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: **Introduction to Bayesian statistics** (10:00 – 11:30)

All you need is… probability. Frequentist and Bayesian probability. Bayes’ theorem for random events and variables, parameters, hypothesis, etc. Sequential updating. Predictive probabilities. **Proportions**: binomial distribution and likelihood function. **Prior distribution**: the beta distribution. **Summarising** posterior inferences. **Estimation and prediction**. Simulated samples: comparison of independent populations.

### Session I: Practice (12:00 – 12:30)

All you need is… lacasitos.

### Session II: **Basic statistical models** (15:00 – 16:30)

**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**.

### Session II: Practice (17:00 – 18:30)

How many u’s in a *Game of Thrones* book page and how tall are you?

## Tuesday

### Session III: **Bayesian inference** (10:00 – 11:30)

The big problem in the Bayesian framework: resolution of integrals that appear when applying the learning process. **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. **Software** for performing MCMC.

### Session III: Practice (12:00 – 13:30)

Programming your own Metropolis-Hasting algorithm.

### Session IV: **Bayesian hierarchical models** (15:00 – 16:30)

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.

### Session IV: Practice (17:00 – 18:30)

**Software** for inference in Bayesian hierarchical models.

EVENTS