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Bayesian Meta-Analysis with Weakly Informative Prior Distributions
Open accessAbstract
Developing meta-analytic methods is an important goal for psychological science. When there are few studies in particular, commonly used methods have several limitations, most notably of which is underestimating between-study variability. Although Bayesian methods are often recommended for small sample situations, their performance has not been thoroughly examined in the context of meta-analysis. Here, we characterize and apply weakly informativepriors for estimating meta-analytic models and demonstrate with extensive simulations that fully Bayesian methods overcome boundary estimates of exactly zero between-study variance, better maintain error rates, and have lower frequentist risk according toKullback-Leibler divergence. While our results show that combining evidence with few studiesis non-trivial, we argue that this is an important goal that deserves further considerationin psychology. Further, we suggest that frequentist properties can provide importantinformation for Bayesian modeling. We conclude with meta-analytic guidelines for appliedresearchers that can be implemented with the provided computer code.
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“12 Results from a complementary Bayesian multilevel meta-analysis model (Harrer etal., 2019; Williams etal., 2018) with weakly informative priors for true pooled effect size (µ ~ N (0, 1)) and between-study heterogeneity ( τ ~ HC (0, 0.5)) aligned with these pooled effect size estimates: Hedge's g = 0.36, 95% CI [0.19, 0.52].”
From When Problem Solving Followed by Instruction Works: Evidence for Productive Failure (2021) · cites this paper as Williams et al., 2018
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Meta-analysis in clinical trials
DerSimonian, R., & Laird, N. (1986) · Controlled Clinical Trials · doi:10.1016/0197-2456(86)90046-2 · Cited by 39,552
Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2003) · doi:10.1201/9780429258480 · Cited by 27,276
Conducting Meta-Analyses in R with the metafor Package
Viechtbauer, W. (2010) · Journal of Statistical Software · doi:10.18637/jss.v036.i03 · Cited by 20,464
Hierarchical Linear Models: Applications and Data Analysis Methods
Davidian, M. (2003) · Journal of the American Statistical Association · doi:10.1198/jasa.2003.s288 · Cited by 13,820
brms : An R Package for Bayesian Multilevel Models Using Stan
Bürkner, P.-C. (2017) · Journal of Statistical Software · doi:10.18637/jss.v080.i01 · Cited by 9,476
Self-citationStatistical Decision Theory and Bayesian Analysis
Berger, J. O. (1985) · Springer Series in Statistics · doi:10.1007/978-1-4757-4286-2 · Cited by 7,722
The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte CarloPreprint
Homan, M. D., & Gelman, A. (2014) · arXiv (Cornell University) · Cited by 3,078
Fixed-and random-effects models in meta-analysis.
Hedges, L. V., & Vevea, J. L. (1998) · Psychological Methods · doi:10.1037/1082-989x.3.4.486 · Cited by 2,977
Park, T., & Casella, G. (2008) · Journal of the American Statistical Association · doi:10.1198/016214508000000337 · Cited by 2,941
Methods of Meta-Analysis: Correcting Error and Bias in Research Findings.
Raudenbush, S. W., Hunter, J. E., & Schmidt, F. L. (1991) · Journal of the American Statistical Association · doi:10.2307/2289738 · Cited by 2,368
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Items 101–124 of 124
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Gambarota, F., Tsuchiya, N., Pastore, M., Polito, N. D., & Sessa, P. (2021) · PsyArXiv (OSF Preprints) · doi:10.31234/osf.io/gt67h · Cited by 1
Integrating and Generalizing Causal Estimates
Dayal, V., & Murugesan, A. (2023) · Springer eBooks · doi:10.1007/978-981-99-3905-3_12
Li, W. H. C., Gleeson, J., Fraser, M., Ciarrochi, J., Hofmann, S. G., Hayes, S. C., & Sahdra, B. K. (2024) · doi:10.31234/osf.io/9j7xv
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Ren, X., & Mok, P. (2025) · Laboratory Phonology Journal of the Association for Laboratory Phonology · doi:10.16995/labphon.17746
Moore, H., Siroux, J., Miguet, M., Fillon, A., Masurier, J., Finlayson, G., Pereira, B., & Thivel, D. (2025) · Pediatric Obesity · doi:10.1111/ijpo.70029
Disparate social structures are underpinned by distinct social rules across a primate radiation
Feder, J. A., Alberts, S. C., Archie, E. A., Arlet, M. E., Baniel, A., Beehner, J. C., Bergman, T. J., Carter, A. J., Charpentier, M. J. E., Chiou, K. L., et al. (2026) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2520774123
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Perla, R., Maran, T. K., Bagci, B., Kraus, S., Kanbach, D. K., & Bouncken, R. B. (2025) · Psychology and Marketing · doi:10.1002/mar.70073 · Cited by 2
Zhang, X., Liang, Z., & Kim, Y. (2025) · Cognitive Therapy and Research · doi:10.1007/s10608-025-10679-x · Cited by 2
Falahati, G., Biglarian, A., Behboudi‐Gandevani, S., & Yarandi, R. B. (2025) · Health Science Reports · doi:10.1002/hsr2.71626
Gravelle, C. D., Zapparrata, N., Abdurokhmonova, G., & Brooks, P. J. (2026) · Journal of Speech Language and Hearing Research · doi:10.1044/2025_jslhr-25-00227
Clinical research on homeopathic preparations: protocol template for a series of systematic reviews
Loef, M., van Haselen, R. A., & Baumgartner, S. (2026) · Systematic Reviews · doi:10.1186/s13643-026-03168-z
Li, S., Yin, Y., Guan, J., & Yu, L. (2026) · Frontiers in Medicine · doi:10.3389/fmed.2026.1760792
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Sevchik, B. L., Singleton, S. P., Lahey, A., Cuijpers, P. J., Harrer, M., Jones, M. T., Nayak, S. M., Strain, E. C., Vandekar, S., Yaden, D. B., et al. (2026) · Neuropsychopharmacology · doi:10.1038/s41386-026-02575-z
Metadata
- Authors
- Williams, D. R., Rast, P., & Bürkner, P. C.
- Affiliations
- University of California, Davis (US)
- University of Münster (DE)
- Publisher
- Center for Open Science
- Published
- 2018-01-10
- OpenAlex
- W2785297454
- Cited by
- 124
- References
- 81
- Citations by year
- 2026: 18 · 2025: 18 · 2024: 27 · 2023: 18 · 2022: 14 · 2021: 15 · 2020: 10 · 2019: 4
- Type
- posted content
- Language
- en
- Open access
- green
- doi.org
- Locations
- PsyArXiv (OSF Preprints) (submittedVersion, cc-by)
- PsyArXiv (OSF Preprints) (submittedVersion)
- OSF Preprints (OSF Preprints) (submittedVersion)
- OSF Preprints (OSF Preprints) (submittedVersion, cc-by)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Psychology Research and Bibliometrics
- Keywords
- Bayesian meta-analysis, weakly informative priors, study heterogeneity, Kullback-Leibler divergence
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