Michael D. Lee, working at the University of California, Irvine, has been a leading advocate and developer of Bayesian methods for cognitive modeling. His work addresses the fundamental challenge of connecting formal cognitive models to empirical data: how to estimate parameters, compare competing models, and characterize individual differences in cognitive processes. His textbook Bayesian Cognitive Modeling (with Wagenmakers) has made these methods accessible to a wide audience.
Bayesian Cognitive Modeling
P(data|M_k) = integral of P(data|theta, M_k) * P(theta|M_k) d_theta
Bayes factor: BF_12 = P(data|M_1) / P(data|M_2)
Marginal likelihood automatically penalizes complexity
Lee has developed and applied Bayesian methods for comparing cognitive models, emphasizing that the marginal likelihood (the quantity that drives Bayesian model comparison) automatically balances goodness of fit against model complexity. This provides a principled alternative to information criteria (AIC, BIC) and avoids the need for ad hoc complexity penalties. His work has shown how Bayes factors can be used to compare models that differ qualitatively in their assumptions about cognitive architecture.
Lee has emphasized that individual differences are not nuisance variance but informative data. His hierarchical Bayesian approach estimates both individual-level cognitive parameters and their population distribution simultaneously, revealing meaningful variation in processes like memory capacity, decision thresholds, and learning rates that correlates with clinical status, developmental stage, and personality measures.
Applications Across Cognitive Domains
Lee has applied Bayesian cognitive modeling to memory, categorization, decision making, number cognition, and wisdom of crowds phenomena. His work on the wisdom of crowds has used cognitive models to identify experts and weight their contributions optimally, demonstrating that model-based aggregation outperforms simple averaging. His contributions to the study of individual differences have shown that latent mixture models can identify qualitatively different cognitive strategies within experimental populations.
Legacy and Impact
Lee's Bayesian Cognitive Modeling textbook has trained a generation of researchers in the application of Bayesian methods to psychological models. His advocacy for graphical model notation, WinBUGS/JAGS/Stan implementations, and open-science practices has made sophisticated Bayesian analysis practical for experimentalists. His work demonstrates that methodological advances in model fitting and comparison can be as important as the cognitive models themselves.