VIBASS7 - Basic Course

The first two days include a basic course on Bayesian learning (12 hours), alternating conceptual and practical hands-on sessions. This is a summary of the contents of both days.

At the end of the course, participants will be able to start applying Bayesian methods to simple models in their field, having acquired an understanding of Bayesian concepts and becoming aware of the possibilities for more specific and more complex methods for in-depth analysis.

• Target public: people with little to no previous knowledge of Bayesian statistics with some concrete motivation. E.g. master/PhD students who are going to use or work with Bayesian statistics, professionals in various fields (medicine, biology, ecology, industry, etc.) seeking to improve their quantitative capacities.

• Prerequisites:

  • Basic knowledge of probability and statistics. Descriptive statistics, probability distributions.

  • Basic knowledge of the R language for statistical computing.

  • A working level of English.

If you want to (and can) prepare yourself in advance in order to make the most out of the training, we can recommend a few books that are freely available on line. They are excellent references to come back in the future, as well.

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.

Monday

Session I: Introduction to Bayesian Statistics: all you need is … probability

Introduction. Bayes’ theorem. Introduction to Bayesian inference.

Session II: Binary data

Introduction. Bayesian learning for binary data: estimation. Bayesian learning for binary data: prediction.

Session III. Count data

Poisson data. Bayesian learning for count data: estimation. Bayesian learning for count data: predicction.

Session IV. Normal data.

Normal data. Bayesian learning for normal data with unknown mean and known variance: estimation and prediction. Bayesian learning for normal data with unknown mean and unknown variance: estimation and prediction.

Session V. Bayesian linear models

Frequentist linear models. Bayesian linear models. Bayesian analysis with conjugate priors.

Session VI: Simulation-based Bayesian inference

Introduction. Simulation by composition.

Tuesday

Session VII. Numerical approaches

Introduction. Importance sampling. Markov chain Monte Carlo methods: Metropolis-Hastings algorithm; Gibbs sampling algorithm.

Session VIII. Bayesian Generalized linear models

Introduction. Bayesian Generalized linear models: Bayesian logistic regression model; Bayesian Poisson regression model.

Session IX. Bayesian hierarchical modelling

Introduction. Bayesian hierarchical: Linear mixed-effects models; Generalized linear mixed-effects models.

Session X. DCD

Doubts, comments and discussion.