BIOST 2059 - CONSTRAINED STATISTICAL INFERENCE WITH APPLICATIONS

Minimum Credits: 2
Maximum Credits: 2
This is an applied biostatistics course for biostatistics graduate students, other quantitative public health students, and health career professionals who will make use of statistical methods in research projects and possibly develop new biostatistical methods in the future. While this course is intended to be an application oriented course motivated by real scientific problems, it will rely on some statistical theory. Students are expected to have basic understanding of statistical theory at the level of BIOST 2044 (Introduction to Statistical Theory 2) and have applied analysis skills at the level of BIOST 2049 (Applied Regression Analysis). Additionally, students are expected to have working knowledge of the programming language R. Topics covered in this course include: (a) Brief review of some important concepts from BIOST 2043, BIOST 2044 and BIOST 2049, such as parametric and nonparametric estimation and testing of hypotheses, linear fixed and mixed effects models, best linear unbiased predictor (BLUP) and generalized linear models. (b) Some real world motivating examples of various types of constraints on parameter spaces. Reasons for constrained inference. (c) Estimation of parameters and testing of hypotheses under inequality constraints in a variety of settings - challenges and solutions. Various estimation and testing procedures such as Pool Adjacent Violators Algorithm (PAVA), Restricted Maximum Likelihood Estimation (RMLE), Isotonic Regression, Likelihood Ratio Test (LRT), Williams' test, Dunnett's test, Jonckheere-Terpstra test. Substantial reduction in samples sizes and gain in power when using constrained inference based methods in comparison to standard methods. (e) Resampling methods for constrained inference, why they fail for confidence intervals but are suitable for some testing problems. (f) Nonparametric problems - various notions of orderings of random variables, univariate and multivariate analysis. (g) Applications in clinical trials, toxicology, high dimensional gene expression studies, microbiome, cell-cycle and circadian clock.
Academic Career: Graduate
Course Component: Lecture
Grade Component: Grad Letter Grade
Course Requirements: PREQ: BIOST 2044 and BIOST 2049

Click here for class schedule information.

Add to Portfolio.

Close Window