140.752.01 ADVANCED METHODS IN BIOSTATISTICS II

Surveys basic statistical inference, estimates, tests and confidence intervals, and exploratory data analysis. Reviews probability distributions and likelihoods, independence and exchangeability, and modes of inference and inferential goals including minimizing MSE. Reviews linear algebra, develops the least squares approach to linear models through projections, and discusses connections with maximum likelihood. Covers linear, least squares regression, transforms, diagnostics, residual analysis, leverage and influence, model selection for estimation and predictive goals, departures from assumptions, efficiency and robustness, large sample theory, linear estimability, the Gauss Markov theorem, distribution theory under normality assumptions, and testing a linear hypothesis.

Upon successful completion of this course, students will be able to: 1) Apply the theories to standard experimental designs; 2) Understand and estimate variance components; 3) Understand theory and application of linear mixed models; 4) Understand the concept of best linear unbiased estimation and prediction; 5) Develop the theory of restricted maximum likelihood; 6) Understand shrinkage estimation.