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Introduction to Bayesian Learning

VIBASS2 - Basic Course

VIBASS2 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 16

Session I: Theory (10:00 – 11:30)

Introduction. All you need is… probability. Proportions: binomial distribution and likelihood function. Prior distribution: the beta distribution. Posterior distribution is also a beta distribution. Summarising posterior inferences. Estimation and prediction. Prediction of new binomial data. Inference and prediction with simulated samples: comparison of independent populations.

Session II: Theory (12:00 – 13:30)

Count data: Poisson distribution. Poisson model parameterized in terms of rate and exposure. Gamma distribution as conjugate prior distributions. Negative binomial predictive distributions. 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. Hypothesis testing. Bayes factor.

Session III and IV: Practice (15:00 – 16.30, 17:00 – 18:30)

All you need is… lacasitos, Winterfell, and to measure your height. Conceptual and computational issues for the Beta-Binomial, Poisson-Gamma, and Normal-Normal models.

Tuesday 17

Session V: Theory (10:00 – 11.30)

Bayesian statistical modelling. Starting with linear and generalized linear models and understanding the basics of how to model a real problem from the Bayesian point of view. Response variables, covariates, factors (fixed and random).

Session VI: Theory (12:00 – 13.30)

The big problem in the Bayesian framework: resolution of integrals that appear when applying the learning process. Numerical approaches: Laplace approximations, Monte Carlo integration and importance sampling. Markov Chain Monte Carlo: Gibbs sampling and Metropolis Hastings. Convergence, inspection of chains, etc. Examples of MCMC. Software for performing MCMC. Hierarchical Bayesian modeling. Hierarchies or levels. Parameters and hyperparameters. Priors and hyperpriors.

Session VII and VIII: Practice (15:00 – 16.30, 17:00-18:30)

Programming your own Metropolis-Hasting algorithm for the data and models of the Sessions III and IV. R Software for inference in Bayesian hierarchical models.