Bayes Factors

Kass, Robert E.; Raftery, Adrian E.

doi:10.2307/2291091

Cited by 7,591 publications

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“…In contrast with the frequentist approach to probability, in Bayesian statistics there is no need to think of a parent distribution that originated the data because the observations, and eventually some prior information on the involved processes, are all that serves for the inference. Bayesian methods condition on the data actually observed and are therefore able to assign posterior probabilities to any number of hypotheses directly [e.g., Kass and Raftery, 1995]. Also, the definition of a measure of the discrepancy between the model M j and the parent distribution f(x) would be pointless under the Bayesian framework; in contrast, one could think of defining a discrepancy D B [M j , D] between the operational model and the data D. A natural choice in the Bayesian framework is to relate D B [M j , D] to the posterior probability of the model M j , conditioned upon the data D, Pr(M j jD): The larger is this posterior probability, the smaller is the discrepancy between the model and the data,…”

Section: Appendix B: Bayesian Information Criterionmentioning

confidence: 99%

Model selection techniques for the frequency analysis of hydrological extremes

Laio

Baldassarre

Montanari

2009

Water Resources Research

170

116

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[1] The frequency analysis of hydrological extremes requires fitting a probability distribution to the observed data to suitably represent the frequency of occurrence of rare events. The choice of the model to be used for statistical inference is often based on subjective criteria, or it is considered a matter of probabilistic hypotheses testing. In contrast, specific tools for model selection, like the well-known Akaike information criterion (AIC) and the Bayesian information criterion (BIC), are seldom used in hydrological applications. The objective of this study is to verify whether the AIC and BIC work correctly when they are applied to identifying the probability distribution of hydrological extremes, i.e., when the available samples are small and the parent distribution is highly asymmetric. An additional model selection criterion, based on the Anderson-Darling goodness-of-fit test statistic, is here proposed, and the performances of the three methods are compared through an extensive numerical analysis. The capability of the three criteria to recognize the correct parent distribution from the available data samples varies from case to case, and it is rather good in some cases (in particular when the parent is a two-parameter distribution) and unsatisfactory in others. An application to flood peak time series from 1000 catchments located in the United Kingdom provides some further information on the qualities and drawbacks of the considered criteria. From the numerical simulations and data-based analyses it can be concluded that the three model selection techniques considered here produce results of comparable quality.

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Section: Appendix B: Bayesian Information Criterionmentioning

confidence: 99%

Model selection techniques for the frequency analysis of hydrological extremes

Laio

Baldassarre

Montanari

2009

Water Resources Research

170

116

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“…In addition, we still cannot have any direct information about whether the collected data supports our hypotheses with the reported RUNNING HEAD: UTILIZING BAYESIAN STATISTICS 19 frequentist indicators; such indicators inform us whether it is possible to reject null hypotheses (Kruschke & Liddell, 2018). If we utilize Bayesian techniques, we simple need to interpret one indicator, a Bayes factor, based on the suggested threshold values (e.g., Kass & Raftery, 1995).…”

Section: Running Head: Utilizing Bayesian Statistics 18mentioning

confidence: 95%

“…Furthermore, as the current debates indicated, conventional P-value thresholds widely used in the field, particularly, p < .05, could only support very week or even could not support RUNNING HEAD: UTILIZING BAYESIAN STATISTICS 23 the presence of positive evidence (Benjamin et al, 2018). Instead, BFs show us the strength of evidence; directly BF thresholds used in the field can also be considered as better thresholds to make practical decisions about accepting a specific hypothesis based on evidence (Kass & Raftery, 1995). Hence, reporting BFs will provide readers, particularly researchers and educators who are interested in developing evidence-based moral educational programs, potentially with more practical information regarding whether findings, suggestions, and arguments in a specific article are well supported by empirical evidence.…”

Section: Running Head: Utilizing Bayesian Statistics 18mentioning

confidence: 96%

“…Since prior odds and posterior odds are the ratio of beliefs about the hypotheses before and after observing the data, BFs can be thought of as quantifying how much one should adjust the prior belief give the data. Guidelines for interpreting BFs exist (Jeffreys, 1961;Kass & Raftery, 1995).…”

