Mathematics provides a powerful language for describing the world around us. However, analyzing real world processes with mathematical models is wrought with difficulties. Observations of the real world are typically sparse or noisy and mathematical models are only approximations of reality. Overcoming these challenges is the goal of statistics. Statistical tools provide a rigorous way of combining observational data with mathematical models while also characterizing the uncertainty that arises in the real-world to math-world translation.

This course will provide an introduction to Bayesian statistics with a particular emphasis on the use of Bayesian techniques for combining computational models with observations. Within this model calibration context, students will be exposed to aspects of probability theory, mathematical and statistical modeling, inverse problems, and broader concepts from data science. The goal of this course is not only to expose students to the field of Bayesian inference, but also to teach students modern data science tools. By the end of the course, students will be able to both formulate Bayesian inverse problems and solve them with cutting edge software frameworks.

Learning Objectives

By the end of this course, students will be able to

Formulate statistical models of real-world processes.

Construct models that blend physical and statistical assumptions to represent complex datasets.

Characterize model parameters with Bayesâ€™ rule using both analytic approaches and basic sampling techniques.

Use modern tools like GitHub and Pandas to share code and work with large datasets.

Instructor

Dr. Matthew Parno
Research Scientist, US Army Cold Regions Research and Engineering Laboratory (CRREL)
Adjunct Professor, Dartmouth College Department of Mathematics matthew.d.parno@dartmouth.edu