Peter Green’s introductory lecture on Bayesian inference can be found here:

Description: Inference is the process of discovering from data about mechanisms that may have caused or generated that data, or at least explain it. The goals are varied – perhaps simply predicting future data, or more ambitiously drawing conclusions about scientific or societal truths. In the language of applied mathematics, these are inverse problems. Bayesian inference is about using probability to do all this. One of its strengths is that all sources of uncertainty in a problem can be simultaneously and coherently considered. It is model-based (in the language of machine learning, these are generative models), and we can use Bayesian methods to choose and criticize the models we use.