3 credits
Fall 2025 Lecture Distance Learning Upper Division
The course introduces the fundamental frameworks of statistical theory, from which statistical methods can be derived. This includes the framework of data and statistical models, decision theory (risk functions, Bayes and minimax criteria), sufficient statistics, exponential distribution families, estimation methods, unbiased estimators and information inequality (Cramer-Rao), the Neyman-Pearson framework of hypothesis testing, monotone likelihood ratio families and likelihood ratio tests, and an introduction of asymptotic approximations. Students will need background in advanced calculus, linear algebra, probability, and some mathematical analysis.
Learning Outcomes1Understand the framework of statistical models and be able to define a statistical model for a data analysis problem.
2Use the decision theory to compare different data analysis methods.
3Derive theoretical properties of some statistical methods.
4Be able to justify some commonly used statistical methods through theory.
Prerequisites
Restrictions
made by Purdue students.