This course aims to teach students to use programming to gain intuition about statistical theory and fundamental concepts and to visualize data appropriately. Specifically, computational methods covered include simulation methods and numerical methods in maximization and integration. Appropriate graphical displays of statistical and simulation results will be emphasized. Statistical concepts covered include sampling distributions, confidence intervals and p-values, the central limit theorem, expectation, and maximum likelihood estimation.

This course introduces probability, random variables, independence, and distribution theory. Inference topics include, but are not limited to, estimation, hypothesis tests, likelihood ratio tests, confidence intervals, sufficiency, and efficient estimators.

Statistics (STA) 649 is an introduction to the principles of experimental design. Many statistics courses are taught from the perspective of analyzing data that has already been collected. However, problems that occur at the analysis stage (e.g., violations of assumptions, too small of sample, etc.) could have been avoided if the experimenter had consulted a statistician before the experiment was conducted and the data collected. This course will introduce common experimental designs so that when the data are collected, the aforementioned shortcomings are avoided.

The main objective of this course is to equip students with the traditional and modern multivariate statistical methods. Students will learn the motivation behind these methods, how to apply them and interpret the results obtained. Focus will be on understanding distributional results rather than the technical derivations. Students will gain competency in writing R scripts for applying the multivariate methods learned.

Course begins with an applied regression module that emphasizes analysis and interpretation of real data, and statistical computing. Second part of course focuses on principles and implementation of experimental design for scientific research purposes. Standard designs presented along with the proper kinds of analysis for each. Continued emphasis on real data and statistical computing using R and/or SAS.

Use of statistical programming languages R and SAS to gain insight into statistical theory, to better understand fundamental statistical concepts, and to visualize data appropriately. Sampling distributions, confidence intervals and p-values, the central limit theorem, expectation, and maximum likelihood estimation. Simulation studies, data management, editing data, running basic statistical procedures, and producing reports.

This course will involve students in small consulting projects intended to illustrate practical biostatistical problems.

Topics to be selected by STA faculty. May be repeated to a maximum of nine credits.

Basic concepts of decision theory, sufficiency and completeness; completeness of multiparametric exponential family; unbiasedness and invariance of decision rules; Bayes, minimax and invariant estimators; testing of hypotheses and optimality properties.

Probability spaces, extension theorem, random variables; independence, conditional probability, conditional expectation; laws of large numbers, law of the iterated logarithm; convergence in distribution; characteristic functions; central limit theorems; martingales.