banneker-aztlan / linear-regression

Data Analysis Week 2: Linear Regression and Optimization

linear-regression

This week is meant to serve as a transition period between strict formalism (e.g., Bayesian-ism) and detailed application (e.g., MCMC). As such, it is designed to introduce students to ways of thinking about statistical modeling and numerical applications using the (ever insightful) vehicle of linear regression. Goals for the week include:

• getting comfortable with random variables (reasoning by representation)
• understanding different statistical perspectives on problems
• learning the basics of model construction and comparisons
• finding best-fit solutions (optimizations)
• learning the basics of deriving errors
• (if time permits) basics of matrix manipulation

As with some of the other courses here, the main goal of this course is not the detailed material we're covering but instead to (1) get students comfortable thinking about statistical modeling (building on last week's material), and (2) motivate why we are interested in sampling from the full posterior distribution (leading up to subsequent weeks' material).

Further reading: This paper is an excellent resource that builds on lots of the concepts discussed here.