Introduction to Probability: Part II – Inference & Processes

The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical inference are the keys to analyzing data and making scientifically sound predictions.

This course is part of a 2-part sequence on the basic tools of probabilistic modeling. Topics covered in this course include:  

• laws of large numbers
• the main tools of Bayesian inference methods
• an introduction to classical statistical methods
• an introduction to random processes (Poisson processes and Markov chains)

This course is a follow-up to Introduction to Probability: Part I - The Fundamentals, which introduced the general framework of probability models, multiple discrete or continuous random variables, expectations, conditional distributions, and various powerful tools of general applicability. The contents of the two parts of the course are essentially the same as those of the corresponding MIT class, which has been offered and continuously refined over more than 50 years. It is a challenging class, but will enable you to apply the tools of probability theory to real-world applications or your research.

Probabilistic models use the language of mathematics. But instead of relying on the traditional "theorem - proof" format, we develop the material in an intuitive - but still rigorous and mathematically precise - manner. Furthermore, while the applications are multiple and evident, we emphasize the basic concepts and methodologies that are universally applicable.

Photo by Pablo Ruiz Múzquiz on Flickr. (CC BY-NC-SA 2.0)

• Bayesian inference: basic concepts and methods
• Inference in linear normal models
• General and linear least mean squares estimation
• Limit theorems (weak law of large numbers, and the central limit theorem)
• An introduction to classical statistics
• The Bernoulli and Poisson processes
• Markov chains