Cover not available

Article published In: Advanced Quantitative Methods in Bi-/Multilingualism
Edited by Christos Pliatsikas, George Pontikas and Ian Cunnings
[Linguistic Approaches to Bilingualism 15:4] 2025
► pp. 453–486

Get fulltext from our e-platform
JBE logo with link
PDF logo with download linkDownload PDF
EPUB logo with download linkDownload EPUB
authorization required

A gentle introduction to Bayesian statistics, with applications to bilingualism research

ORCiD logo with link | University of Lisbon
Published online: 20 May 2025
DOI logo with link
https://doi.org/10.1075/lab.24027.ver
Abstract
Bayesian analyses have been increasingly adopted in psychology and linguistics as an addition (or replacement) to traditional frequentist methods. However, Bayesian methods are not yet widely applied in bilingualism research, possibly because existing introductions and tutorials have not been directed specifically at our field. The current paper highlights the advantages of Bayesian statistics to the bilingualism researcher, by providing both an introduction to its foundational principles and a practical tutorial on estimation and hypothesis testing using the brms R package. The examples build up from simple linear regression to more advanced mixed-effects models and showcase different aspects of a Bayesian workflow. All data, code, models, and supplementary materials are publicly available at https://​osf​.io​/n3jgm/.
Article outline
  • 1.Introduction
  • 2.Fundamental Bayesian principles
    • 2.1Principle 1: Parameters are associated with full probability distributions
    • 2.2Principle 2: Posteriors are probabilities of parameter values given the data
    • 2.3Principle 3: Belief updating through the integration of prior knowledge
      • 2.3.1Bringing priors into the open
  • 3.Estimation and hypothesis testing
  • 4.Bayesian mixed-effects models
    • 4.1Model specification
    • 4.2Prior choice and model checks
    • 4.3Model predictions and inference from posteriors
  • 5.Conclusions
  • Data availability statement
  • Notes
  • References
References (62)
References
Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59(4), 390–412. Google Scholar logo with link to Google Scholar
Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3), 255–278. Google Scholar logo with link to Google Scholar
Bayarri, M. J., & Berger, J. O. (2004). The interplay of Bayesian and frequentist analysis. Statistical Science, 19(1). Google Scholar logo with link to Google Scholar
Broos, W. P. J., Bencivenni, A., Duyck, W., & Hartsuiker, R. J. (2021). Delayed picture naming in the first and second language. Bilingualism: Language and Cognition, 24(2), 389–400. Google Scholar logo with link to Google Scholar
Bürki, A., Elbuy, S., Madec, S., & Vasishth, S. (2020). What did we learn from forty years of research on semantic interference? A Bayesian meta-analysis. Journal of Memory and Language, 1141, 104125. Google Scholar logo with link to Google Scholar
Bürkner, P.-C. (2017). brms: An R package for Bayesian multilevel models using Stan. Journal of Statistical Software, 80(1), 1–28. Google Scholar logo with link to Google Scholar
Bylund, E., Antfolk, J., Abrahamsson, N., Olstad, A. M. H., Norrman, G., & Lehtonen, M. (2023). Does bilingualism come with linguistic costs? A meta-analytic review of the bilingual lexical deficit. Psychonomic Bulletin & Review, 30(3), 897–913. Google Scholar logo with link to Google Scholar
Ciaccio, L. A., & Veríssimo, J. (2022). Investigating variability in morphological processing with Bayesian distributional models. Psychonomic Bulletin & Review, 29(6), 2264–2274. Google Scholar logo with link to Google Scholar
Clark, M. (2022). Bayesian demonstration. Retrieved November 29, 2024, from [URL]
Cohen, J. (1994). The earth is round (p .05). American Psychologist, 49(12), 997–1003. Google Scholar logo with link to Google Scholar
