Bayesian Statistical Methods in Psychology

by

Sarah Depaoli

• LAST REVIEWED: 24 February 2021
• LAST MODIFIED: 24 February 2021
• DOI: 10.1093/obo/9780199828340-0277

Introduction

The use of Bayesian statistics within psychology is on the rise, and this trajectory will likely continue to accelerate in the coming years. There are many different reasons why a researcher may want to implement Bayesian methodology. First, there are cases where models are too “complex” for traditional (frequentist) methods to handle. Second, Bayesian methods are sometimes preferred if only small samples are available, since the use of priors can improve estimation accuracy with minimal data. Third, the researcher may prefer to include background information in the estimation process, and this can be done via the priors. Finally, Bayesian methods produce results that are rich with detail and can be more informative about the population parameters. Specifically, information surrounding the entire posterior distribution is provided through Bayesian estimation, as opposed to a point estimate obtained through traditional (frequentist) methods. All of these reasons make Bayesian methods attractive to the psychological sciences. This bibliography begins with a section on General Overviews, which presents works that provide general introductions to Bayesian methods. A subsection within this overview section covers Papers Introducing Bayesian Methods to Subfields in Psychology, and a second subsection includes Resources for Particular Model Types Popular in Psychological Research. Next, some of the more comprehensive Bayesian Textbooks are presented, and this is followed by a treatment of the Philosophy that underlies Bayesian statistics. The next section is Markov Chain Monte Carlo and Samplers. One of the most common tools for Bayesian estimation is the Markov chain Monte Carlo (MCMC) algorithm. MCMC is used to construct chains through samplers, and these chains represent draws from the posterior. A subsection on Convergence is included here to highlight the importance of assessing Markov chain convergence. This is followed by a section on Prior Distributions, which includes subsections on Expert Elicitation of Priors and the Data-Prior Conflict. A section on Software Resources is presented, which covers some of the main software programs implementing Bayesian statistical modeling. Finally, a section on Model Assessment and Fit is presented. Each of these sections and subsections were selected to highlight an understanding of Bayesian statistics, the role it plays in psychology, and proper implementation.

General Overviews

Van de Schoot, et al. 2017 highlights the use of Bayesian statistics within psychology through a systematic review of the literature from 1990 to 2015. A gentle introduction to Bayesian statistics is presented in van de Schoot, et al. 2013, which does not contain any equations but rather focuses on conceptual definitions of concepts. Etz and Vandekerckhove 2018 is another introductory piece, which highlights the main concepts of Bayesian statistics within psychology. Wagenmakers, et al. 2018 presents an overview of Bayesian methods with a focus on hypothesis testing an inference. A basic overview of Bayesian statistics, as well as elements that are commonly misused or misinterpreted, is presented in Depaoli and van de Schoot 2017.

• Depaoli, S., and R. van de Schoot. 2017. Improving transparency and replication in Bayesian statistics: The WAMBS-checklist. Psychological Methods 22.2: 240–261.

  DOI: 10.1037/met0000065

  This paper presents an overview of the main elements required for complete and transparent reporting of Bayesian analyses. It focuses on a 10-point checklist for avoiding common misuse of Bayesian methods. It is a good resource for novice researchers implementing Bayesian methods because it provides guidance for application and reporting.

• Etz, A., and J. Vandekerckhove. 2018. Introduction to Bayesian inference for psychology. Psychonomic Bulletin & Review 25:5–34.

  DOI: 10.3758/s13423-017-1262-3

  This paper provides a basic introduction to Bayesian inference, with a treatment of probability theory. This article is a good introduction for beginners because it provides several examples and highlights methodology and interpretation. It specifically highlights how simple these methods can be to implement, and it works to describe the methods in an accessible manner by removing some of the mystery that typically surrounding Bayesian methods.

• van de Schoot, R., D. Kaplan, J. Denissen, J. B. Asendorpf, F. J. Neyer, and M. A. G. van Aken. 2013. A gentle introduction to Bayesian analysis: Applications to developmental research. Child Development 85.3: 842–860.

  DOI: 10.1111/cdev.12169

  This paper presents a conceptual introduction to Bayesian methods, without the use of equations. It would be a good initial piece to introduce to students new to the topic, or those who are from more of a nontechnical background. It is written for developmental psychologists, but students and researchers new to Bayesian methods from other subfields of psychology will likely find the simplicity of the technical descriptions helpful as an introductory to Bayesian methods.

• van de Schoot, R., S. Winter, M. Zondervan-Zwijnenburg, O. Ryan, and S. Depaoli. 2017. A systematic review of Bayesian applications in psychology: The last 25 years. Psychological Methods 22.2: 217–239.

  DOI: 10.1037/met0000100

  The focus of this systematic review spanned twenty-five years. It shows the use of Bayesian methods has steadily increased over the years, with an emphasis on a more drastic increase in the number of applications using Bayesian methods. It is a good resource for learning more about trends in publishing standards, shifts in journals that publish Bayesian methods, and the different subfields within psychology that are exhibiting an increase in use.

• Wagenmakers, E-J., M. Marsman, T. Jamil, et al. 2018. Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications. Psychonomic Bulletin & Review 25:35–57.

  DOI: 10.3758/s13423-017-1343-3

  This paper highlights advantages of Bayesian methods, including in the context of hypothesis testing and inference. The focus on hypothesis testing is compelling and acts as a terrific overview of the benefits that Bayesian methods can provide compared to methods implementing classical (frequentist) inference.