Methods for Default and Robust Bayesian Model Comparison: The Fractional Bayes Factor Approach

1999 ◽  
Vol 67 (3) ◽  
pp. 267 ◽  
Author(s):  
Fulvio de Santis ◽  
Fulvio Spezzaferri
Keyword(s):  
Bayesian Model ◽  
Model Comparison ◽  
Bayes Factor ◽  
Bayesian Model Comparison ◽  
Fractional Bayes Factor

Uncertainty of prior and posterior model probability: Implications for interpreting Bayes factors

2021 ◽  
Author(s):  
John K. Kruschke
Keyword(s):  
Posterior Distribution ◽  
Bayesian Model ◽  
Model Comparison ◽  
Bayes Factor ◽  
Bayes Factors ◽  
Prior Model ◽  
Bayesian Hypothesis Testing ◽  
Bayesian Model Comparison ◽  
Posterior Model Probability ◽  
Model Probability

In most applications of Bayesian model comparison or Bayesian hypothesis testing, the results are reported in terms of the Bayes factor only, not in terms of the posterior probabilities of the models. Posterior model probabilities are not reported because researchers are reluctant to declare prior model probabilities, which in turn stems from uncertainty in the prior. Fortunately, Bayesian formalisms are designed to embrace prior uncertainty, not ignore it. This article provides a novel derivation of the posterior distribution of model probability, and shows many examples. The posterior distribution is useful for making decisions taking into account the uncertainty of the posterior model probability. Benchmark Bayes factors are provided for a spectrum of priors on model probability. R code is posted at https://osf.io/36527/. This framework and tools will improve interpretation and usefulness of Bayes factors in all their applications.

scholarly journals From theories to models to predictions: A Bayesian model comparison approach

2017 ◽  
Author(s):  
Jeffrey Rouder ◽  
Julia M. Haaf ◽  
Frederik Aust
Keyword(s):  
Statistical Models ◽  
Bayesian Model ◽  
Model Comparison ◽  
Bayes Factor ◽  
Significance Testing ◽  
Bayesian Model Comparison ◽  
Comparison Approach ◽  
Competing Models ◽  
Competing Hypotheses

A key goal in research is to use data to assess competing hypotheses or theories. Analternative to the conventional significance testing is Bayesian model comparison. The mainidea is that competing theories are represented by statistical models. In the Bayesianframework, these models then yield predictions about data even before the data are seen.How well the data match the predictions under competing models may be calculated, andthe ratio of these matches—the Bayes factor—is used to assess the evidence for one modelcompared to another. We illustrate the process of going from theories to models and topredictions in the context of two hypothetical examples about how exposure to media affectsattitudes toward refugees.

Bayesian model comparison

2014 ◽  
pp. 101-117
Author(s):  
Michael D. Lee ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Bayesian Model ◽  
Model Comparison ◽  
Bayesian Model Comparison

scholarly journals A Bayesian model comparison approach to test the specificity of visual integration impairment in schizophrenia or psychosis

2018 ◽  
Vol 265 ◽  
pp. 271-278 ◽  
Author(s):  
Tyler B. Grove ◽  
Beier Yao ◽  
Savanna A. Mueller ◽  
Merranda McLaughlin ◽  
Vicki L. Ellingrod ◽  
...  
Keyword(s):  
Bayesian Model ◽  
Model Comparison ◽  
Visual Integration ◽  
Bayesian Model Comparison ◽  
Comparison Approach

Combined-chain nested sampling for efficient Bayesian model comparison

2017 ◽  
Vol 70 ◽  
pp. 84-93 ◽  
Author(s):  
R. Wesley Henderson ◽  
Paul M. Goggans ◽  
Lei Cao
Keyword(s):  
Bayesian Model ◽  
Model Comparison ◽  
Nested Sampling ◽  
Bayesian Model Comparison

scholarly journals Capturing Ordinal Theoretical Constraint in Psychological Science

2018 ◽  
Author(s):  
Julia M. Haaf ◽  
Fayette Klaassen ◽  
Jeffrey Rouder
Keyword(s):  
Social Sciences ◽  
Linear Model ◽  
Bayesian Model ◽  
Model Comparison ◽  
Social Scientists ◽  
Psychological Science ◽  
Bayesian Model Comparison ◽  
Comparison Approach ◽  
The Social ◽  
Ordinal Level

Most theories in the social sciences are verbal and provide ordinal-level predictions for data. For example, a theory might predict that performance is better in one condition than another, but not by how much. One way of gaining additional specificity is to posit many ordinal constraints that hold simultaneously. For example a theory might predict an effect in one condition, a larger effect in another, and none in a third. We show how common theoretical positions naturally lead to multiple ordinal constraints. To assess whether multiple ordinal constraints hold in data, we adopt a Bayesian model comparison approach. The result is an inferential system that is custom-tuned for the way social scientists conceptualize theory, and that is more intuitive and informative than current linear-model approaches.

scholarly journals What counts in preschool number knowledge? A Bayes factor analytic approach towards theoretical model development

2017 ◽  
Author(s):  
Yi Mou ◽  
Ilaria Berteletti ◽  
Daniel C. Hyde
Keyword(s):  
Individual Differences ◽  
Model Comparison ◽  
Bayes Factor ◽  
Model Development ◽  
Language Abilities ◽  
Numerical Ability ◽  
Selection Strategies ◽  
Bayesian Model Comparison ◽  
Mathematics Knowledge ◽  
Number Knowledge

Preschool children vary tremendously in their numerical knowledge and these individual differences strongly predict later mathematics achievement. To better understand the sources of these individual differences, we measured a variety of cognitive and linguistic abilities motivated by previous literature to be important and then analyzed which combination of these variables best-explained individual differences in actual number knowledge. Through various data-driven Bayesian model comparison and selection strategies on competing multiple regression models, our analyses identified five variables of unique importance to explaining individual differences in preschool children’s symbolic number knowledge: knowledge of the count list, non-verbal approximate numerical ability, working memory, executive conflict processing, and knowledge of letters and words. Further our analyses revealed that knowledge of the count list, likely a proxy for explicit practice or experience with numbers, and non-verbal approximate numerical ability were much more important to explaining individual differences in number knowledge than general cognitive and verbal abilities. These findings suggest that children bring a diverse set of number-specific, general cognitive and language abilities that are involved in children’s learning of mathematics knowledge, and further suggest that number-specific abilities overshadow more general ones in their contribution to children’s early learning of symbolic numbers.

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