Bayes Rule provides a simple and powerful framework for machine learning. This tutorial will be organised as follows:

1. I will give motivation for the Bayesian framework from the point of view of rational coherent inference, and highlight the important role of the marginal likelihood in Bayesian Occam's Razor.

2. I will discuss the question of how one should choose a sensible prior. When Bayesian methods fail it is often because no thought has gone into choosing a reasonable prior.

3. Bayesian inference usually involves solving high dimensional integrals and sums. I will give an overview of numerical approximation techniques (e.g. Laplace, BIC, variational bounds, MCMC, EP...).

4. I will talk about more recent work in non-parametric Bayesian inference such as Gaussian processes (i.e. Bayesian kernel "machines"), Dirichlet process mixtures, etc.