Bayesian Inference: concepts and key methods
Laws of large numbers and their applications
Basic concepts of classical statistical inference
Basic random process models (Bernoulli, Poisson and Markov) and their main properties
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
6.041.1x or equivalent. Calculus (single-variable and multivariable). Comfort with mathematical reasoning, sequences, limits, infinite series, the chain rule, and ordinary or multiple integrals.