VIBASS4 - 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.

Monday

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 parameterized 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.

Tuesday

Session I: All you need is… modelling

The big problem in the Bayesian framework: resolution of integrals that appear when applying the learning process.

Session II. Numerical approaches to the posterior distribution.

Numerical approaches: Gaussian approximations, Laplace approximations, Monte Carlo integration and importance sampling. Markov chain Monte Carlo: Gibbs sampling and Metropolis Hastings. Convergence, inspection of chains, etc.

Session III. Software for Bayesian Analysis

Software for inference in Bayesian hierarchical models.

Session IV. Bayesian hierarchical models

Incorporating random effects: Bayesian hierarchical models (BHMs), the coolest tool for modelling highly structured models. Hierarchies, hyperparameters, and hyperpriors. (Generalized) linear mixed models as basic examples of BHMs.