Introduction to Bayesian Learning
VIBASS6 - Basic Course
The first two days include a basic course on Bayesian learning (12 hours), with conceptual sessions in the morning and practical sessions with basic Bayesian packages in the afternoon. This is a summary of the contents of both days.
We use the R package
vibass which contains the practical activities and a few interactive apps. Please make sure that you bring a recent R version, with recently updated packages. Follow the instructions on the package website for installing it, ideally prior to the workshop, to make the most of our time together.
Session I: All you need is… probability
Frequentist and Bayesian probability. Bayes’ theorem for random events and variables, parameters, hypothesis, etc. Sequential updating. Predictive probabilities.
Session II: Binary data
Proportions: binomial distribution and likelihood function. Prior distribution: the beta distribution. Summarising posterior inferences.
Session III. Inference and prediction with simulated samples
Estimation and prediction. Simulated samples: comparison of independent populations.
Session IV. Count data
Count data: Poisson distribution. Poisson model parameterised in terms of rate and exposure. Gamma distribution as conjugate prior distributions. Negative binomial predictive distributions.
Session V. Normal data.
Normal data: Estimation of a normal mean with known variance. Prediction of a future observation. Normal data with unknown mean and variance. Nuisance parameters. Joint prior distributions. Joint, conditional and marginal posterior distributions.
Session I: Numerical approaches.
The big problem in the Bayesian framework: resolution of integrals that appear when applying the learning process. Gaussian approximations, Laplace approximations, Monte Carlo integration and importance sampling, Markov chain Monte Carlo.
Session II. Bayesian linear models.
Apply basic Importance Sampling and MCMC methods via available software for fitting regression models.
Session III. Bayesian generalised linear models.
Extending regression models to non-Gaussian responses.
Session IV. Bayesian hierarchical models.
Incorporating random effects: Bayesian hierarchical models (BHMs), the coolest tool for modelling highly structured models. Hierarchies, hyperparameters, and hyperpriors. (Generalised) linear mixed models as basic examples of BHMs. Software for inference in Bayesian hierarchical models.