Section: Running Head: Utilizing Bayesian Statisticsmentioning

confidence: 99%

“…In this situation, practically, both divergent outcomes, including the unfavorable outcome from Bayesian analysis, might need to be reported when Bayesian techniques are applied. Researchers may consider reporting something like the following: "Although the result from classical inference indicated that effect of the factor was significant (p < .05), Bayesian inference showed that the supporting evidence is rather weak (2 ≤ 2logBF < 6) (see Kass and Raftery (1995) for criteria). Thus, we need to interpret the effect of the factor with a caution."…”

Section: Running Head: Utilizing Bayesian Statistics 18mentioning

confidence: 99%

See 2 more Smart Citations

Why do we need to employ Bayesian statistics and how can we employ it in studies of moral education?: With practical guidelines to use JASP for educators and researchers

Han

Park

Thoma

2018

Journal of Moral Education

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In this paper, we discuss the benefits of and how to utilize Bayesian statistics in studies of moral education. To demonstrate concrete examples of the applications of Bayesian statistics to studies of moral education, we reanalyzed two datasets previously collected: one small dataset collected from a moral educational intervention experiment, and one big dataset from a largescale Defining Issues Test-2 survey. Results suggest that Bayesian analysis of datasets collected from moral educational studies can provide additional useful statistical information, particularly that associated with the strength of evidence supporting alternative hypotheses, which has not been provided by the classical frequentist approach focusing on P-values. Finally, we introduce several practical guidelines pertaining to how to utilize Bayesian statistics, including the utilization of newly developed free statistical software, Jeffrey's Amazing Statistics Program (JASP), and thresholding based on Bayes Factors, to scholars in the field of moral education.

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Role of GABRA2 in Trajectories of Externalizing Behavior Across Development and Evidence of Moderation by Parental Monitoring

Dick

Latendresse²,

Lansford³

et al. 2009

Arch Gen Psychiatry

154

148

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Context As we identify genes involved in psychiatric disorders, the next step will be to study how the risk associated with susceptibility genes manifests across development and in conjunction with the environment. We describe analyses aimed at characterizing the pathway of risk associated with GABRA2, a gene previously associated with adult alcohol dependence, in a community sample of children followed longitudinally from childhood through young adulthood. Objective To test for an association between GABRA2 and trajectories of externalizing behavior from adolescence to young adulthood and for moderation of genetic effects by parental monitoring. Design Data were analyzed from the Child Development Project, with yearly assessments conducted since that time. A saliva sample was collected for DNA at the 2006 follow-up, with a 93% response rate in the target sample. Growth mixture modeling was conducted using Mplus to identify trajectories of externalizing behavior and to test for effects of GABRA2 sequence variants and parental monitoring. Setting Nashville and Knoxville, Tennessee, and Bloomington, Indiana. Participants A community-based sample of families enrolled at 3 sites as children entered kindergarten in 1987 and 1988. Analyses for the white subset of the sample (n=378) are reported here. Main Outcome Measures Parental monitoring measured at 11 years of age; Child Behavior Checklist youth reports of externalizing behavior at ages 12, 14, 15, 16, 17, 19, 20, 21, and 22 years. Results Two classes of externalizing behavior emerged: a stable high externalizing class and a moderate decreasing externalizing behavior class. The GABRA2 gene was associated with class membership, with subjects who showed persistent elevated trajectories of externalizing behavior more likely to carry the genotype previously associated with increased risk of adult alcohol dependence. A significant interaction with parental monitoring emerged; the association of GABRA2 with externalizing trajectories diminished with high levels of parental monitoring. Conclusions These analyses underscore the importance of studying genetic effects across development and of identifying environmental factors that moderate risk.

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Bayes Factors

Cited by 7,591 publications

References 0 publications

Model selection techniques for the frequency analysis of hydrological extremes

Model selection techniques for the frequency analysis of hydrological extremes

Why do we need to employ Bayesian statistics and how can we employ it in studies of moral education?: With practical guidelines to use JASP for educators and researchers

Role of GABRA2 in Trajectories of Externalizing Behavior Across Development and Evidence of Moderation by Parental Monitoring

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