Bayesian modeling and inference is a powerful modern approach to representing the statistics of the world, reasoning about the world in the face of uncertainty, and learning about it from data. It cleanly separates the notions of representation, reasoning, and learning. It provides a principled framework for combining multiple source of information such as prior knowledge about the world with evidence about a particular case in observed data. This course will provide a solid introduction to the methodology and associated techniques, and show how they are applied in diverse domains ranging from computer vision to molecular biology to astronomy. Graduate-level requirements include different exams requiring greater depth of understanding of topics, and will be assigned questions based on graduate-student specific assignments topics.