Coretta, S., Casillas, J. V., & Roettger, T. (2023). learnB4SS: Learning materials for the learnB4SS workshop. Retrieved November 29, 2024, from [URL]
Cumming, G. (2014). The new statistics: Why and how. Psychological Science, 25(1), 7–29. Google Scholar logo with link to Google Scholar
Davis, C. J., & Lupker, S. J. (2006). Masked inhibitory priming in English: Evidence for lexical inhibition. Journal of Experimental Psychology: Human Perception and Performance, 321, 668–687. Google Scholar logo with link to Google Scholar
Dickey, J. M., & Lientz, B. P. (1970). The weighted likelihood ratio, sharp hypotheses about chances, the order of a Markov chain. The Annals of Mathematical Statistics, 41(1), 214–226. Google Scholar logo with link to Google Scholar
Dienes, Z., & Mclatchie, N. (2018). Four reasons to prefer Bayesian analyses over significance testing. Psychonomic Bulletin & Review, 25(1), 207–218. Google Scholar logo with link to Google Scholar
Feldman, L. B., Kostić, A., Basnight-Brown, D. M., Đurđević, D. F., & Pastizzo, M. J. (2010). Morphological facilitation for regular and irregular verb formations in native and non-native speakers: Little evidence for two distinct mechanisms. Bilingualism: Language and Cognition, 13(2), 119–135. Google Scholar logo with link to Google Scholar
Fernandes, A. I., Luna, K., Soares, A. P., & Comesaña, M. (2023). Is there an early morphological decomposition during L2 lexical access? A meta-analysis on the morphological priming effect. Brain Sciences, 13(1), 127. Google Scholar logo with link to Google Scholar
Foote, R. (2017). The storage and processing of morphologically complex words in L2 Spanish. Studies in Second Language Acquisition, 39(4), 735–767. Google Scholar logo with link to Google Scholar
Forster, K. I., Mohan, K., & Hector, J. (2003). The mechanics of masked priming. In S. Kinoshita & S. J. Lupker (Eds.), Masked priming: The state of the art (pp. 3–37). Psychology Press.Google Scholar logo with link to Google Scholar
Garcia, G. D. (2024). Bayesian estimation in multiple comparisons. Google Scholar logo with link to Google Scholar
Gelman, A., & Tuerlinckx, F. (2000). Type S error rates for classical and Bayesian single and multiple comparison procedures. Computational Statistics, 15(3), 373–390. Google Scholar logo with link to Google Scholar
Gibson, E., & Fedorenko, E. (2013). The need for quantitative methods in syntax and semantics research. Language and Cognitive Processes, 28(1–2), 88–124. Google Scholar logo with link to Google Scholar
Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90(430), 773–795. Google Scholar logo with link to Google Scholar
Kruschke, J. K. (2015). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan (Edition 2). Academic Press.Google Scholar logo with link to Google Scholar
Kruschke, J. K., & Liddell, T. M. (2018). The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychonomic Bulletin & Review, 25(1), 178–206. Google Scholar logo with link to Google Scholar
Lago, S., Stone, K., Oltrogge, E., & Veríssimo, J. (2023). Possessive processing in bilingual comprehension. Language Learning, 73(3), 904–941. Google Scholar logo with link to Google Scholar
Lakens, D., Scheel, A. M., & Isager, P. M. (2018). Equivalence testing for psychological research: A tutorial. Advances in Methods and Practices in Psychological Science, 1(2), 259–269. Google Scholar logo with link to Google Scholar
Lee, M. D., & Wagenmakers, E.-J. (2013). Bayesian cognitive modeling: A practical course. Cambridge University Press.Google Scholar logo with link to Google Scholar
Linck, J. A., & Cunnings, I. (2015). The utility and application of mixed-effects models in second language research. Language Learning, 65(S1), 185–207. Google Scholar logo with link to Google Scholar
Makowski, D., Ben-Shachar, M. S., Chen, S. H. A., & Lüdecke, D. (2019). Indices of effect existence and significance in the Bayesian framework. Frontiers in Psychology, 101. Google Scholar logo with link to Google Scholar
