A Conceptual Introduction to Bayesian Model Averaging

Hinne, Max; Gronau, Quentin Frederik; Bergh, Don van den; Wagenmakers, Eric–Jan

doi:10.1177/2515245919898657

Cited by 234 publications

(219 citation statements)

References 65 publications

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“…However, only presenting conditional posterior distributions can potentially be misleading in cases where the null hypothesis remains relatively plausible after seeing the data. A general benefit of Bayesian analysis is that one can compute anunconditional posterior distribution for the parameter using model averaging (e.g., Clyde, Ghosh, & Littman, 2011;Hinne, Gronau, Bergh, & Wagenmakers, 2020). An unconditional posterior distribution for a parameter accounts for both the uncertainty about the parameter within any one model and the uncertainty about the model itself, providing an estimate of the parameter that is a compromise between the candidate models (for more details see Hoeting, Madigan, Raftery, & Volinsky, 1999).…”

Section: Stage 3: Interpreting the Resultsmentioning

confidence: 99%

The JASP guidelines for conducting and reporting a Bayesian analysis

et al. 2020

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Despite the increasing popularity of Bayesian inference in empirical research, few practical guidelines provide detailed recommendations for how to apply Bayesian procedures and interpret the results. Here we offer specific guidelines for four different stages of Bayesian statistical reasoning in a research setting: planning the analysis, executing the analysis, interpreting the results, and reporting the results. The guidelines for each stage are illustrated with a running example. Although the guidelines are geared towards analyses performed with the open-source statistical software JASP, most guidelines extend to Bayesian inference in general.

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Section: Stage 3: Interpreting the Resultsmentioning

confidence: 99%

The JASP guidelines for conducting and reporting a Bayesian analysis

et al. 2020

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“…Instead, we weighted the results from both models according to their posterior probability, thus fully acknowledging the uncertainty with respect to the choice between a fixed or random-effect model. [28,29] To conduct a Bayesian meta-analysis, prior distributions were assigned to the model parameters. [28] For the standardized effect size, we used a default, zero-centered Cauchy distribution with scale parameter equal to 1…”

Section: Model-averaged Bayesian Meta-analysismentioning

confidence: 99%

Comparing the Evidential Strength for Psychotropic Drugs: A Bayesian Meta-Analysis

Pittelkow

Vries

Monden

et al. 2021

Preprint

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Objective: Approval and prescription of drugs should be informed by the strength of evidence for efficacy. While there is no formal policy towards different standards for drug approval, the typical strength of evidence might differ for different psychotropic drug groups. Using a Bayesian framework, we examine (1) whether psychotropic drugs are supported by substantial evidence (at the time of Food and Drug Administration [FDA] approval), and (2) whether there are systematic differences across drug groups. Methods: Data from short-term, placebo-controlled phase II/III clinical trials for 15 antipsychotics, 16 antidepressants for depression, nine antidepressants for anxiety, and 20 drugs for ADHD were extracted from FDA reviews evaluating efficacy prior to marketing approval. Bayesian model-averaged meta-analysis was performed and strength of evidence was quantified with the Bayes factor (BFBMA). Results: We observed substantial variation in strength of evidence and trialling between approved psychotropic drugs: Median evidential strength was extremely strong for ADHD medication (BFBMA = 1820.4), but considerably lower and more frequently classified as weak or moderate for antidepressants for both depression (BFBMA = 94.2) and anxiety (BFBMA = 49.8). Differences might be accounted for by varying median effect sizes (schizophrenia: ESBMA = 0.45, depression: ESBMA = 0.30, anxiety: ESBMA = 0.37, ADHD: ESBMA = 0.72), sample sizes (schizophrenia: N = 324, depression: N = 218, anxiety: N = 254, ADHD: N = 189.5), and numbers of trials (schizophrenia: Nr = 3, depression: Nr = 5.5, anxiety: Nr = 3, ADHD: Nr = 2). Limitations: The analysis only included pre-marketing studies. Conclusion: Evidential strength varied across drug groups: Although most psychotropic drugs were supported by strong evidence at the time of approval, some drugs only had moderate or even ambiguous evidence. These results show the need for more systematic quantification and classification of statistical evidence for psychotropic drugs, and for transparent and clear communication of evidential strength toward clinical decision makers.

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“…A general description of Bayesian testing, model averaging, and reporting is provided by van Doorn et al (2020), Jeffreys (1939), Ly et al (2016aLy et al ( , 2016b, and Ly et al (2020), whereas a more specialized account of Bayesian linear regression is given by Bayarri et al, (2012), Li and Clyde (2018), Liang et al, (2008), Rouder and Morey (2012), and Zellner and Siow (1980). For more on Bayesian model averaging we refer to Hinne et al (2020), Hoeting et al (1999), Scott and Berger (2006, 2020a, 2020b, and Wasserman (2000). Key software implementations in R are the Note.…”

Section: Further Informationmentioning

confidence: 99%

A Review of Applications of the Bayes Factor in Psychological Research

Heck¹,

Hoijtink²,

Fu³

et al. 2020

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The last 25 years have shown a steady increase in attention for the Bayes factor as a tool for hypothesis evaluation and model selection. The present review highlights the potential of the Bayes factor in psychological research. We discuss six types of applications: Bayesian evaluation of point null, interval, and informative hypotheses, Bayesian evidence synthesis, Bayesian variable selection and model averaging, and Bayesian evaluation of cognitive models. We elaborate what each application entails, give illustrative examples, and provide an overview of key references and software with links to other applications. The paper is concluded with a discussion of the opportunities and pitfalls of Bayes factor applications and a sketch of corresponding future research lines.

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A Conceptual Introduction to Bayesian Model Averaging

Cited by 234 publications

References 65 publications

The JASP guidelines for conducting and reporting a Bayesian analysis

The JASP guidelines for conducting and reporting a Bayesian analysis

Comparing the Evidential Strength for Psychotropic Drugs: A Bayesian Meta-Analysis

A Review of Applications of the Bayes Factor in Psychological Research

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