SDS X84 SDS 384 Topics in Statistics and Probability 3 Hours
3 Lecture Hours 0 Lab Hours
Concepts of probability and mathematical statistics with applications in data analysis and research. Statistics and Data Sciences 384 and Statistics and Scientific Computation 384 may not both be counted unless topics vary. Three lecture hours a week for one semester.
Pre/Corequisites: Graduate standing; and Statistics and Data Sciences 382 (or Statistics and Scientific Computation 382), an introductory probability course and a statistics course, or consent of instructor.
Grading: Student Option
Repeatable for credit: May be repeated for credit when the topics vary.
Academic Level: Doctoral
Topic 1: Applied Probability. Basic probability theory, combinatorial analysis of random phenomena, conditional probability and independence, parametric families of distributions, expectation, distribution of functions of random variables, and limit theorems. Statistics and Data Sciences 384 (Topic 1) and Statistics and Scientific Computation 384 (Topic 1) may not both be counted.
Topic 2: Mathematical Statistics I. The general theory of mathematical statistics. Includes distributions of functions of random variables, properties of a random sample, principles of data reduction, an overview of hierarchical models, decision theory, Bayesian statistics, and theoretical results relevant to point estimation, interval estimation, and hypothesis testing. Only one of the following may be counted: Computational Science, Engineering, and Mathematics 384R, Mathematics 384C, Statistics and Data Sciences 384 (Topic 2). Three lecture hours a week for one semester. Same as: CSE 384R, M 384C Additional prerequisite: Graduate standing; and Mathematics 362K and 378K, or consent of instructor.
Topic 3: Mathematical Statistics II. Continuation of Computational Science, Engineering, and Mathematics 384R and Mathematics 384C. Only one of the following may be counted: Computational Science, Engineering, and Mathematics 384S, Mathematics 384D, Statistics and Data Sciences 384 (Topic 3). Three lecture hours a week for one semester. Same as: CSE 384S, M 384D Additional prerequisite: Graduate standing; Computational Science, Engineering, and Mathematics 384R, or Mathematics 384C; and Mathematics 362K and 378K, Statistics and Data Sciences 382, or consent of instructor.
Topic 4: Regression Analysis. Simple and multiple linear regression, inference in regression, prediction of new observations, diagnosis and remedial measures, transformations, and model building. Emphasis on both understanding the theory and applying theory to analyze data. Only one of the following may be counted: Computational Science, Engineering, and Mathematics 384T, Mathematics 384G, Statistics and Data Sciences 384 (Topic 4). Three lecture hours a week for one semester. Same as: CSE 384T, M 384G Additional prerequisite: Graduate standing; and Mathematics 362K and 378K, Statistics and Data Sciences 382, or consent of instructor.
Topic 6: Design and Analysis of Experiments. Design and analysis of experiments, including one-way and two-way layouts; components of variance; factorial experiments; balanced incomplete block designs; crossed and nested classifications; fixed, random, and mixed models; and split plot designs. Only one of the following may be counted: Computational Science, Engineering, and Mathematics 384U, Mathematics 384E, Statistics and Data Sciences 384 (Topic 6). Three lecture hours a week for one semester. Same as: CSE 384U, M 384E Additional prerequisite: Graduate standing; and Mathematics 362K and 378K, Statistics and Data Sciences 382, or consent of instructor.
Topic 7: Bayesian Statistical Methods. Fundamentals of Bayesian inference in single-parameter and multi-parameter models for inference and decision making, including simulation of posterior distributions, Markov chain Monte Carlo methods, hierarchical models, and empirical Bayes models. Statistics and Data Sciences 384 (Topic 7) and Statistics and Scientific Computation 384 (Topic 7) may not both be counted.
Topic 8: Time Series Analysis. Introduction to statistical time series analysis. Includes autoregressive integrated moving average (ARIMA) and more general models, forecasting, spectral analysis, time domain regression, model identification, estimation of parameters, and diagnostic checking. Statistics and Data Sciences 384 (Topic 8) and Statistics and Scientific Computation 384 (Topic 8) may not both be counted. Additional prerequisite: Mathematics 384D.
Topic 9: Computational Statistics. Modern, computation intensive statistical methods, including simulation, optimization methods, Monte Carlo integration, maximum likelihood estimation and expectation-maximization parameter estimation, Markov chain Monte Carlo methods, resampling methods, and nonparametric density estimation. Statistics and Data Sciences 384 (Topic 9) and Statistics and Scientific Computation 384 (Topic 9) may not both be counted.
Topic 10: Stochastic Processes. Concepts and techniques of stochastic processes, with emphasis on the nature of change of variables with respect to time. Includes characterization, structural properties, and inference. Statistics and Data Sciences 384 (Topic 10) and Statistics and Scientific Computation 384 (Topic 10) may not both be counted.
Topic 11: Theoretical Statistics. Examination of asymptotic theory and empirical processes. The former would include minimax theory, Bernstein von Mises theorem, and Bayesian asymptotics. The latter, would include U statistics and robust estimation. Statistics and Data Sciences 391P (Topic 6) and 384 (Topic 11) may not both be counted. Additional prerequisite: Statistics and Data Sciences 384 (Topic 3) or the equivalent; and advanced probability.