A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion

Kass, Robert E.; Wasserman, Larry

doi:10.1080/01621459.1995.10476592

Cited by 903 publications

(454 citation statements)

References 10 publications

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“…To this end we used the method proposed by Wagenmakers (2007) and Masson (2011). This method uses Bayesian information criteria (BIC), calculated using a simple transformation of sum-of-squares values generated by the standard ANOVA, to estimate the Bayes factor and generate p ( H 0 | D ), assuming a “unit information prior” (for further details, see Kass & Wasserman, 1995; see also Jarosz & Wiley, 2014). …”

Section: Resultsmentioning

confidence: 99%

More attentional focusing through binaural beats: evidence from the global–local task

Colzato

Barone

Sellaro

2015

Psychological Research

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A recent study showed that binaural beats have an impact on the efficiency of allocating attention over time. We were interested to see whether this impact affects attentional focusing or, even further, the top-down control over irrelevant information. Healthy adults listened to gamma-frequency (40 Hz) binaural beats, which are assumed to increase attentional concentration, or a constant tone of 340 Hz (control condition) for 3 min before and during a global–local task. While the size of the congruency effect (indicating the failure to suppress task-irrelevant information) was unaffected by the binaural beats, the global-precedence effect (reflecting attentional focusing) was considerably smaller after gamma-frequency binaural beats than after the control condition. Our findings suggest that high-frequency binaural beats bias the individual attentional processing style towards a reduced spotlight of attention.

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Section: Resultsmentioning

confidence: 99%

More attentional focusing through binaural beats: evidence from the global–local task

Colzato

Barone

Sellaro

2015

Psychological Research

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“…Note that the information in the data about β can be conceptualized as (Kass & Wasserman, 1995). Hence, g is a scaling factor controlling the information that we give the prior on β , relative to the information in the sample.…”

Section: Default Prior Distributions For the Linear Modelmentioning

confidence: 99%

A default Bayesian hypothesis test for correlations and partial correlations

2012

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We propose a default Bayesian hypothesis test for the presence of a correlation or a partial correlation. The test is a direct application of Bayesian techniques for variable selection in regression models. The test is easy to apply and yields practical advantages that the standard frequentist tests lack; in particular, the Bayesian test can quantify evidence in favor of the null hypothesis and allows researchers to monitor the test results as the data come in. We illustrate the use of the Bayesian correlation test with three examples from the psychological literature. Computer code and example data are provided in the journal archives.

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“…This approximation is particularly good if the models under comparison are nested, such that one is a simplified version of the other (Kass & Wasserman, 1995). Another advantage of the BIC is that it is relatively straightforward to compute; the BIC is given by BIC ϭ Ϫ2 ϫ ln L ϩ k ϫ ln n, where ln L is the log maximum likelihood, k is the number of free parameters, and n is the sample size.…”

Section: Alternative Methods For Comparing Toolbox Modelsmentioning

confidence: 99%

“…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

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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.

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A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion

Cited by 903 publications

References 10 publications

More attentional focusing through binaural beats: evidence from the global–local task

More attentional focusing through binaural beats: evidence from the global–local task

A default Bayesian hypothesis test for correlations and partial correlations

Testing adaptive toolbox models: A Bayesian hierarchical approach.

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