Course Description
Following an overview of probability measures and distribution functions, modes of convergence, laws of large numbers and central limit theorems, decision theory, hypothesis testing, and Bayesian inference are considered. Emphasis is given to results needed to develop and evaluate biostatistical methods rather than rigorous mathematical proofs.
Athena Title
Advanced Biostatistical Infere
Prerequisite
STAT 6820
Semester Course Offered
Offered fall
Grading System
A - F (Traditional)
Course Objectives
The aim of this course and its sequel (BIOS 8320) is to train students in the theoretical foundations required to evaluate the mathematical and statistical properties of new and innovative biostatistical methods. Students completing this course should be able to: 1. Explain elements of probability theory, including probability measures, measurable functions, and integration; 2. Explain the distinction between the different modes of convergence, including almost sure convergence, convergence in probability, convergence in moments, and convergence in distribution; 3. Explain conditions for weak and strong laws of large numbers; 4. Explain conditions for central limit theorems, including those of Lypounov and Linderberg-Feller; 5. Describe elements of decision theory, including decision rules, loss functions, admissibility, and minimax; 6. Explain Neyman-Pearson, unbiased, UMP, UMPU, and permutation tests of hypotheses; 7. Develop likelihood ratio, Wald and score tests for simple and composite null hypotheses; 8. Explain and evaluate methods for Bayesian inference, including Bayesian decision theory, Bayes rules and risk, propriety of posterior distributions, and Bayesian estimation and interval estimation.
Topical Outline
1. Overview of Probability Measures and Distribution Functions 2. Random Variables 3. Modes of Convergence 4. Laws of Large Numbers 5. Central Limit Theorems 6. Decision Theory 7. Hypothesis Testing 8. Bayesian Inference
Syllabus
Public CV