Introduction to Bayesian Data Analysis using R - Online

Markov Chain Monte Carlo (MCMC) Methods– While simple Bayesian models can sometimes be solved analytically, most real-world problems require numerical methods. We will introduce MCMC and demonstrate how the brms package in R uses Stan to fit a wide variety of Bayesian models. By replicating earlier analyses with MCMC, we’ll see how these methods generalise to more complex settings.

Bayesian Linear Models– We next compare Bayesian linear regression using brm to classical regression with lm. By examining similarities and differences, participants will gain insight into how Bayesian estimation, inference, and model comparison can enrich their analysis. We will also explore categorical predictors and move toward varying intercept and slope models as a bridge to more complex structures.

Bayesian Model Evaluation and Comparison– We next consider how to evaluate and compare Bayesian models, particularly by using posterior predictive checks and using fast and efficient cross-validation. These methods allow us to evaluate whether any given Bayesian model matches the observed data, and to compare competing statistical models or hypotheses.

Extending the Linear Model– Bayesian methods make it straightforward to relax standard assumptions. For instance, we can use t-distributions to handle outliers more robustly or model residual variance as a function of predictor variables. We will see how these flexible extensions can improve the fit and interpretability of our models.

Bayesian Generalised Linear Models (GLMs)– We then move to GLMs, including logistic (binary, ordinal, multinomial), Poisson, negative binomial, and zero-inflated models. Using real data examples, we will show how Bayesian methods can handle a wide range of distributions and link functions, making it easier to choose models that align with the data’s structure and research goals.

Bayesian Multilevel and Mixed Effects Models– Finally, we explore multilevel (hierarchical) and mixed effects models in a Bayesian context. We will see how to model nested and crossed data structures, incorporate group-level predictors, and handle complex correlation patterns. Bayesian methods often simplify fitting these models and can help avoid some of the convergence issues that can arise in a classical framework.