Statistics 3965 (STAT 235). Elementary Stochastic Processes
Prerequisite: Statistics 3025Q or 3375Q or 5585 or consent of instructor.
Conditional probability and expectation, moments and distribution of random sums, transition probabilities of Markov chains, first step analysis of Markov chains, long run behavior of Markov chains, classification of states, homogeneous and nonhomogeneous Poisson processes, interarrival time and waiting time distributions, spatial Poisson process, compound Poisson process, birth and death processes, branching processes, queuing processes with exponential interarrival times and service times.
Statistics 3515Q/5515 (STAT 243Q/343). Design of Experiments
Prerequisite: A previous statistical methods course and consent of instructor.
Completely randomized, randomized block, Latin squares, nested and repeated measures designs, multiple comparisons, factorial experiments, random and mixed models, confounding and fractional factorials, analysis using SAS computer package.
Statistics 4875 (STAT 253). Nonparametric Methods
Prerequisite: Statistics 3375Q or 5585 or consent of instructor.
Intuitive approach and basic concepts, one and two-sample problems, estimation, testing and confidence procedures, small sample and asymptotic distribution theory, Pitman efficiency, C sample problems, rank correlation.
Statistics 5099 (STAT 300). Student Seminar/Internship
Statistics 5015 (STAT 310). Distribution Theory for Statistics
Prerequisite: Consent of Instructor.
Mathematical foundations for advanced courses in the department, with special reference to the advanced probability sequence Statistics 6325, 6894. Topics will vary but will typically center on real analysis: sequences, series, limits and continuity of functions, differentiation, sequences and series of functions. As time permits, other topics such as metric spaces and vector spaces will be treated.
Statistics 5585/5685 (STAT 315/316). Mathematical Statistics.
Prerequisite: 3 semesters of calculus, the third possibly concurrent.
Distribution and density functions of random variables , conditional probability and independence, moment generating functions and moments, common families of distributions, multi-parameter exponential family, multiple random variables, change-of-variable techniques, models of convergence, central limit theorem, distribution of order statistics, sufficiency principle, minimal sufficiency, ancillarity, completeness, likelihood principle, point estimation, interval estimation, hypothesis testing, evaluation of estimators and tests.
Statistics 5505/5605 (STAT 320/321). Applied Statistics
Prerequisites: A previous statistical methods course, calculus, and/or consent of instructor.
Statistics from a data analytic viewpoint incorporating parametric and nonparametric methods, exploratory data analysis, graphical methods, one-sample problems, jackknifing, bootstrapping, robustness, two-sample problems, k-sample problems including one-way ANOVA, randomized block designs, two-way ANOVA, additivity, simple linear regression, multiple linear regression, analysis of covariance, categorical data.
Statistics 6315 (STAT 330). Inference I
Prerequisite: Statistics 5685.
Exponential families, sufficient statistics, loss, decision rules and risk, convexity, prior information, unbiasedness (including multi-parameter case), Bayesian analysis, minimax analysis, minimaxity and admissibility in exponential families, simultaneous estimation and shrinkage estimators, efficient likelihood estimations, equivariant estimation.
Statistics 6515 (STAT 331). Inference II
Prerequisite: Statistics 6315 and consent of instructor.
Real analysis for inference, statistics and subfields, conditional expectations and probability distributions, UMP tests with applications to normal distributions and confidence sets, invariance, asymptotic theory of estimation and likelihood based inference.
Statistics 5725 (STAT 332). Linear Models I
Prerequisites: Statistics 5685 or 3445, linear algebra, consent of instructor.
Introduction to matrices with applications in statistics, multivariate distribution theory, distribution of quadratic forms, theory for the full rank and less than full rank model (including geometric developments), analysis of covariance, comparison of regression and dummy variable modeling.
Statistics 6325/6894 (STAT 333/450). Probability Theory
Prerequisite: Statistics 5015 and consent of instructor.
Concepts from abstract analysis, Lebesgue measure, abstract measures, extension of measures, Lebesgue-Stieltjes measures, measurable functions and integration. Radon-Nikodym Theorem, product measures and Fubini's Theorem, measures on infinite product spaces, basic concepts of probability theory, conditional probability and expectation, regular conditional probability, strong law of large numbers, martingale theory, martingale convergence theorems, uniform integrability, optional sampling theorems, Kolmogorov's Three series Theorem, weak convergence of distribution functions, the fundamental weak compactness theorems, convergence to a normal distribution, Lindeberg's Theorem.
Statistics 5525 (STAT 352). Sampling Theory
Prerequisite: Statistics 5685 or 3445.
Concepts of sampling error, non-sampling error, bias, sampling designs, simple random sampling with replacement, simple random sampling without replacement, sampling with unequal probabilities stratified sampling, optimum allocation, proportional allocation, ratio estimators, regression estimators, systematic sampling, super population approaches, inference in finite sampling.
Statistics 5361 (STAT 361). Statistical Computing
Prerequisite: Statistics 3025Q, 3445 or 5685 and/or consent of instructor.
An introduction to computing for statistical problems and research. Topics covered are basic numerical methods, nonlinear statistical methods, numerical integration and differentiation, random generation, and simulation. Should time allow, statistical graphics is considered.
Statistics 5625 (STAT 372). Introduction to Biostatistics
Rates and proportions, sensitivity, specificity, two-way tables, odds ratios, relative risk, ordered and non-ordered classifications, trends, case-control studies, elements of regression including logistic and Poisson, additivity and interaction, combination of studies and meta-analysis.
Statistics 5635 (STAT 373). Clinical Trials
Basic concepts of clinical trial analysis: controls, randomization, blinding, surrogate endpoints, sample size calculations, sequential monitoring, side-effect evaluation and intention-to-treat analyses. Also, experimental designs including dose response study, multicenter trials, clinical trials for drug development, stratification, and cross-over trials.
Statistics 5645 (STAT 374). Concepts and Analysis of Survival Data
Survival models, censoring and truncation, nonparametric estimation of survival functions, comparison of treatment groups, mathematical and graphical methods for assessing goodness of fit, parametric and nonparametric regression models.
Statistics 5825 (STAT 380). Applied Time Series
Introduction to prediction using time-series regression methods with non-seasonal and seasonal data. Smoothing methods for forecasting. Modeling and forecasting using univariate autoregressive moving average models.
Statistics 5665 (STAT 382). Applied Multivariate Analysis
Prerequisite: Matrix algebra, a prior statistical methods course, Statistics 3375Q or 5585 or consent of instructor
Multinormal techniques with applications, topics covered: Hotelling's T2 test, multivariate analysis of variance, discriminant analysis, principal components, factor analysis, cluster analysis, introduction to and use of SAS computer package.
Statistics 6694 (STAT 430). Linear Models II
Prerequisite: Statistics 5725.
Further topics in regression (including robust, ridge & reverse regression). Models not of full rank (including design models). Multi-way crossed classification, variance components, simultaneous inference, analysis of covariance, cross validation, regression diagnostics, generalized linear models.
In addition, special topics courses are offered in areas such as: bioinformatics, categorical data analysis, time series methods, generalized linear models, Bayesian data analysis, spatial and longitudinal data modeling, sequential analysis, stochastic geometry, survival analysis, approximations and inequalities, nonparametric methods, and advanced topics in inference. |
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