Marsman, M., & Wagenmakers, E.-J. (2017). Three insights from a Bayesian interpretation of the one-sided P value. Educational and Psychological Measurement, 77(3), 529–539. Google Scholar logo with link to Google Scholar
Matzke, D., & Wagenmakers, E.-J. (2009). Psychological interpretation of the ex-Gaussian and shifted Wald parameters: A diffusion model analysis. Psychonomic Bulletin & Review, 16(5), 798–817. Google Scholar logo with link to Google Scholar
Maxwell, S. E., Lau, M. Y., & Howard, G. S. (2015). Is psychology suffering from a replication crisis? What does “failure to replicate” really mean? American Psychologist, 70(6), 487–498. Google Scholar logo with link to Google Scholar
Mayo, D. G. (2018). Statistical inference as severe testing: How to get beyond the statistics wars (1st ed.). Cambridge University Press. Google Scholar logo with link to Google Scholar
McElreath, R. (2020). Statistical rethinking: A Bayesian course with examples in R and Stan (2nd ed.). CRC Press. Google Scholar logo with link to Google Scholar
Morey, R. D., Hoekstra, R., Rouder, J. N., Lee, M. D., & Wagenmakers, E.-J. (2016). The fallacy of placing confidence in confidence intervals. Psychonomic Bulletin & Review, 23(1), 103–123. Google Scholar logo with link to Google Scholar
Morey, R. D., Rouder, J. N., Verhagen, J., & Wagenmakers, E.-J. (2014). Why hypothesis tests are essential for psychological science: A comment on Cumming (2014). Psychological Science, 25(6), 1289–1290. Google Scholar logo with link to Google Scholar
Nicenboim, B., Schad, D. J., & Vasishth, S. (2024). An introduction to Bayesian data analysis for cognitive science. Retrieved from [URL]
Nickerson, R. S. (2000). Null hypothesis significance testing: A review of an old and continuing controversy. Psychological Methods, 5(2), 241–301. Google Scholar logo with link to Google Scholar
Norouzian, R., De Miranda, M., & Plonsky, L. (2018). The Bayesian revolution in second language research: An applied approach. Language Learning, 68(4), 1032–1075. Google Scholar logo with link to Google Scholar
O’Hagan, A. (2019). Expert knowledge elicitation: Subjective but scientific. The American Statistician, 731, 69–81. Google Scholar logo with link to Google Scholar
Pliatsikas, C., Johnstone, T., & Marinis, T. (2014). fMRI evidence for the involvement of the procedural memory system in morphological processing of a second language. PLoS ONE, 9(5), e97298. Google Scholar logo with link to Google Scholar
Plonsky, L., Mohebbi, H., & Coombe, C. A. (2021). Quantitative research methods and the reform movement in applied linguistics. In Research questions in language education and applied linguistics: A reference guide (pp. 749–753). Springer. Google Scholar logo with link to Google Scholar
Rastle, K., & Davis, M. H. (2008). Morphological decomposition based on the analysis of orthography. Language and Cognitive Processes, 23(7–8), 942–971. Google Scholar logo with link to Google Scholar
Rouder, J. N., Haaf, J. M., & Vandekerckhove, J. (2018). Bayesian inference for psychology, part IV: Parameter estimation and Bayes factors. Psychonomic Bulletin & Review, 25(1), 102–113. Google Scholar logo with link to Google Scholar
Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., & Iverson, G. (2009). Bayesian t tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin & Review, 16(2), 225–237. Google Scholar logo with link to Google Scholar
Schad, D. J., Betancourt, M., & Vasishth, S. (2021). Toward a principled Bayesian workflow in cognitive science. Psychological Methods, 26(1), 103–126. Google Scholar logo with link to Google Scholar
Schad, D. J., Nicenboim, B., Bürkner, P.-C., Betancourt, M., & Vasishth, S. (2022). Workflow techniques for the robust use of Bayes factors. Psychological Methods. Google Scholar logo with link to Google Scholar
