge. Selecting appropriate prior distributions is of ongoing concern to Bayesian statisticians (e.g., Kass & Wasserman, 1995;Liang, Paulo, Molina, Clyde, & Berger, 2008). In some cases, for example, if the parameter space is bounded, the absence of prior knowledge can be expressed though uniform distributions, indicating that all values within the predefined range are equally likely a priori.…”

Section: Formal Specification Of a Cognitive Toolboxmentioning

confidence: 99%

Testing adaptive toolbox models: A Bayesian hierarchical approach.

Scheibehenne

Rieskamp

Wagenmakers

2013

Psychological Review

103

View full text Add to dashboard Cite

Many theories of human cognition postulate that people are equipped with a repertoire of strategies to solve the tasks they face. This theoretical framework of a cognitive toolbox provides a plausible account of intra-and interindividual differences in human behavior. Unfortunately, it is often unclear how to rigorously test the toolbox framework. How can a toolbox model be quantitatively specified? How can the number of toolbox strategies be limited to prevent uncontrolled strategy sprawl? How can a toolbox model be formally tested against alternative theories? The authors show how these challenges can be met by using Bayesian inference techniques. By means of parameter recovery simulations and the analysis of empirical data across a variety of domains (i.e., judgment and decision making, children's cognitive development, function learning, and perceptual categorization), the authors illustrate how Bayesian inference techniques allow toolbox models to be quantitatively specified, strategy sprawl to be contained, and toolbox models to be rigorously tested against competing theories. The authors demonstrate that their approach applies at the individual level but can also be generalized to the group level with hierarchical Bayesian procedures. The suggested Bayesian inference techniques represent a theoretical and methodological advancement for toolbox theories of cognition and behavior.

show abstract

Mixtures of g Priors for Bayesian Variable Selection

Cited by 984 publications

References 27 publications

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

Developing constraint in bayesian mixed models.

Testing adaptive toolbox models: A Bayesian hierarchical approach.

Contact Info

Product

Resources

About