Review and Introduction

Review Materials (on your own, as needed)

Prerequisites for this course include STA 360 (Bayesian Inference) and all its prerequisite at Duke (linear algebra, multivariable calculus, probability, inference, and regression).

Review slides are provided for linear algebra as well as some probability and inference material, including the following. Please familiarize yourself with the content of these notes if your recollection is fuzzy.

• basic properties of vectors and matrices
• linear independence, dependence, and rank of a matrix
• inversion of full-rank and less than full-rank matrices
• common distributions
• maximum likelihood estimation

Review Resources

Penn State University maintains some very nice review materials online (these are shorter in length than the slides below.)

Matrix definitions

Matrix arithmetic

Matrix properties

Matrix inverse

Advanced matrix properties

Slides

Hierarchical Models: Overview

Slides for Your Own Review

Basics: Vectors and matrices

Linear dependence and rank

Determinants and inverses

Random vectors and matrices

Important distributions

Maximum likelihood