Stat 547Q : Statistical Modeling with Stochastic Processes

Kingman's coalescent emerging from a Wright-Fisher model. Note also the connection with perfect sampling.



Lecture notes

Lecture slides


Stochastic processes are powerful tools for constructing the rich models needed to capture the complexity of our world. Motivated by problems in machine learning and phylogenetics, we will discuss an array of concrete examples where stochastic processes are used to perform sophisticated statistical inferences. After going through these examples, you will be familar with the main building blocks, you will know how to compose them to create new models, you will be able to design inference algorithms for your models and you will have a better understanding of the limits of these models and algorithms.

I will not assume previous exposure to stochastic processes. Probabilists interested in applications of their work are encouraged to participate: in contrast to MATH 303 and MATH 419, the focus will be on statistical and computational issues.

Tentative syllabus

List of topics:

Evaluation: assignments (best 2 of 3), scribing for at least one lecture, and a final project. If you choose to do all 3 projects, you also have the option of substituting the final project by a literature review.