Schad, D. J., Nicenboim, B., & Vasishth, S. (2024). Data aggregation can lead to biased inferences in Bayesian linear mixed models and Bayesian analysis of variance. Psychological Methods. Google Scholar logo with link to Google Scholar
Schad, D. J., Vasishth, S., Hohenstein, S., & Kliegl, R. (2020). How to capitalize on a priori contrasts in linear (mixed) models: A tutorial. Journal of Memory and Language, 1101, 104038. Google Scholar logo with link to Google Scholar
Schmalz, X., Biurrun Manresa, J., & Zhang, L. (2023). What is a Bayes factor? Psychological Methods, 28(3), 705–718. Google Scholar logo with link to Google Scholar
Silva, R., & Clahsen, H. (2008). Morphologically complex words in L1 and L2 processing: Evidence from masked priming experiments in English. Bilingualism: Language & Cognition, 111, 245–260. Google Scholar logo with link to Google Scholar
Sinharay, S., & Stern, H. S. (2002). On the sensitivity of Bayes factors to the prior distributions. The American Statistician, 56(3), 196–201. Google Scholar logo with link to Google Scholar
van de Schoot, R., Kaplan, D., Denissen, J., Asendorpf, J. B., Neyer, F. J., & Van Aken, M. A. G. (2014). A gentle introduction to bayesian analysis: Applications to developmental research. Child Development, 85(3), 842–860. Google Scholar logo with link to Google Scholar
Van De Schoot, R., Winter, S. D., Ryan, O., Zondervan-Zwijnenburg, M., & Depaoli, S. (2017). A systematic review of Bayesian articles in psychology: The last 25 years. Psychological Methods, 22(2), 217–239. Google Scholar logo with link to Google Scholar
Vasishth, S., Nicenboim, B., Beckman, M. E., Li, F., & Kong, E. J. (2018). Bayesian data analysis in the phonetic sciences: A tutorial introduction. Journal of Phonetics, 711, 147–161. Google Scholar logo with link to Google Scholar
Vehtari, A., Gelman, A., & Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing, 27(5), 1413–1432. Google Scholar logo with link to Google Scholar
Veríssimo, J. (2021a). Analysis of rating scales: A pervasive problem in bilingualism research and a solution with Bayesian ordinal models. Bilingualism: Language and Cognition, 24(5), 842–848. Google Scholar logo with link to Google Scholar
(2021b). BLC mini-series: New statistical approaches and research practices for bilingualism research. Bilingualism: Language and Cognition, 24(5), 799–800. Google Scholar logo with link to Google Scholar
Veríssimo, J., Heyer, V., Jacob, G., & Clahsen, H. (2018). Selective effects of age of acquisition on morphological priming: Evidence for a sensitive period. Language Acquisition, 25(3), 315–326. Google Scholar logo with link to Google Scholar
Wagenmakers, E.-J., Gronau, Q. F., Dablander, F., & Etz, A. (2022). The support interval. Erkenntnis, 87(2), 589–601. Google Scholar logo with link to Google Scholar
Wagenmakers, E.-J., Lee, M., Lodewyckx, T., & Iverson, G. J. (2008). Bayesian versus frequentist inference. In H. Hoijtink, I. Klugkist, & P. A. Boelen (Eds.), Bayesian evaluation of informative hypotheses (pp. 181–207). Springer New York. Google Scholar logo with link to Google Scholar
Cited by (3)

Cited by three other publications

Laméris, Tim Joris & Yōsuke Igarashi
2025. Individual variation in epenthetic vowel production by Brazilian Portuguese–Japanese bilinguals. Linguistic Approaches to Bilingualism DOI logo
Pliatsikas, Christos, George Pontikas & Ian Cunnings
2025. Applying advanced quantitative methods in bi-/multilingualism. Linguistic Approaches to Bilingualism 15:4 ► pp. 425 ff. DOI logo
Zhou, Chao & João Veríssimo
2025. L2 difficulties in the perception of Mandarin tones: Phonological universals or domain-general aptitude?. Bilingualism: Language and Cognition ► pp. 1 ff. DOI logo

This list is based on CrossRef data as of 14 november 2025. Please note that it may not be complete. Sources presented here have been supplied by the respective publishers. Any errors therein should be reported to them.

Mobile Menu Logo with link to supplementary files background Layer 1 prag Twitter_Logo_Blue