Introduction to Bayesian Learning

# VIBASS5 - Basic Course

VIBASS5 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: Numerical approaches.

The big problem in the Bayesian framework: resolution of integrals that appear when applying the learning process. Gaussian approximations, Laplace approximations, Monte Carlo integration and importance sampling, Markov chain Monte Carlo.

### Session II. Bayesian linear models.

Apply basic Importance Sampling and MCMC methods via available software for fitting regression models.

### Session III. Bayesian generalised linear models.

Extending regression models to non-gaussian responses.

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

EVENTS