VIBASS 4
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Introduction to Bayesian Learning

# VIBASS4 - Basic Course

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.