VIBASS 2
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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.