Beta-Bernoulli updates (scripts available on eCommons)
statistical modeling in general and Bayesian modeling in particular: recap; introduction to Markov Chain Monte Carlo (MCMC) and the Metropolis-Hastings family of algorithms (scripts available on eCommons)
the mean model: simulated data, R analysis, JAGS analysis; the structure of JAGS models, reexpressing parameters, number of chains, number of iterations, burnin, thinning, the Brooks-Gelman-Rubin (BGR) convergence diagnostic (a.k.a. Rhat), graphical summaries of posterior distributions; binomial proportion inference with JAGS instead of the Metropolis algorithm we built “by hand” for this purpose; comparison of 3 models for the same binomial proportion data with different uniform priors: posterior estimation with JAGS and computing the evidence / marginal likelihood for each model based on the JAGS posterior samples; inference for 2 binomial proportions with JAGS instead of the Metropolis algorithm we built “by hand” for this purpose (scripts available on eCommons)
essentials of linear models; t-tests with equal and unequal variances (simulated data, R analysis, JAGS analysis) (scripts available on eCommons)
simple linear regression (simulated data, R analysis, JAGS analysis); goodness-of-fit assessment in Bayesian analyses (posterior predictive distributions and Bayesian p-values); interpretation of confidence vs. credible intervals, fixed-effects 1-way ANOVA (simulated data, R analysis, JAGS analysis); random-effects 1-way ANOVA (simulated data, R analysis, JAGS analysis); inferring binomial proportions with hierarchical priors (random-effects for “coins”, i.e., basically, random-effects “binomial” ANOVA) (scripts available on eCommons)
2-way ANOVA w/o and w/ interactions (simulated data, R analysis, JAGS analysis); linear mixed-effects models — random intercepts only, independent random intercepts and slopes, correlated random intercepts and slopes (simulated data, R analysis, JAGS analysis) (scripts available on eCommons)
a different approach to introducing random-effects models (random effects by subject) following a chapter of Lee & Wagenmakers 2012 (“Bayesian Cognitive Modeling: A Practical Course”) and associated R &BUGS code very closely: the approach is driven by having to simultaneously satisfy both (i) the goal of having an informative posterior predictive distribution for the “average” subject and (ii) the goal of having a good model fit to each of the subjects we have data from (scripts available on eCommons)