Psychology faces distinctive statistical challenges: small sample sizes per participant, large individual differences, complex experimental designs, and the replication crisis that revealed how fragile frequentist conclusions can be. Bayesian methods address all of these challenges. Hierarchical models handle individual differences naturally, priors regularize estimates when data are sparse, and posterior distributions replace the dichotomous thinking of null-hypothesis significance testing with continuous measures of evidence.
Hierarchical Modeling of Experimental Data
The standard structure of psychological experiments — multiple participants each completing multiple trials across multiple conditions — demands hierarchical modeling. Bayesian hierarchical models estimate participant-level parameters while shrinking extreme estimates toward the group mean, producing more accurate predictions for individual participants and more powerful group-level inferences.
μᵢ ~ Normal(μ_pop, τ²) [participant-level intercept]
μ_pop ~ Normal(6, 1) [population mean, log-ms scale]
τ ~ HalfCauchy(0, 0.5) [between-participant SD]
Packages like brms (Bayesian Regression Models using Stan) have made hierarchical Bayesian modeling accessible to psychologists without requiring expertise in probabilistic programming. A brms formula like RT ~ condition + (1 + condition | participant) specifies a full hierarchical model that is automatically translated to Stan code and fitted via MCMC.
Bayesian Cognitive Models
Cognitive process models go beyond describing data patterns to modeling the underlying mental processes. The drift-diffusion model, for instance, decomposes reaction time distributions into drift rate (evidence accumulation speed), boundary separation (response caution), and nondecision time (encoding and motor execution). Bayesian estimation of these models recovers the latent cognitive parameters that drive observable behavior.
The replication crisis in psychology exposed the problems with p-value-driven research: p-hacking, optional stopping, and publication bias inflated false-positive rates far beyond the nominal 5%. Bayesian methods offer structural solutions. Bayes factors quantify evidence for and against hypotheses without requiring fixed sample sizes. Sequential Bayesian designs allow continuous monitoring of accumulating evidence. And Bayesian estimation with regularizing priors naturally penalizes the overfitting that drives non-replicable findings.
Bayesian Hypothesis Testing in Psychology
The Bayes factor has gained traction in psychology as an alternative to p-values. The "default" Bayes factor tests developed by Rouder, Morey, and colleagues use principled default priors (JZS priors) that require minimal subjective input while maintaining desirable properties like consistency and predictive matching. Unlike p-values, Bayes factors can provide evidence for the null hypothesis — a critical capability when the research question is whether an effect exists at all.
The JASP software package, developed at the University of Amsterdam, provides a point-and-click interface for Bayesian t-tests, ANOVA, regression, and other standard analyses, making Bayesian methods accessible to researchers without programming experience.
"In psychology, we study the most variable phenomenon in nature — human behavior. Our statistical methods must embrace this variability, not pretend it away. Bayesian hierarchical models let each person be different while still learning about people in general." — Michael D. Lee and Eric-Jan Wagenmakers, Bayesian Cognitive Modeling
Model Comparison and Theory Testing
Cognitive science often pits competing theoretical models against each other: does learning follow a power law or an exponential? Does memory retrieval use a threshold or a signal-detection process? Bayesian model comparison via Bayes factors or leave-one-out cross-validation provides principled tools for distinguishing between theories. The marginal likelihood automatically penalizes model complexity, favoring the simplest theory consistent with the data — a property that aligns with scientific parsimony.
Clinical and Applied Psychology
Bayesian methods are increasingly used in clinical psychology for individual-level assessment. Bayesian reliable change indices determine whether a patient's improvement exceeds measurement error. Bayesian network models map the conditional dependencies among psychiatric symptoms, revealing how symptoms maintain each other and suggesting targeted intervention points. And Bayesian adaptive testing selects the most informative items for each test-taker, reducing assessment time while maintaining measurement precision.