Particle physics is a field in which data has traditionally been analyzed almost exclusively using methods associated with the frequentist notion of probability. During recent years, however, Bayesian methods have slowly begun to enter the field.

I will review the theoretical foundations of Bayesian probability theory, its role in scientific inference, and how the different types of Bayesian analysis differ. Special emphasis will be put on Bayesian model comparison and model averaging, which also allows for rigorous methods for testing the compatibility of different data sets and detecting systematic biases. Then, I will discuss some practical and numerical methods for performing these analyses, and consider a few applications to neutrino physics in detail.