| Statistics | STAT | 401 | Introduction to Probability | 3 OR 4 hours. | Probability spaces, random variables and their distributions, conditional distribution and stochastic independence, special distributions, sampling distributions, limit theorems. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 210. |
| Statistics | STAT | 411 | Statistical Theory | 3 OR 4 hours. | Estimation, tests of statistical hypotheses, best tests, sufficient statistics, Rao-Cramer inequality, sequential probability ratio tests, the multivariate normal distribution, nonparametric methods. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 401. |
| Statistics | STAT | 416 | Nonparametric Statistical Methods | 3 OR 4 hours. | Distribution free tests for location and dispersion problems, one-way and two-way layouts, the independence problem, regression problems involving slopes, detecting broad alternatives, resampling methods. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 381 or STAT 411. |
| Statistics | STAT | 431 | Introduction to Survey Sampling | 3 OR 4 hours. | Simple random sampling; sampling proportions; estimation of sample size; stratified random sampling; ratio estimators; regression estimators; systematic and cluster sampling. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 411 or STAT 481. |
| Statistics | STAT | 451 | Computational Statistics | 3 OR 4 hours. | Modern computationally-intensive statistical methods including Monte Carlo integration and simulation, optimization and maximum likelihood estimation, EM algorithm, MCMC, sampling and resampling methods, non-parametric density estimation. 3 undergraduate hours. 4 graduate hours. Extensive computer use required. Prerequisite(s): STAT 411. |
| Statistics | STAT | 461 | Applied Probability Models I | 3 OR 4 hours. | Computing probabilities and expectations by conditioning, Markov chains, Chapman-Kolmogorov equations, branching processes, Poisson processes and exponential distribution, continuous-time Markov chains, reversibility, uniformization. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 401. |
| Statistics | STAT | 471 | Linear and Non-Linear Programming | 3 OR 4 hours. | Linear programming, simplex algorithm, degeneracy, duality theorem sensitivity analysis, convexity, network simplex methods, assignment problems. Constrained and unconstrained minima. Quasi-Newton methods. Ellipsoidal methods of Kachian. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 310. |
| Statistics | STAT | 473 | Game Theory | 3 OR 4 hours. | Games in extensive and normal form. Minimax theorem. Solving matrix games via linear programming. Nash equilibria for nonzero-sum games, Shapley value, bargaining models. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in MATH 310 or STAT 401. |
| Statistics | STAT | 475 | Mathematics and Statistics for Actuarial Sciences I | 3 OR 4 hours. | Financial mathematics as it pertains to the valuation of deterministic cash flows. Basic concepts and techniques regarding the theory of interest. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Math 210. |
| Statistics | STAT | 481 | Applied Statistical Methods II | 3 OR 4 hours. | Linear regression, introduction to model building, analysis of variance, analysis of enumerative data, nonparametric statistics, product and system reliability, quality control. SAS and SPSSX applications. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 381. |
| Statistics | STAT | 486 | Statistical Consulting | 3 OR 4 hours. | Introduction to statistical consulting methods and techniques. Handling and transformation of raw data sets in CMS. Statistical analysis of data sets with SAS and SPSSX. 3 undergraduate hours. 4 graduate hours. Prerequisite(s): Grade of C or better in STAT 411 or STAT 481. |
| Statistics | STAT | 494 | Special Topics in Statistics, Probability and Operations Research | 3 OR 4 hours. | Course content announced prior to each semester in which it is given. Topics drawn from areas such as distribution theory; Bayesian inference; discrete optimization; applied probability models; resampling techniques; biostatistics; environmental sampling. 3 undergraduate hours. 4 graduate hours. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. |
| Statistics | STAT | 496 | Independent Study | 1 TO 4 hours. | Reading course supervised by a faculty member. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the instructor and approval of the department. |
| Statistics | STAT | 501 | Probability Theory I | 4 hours. | Abstract measure theory, probability measures, Kolmogorov extension theorem, sums of independent random variables, the strong and weak laws of large numbers, the central limit theorem, characteristic functions, law of iterated logarithm, infinitely divisible laws. Prerequisite(s): MATH 534 or consent of the instructor. |
| Statistics | STAT | 502 | Probability Theory II | 4 hours. | Radon-Nikodym theorem, conditional expectations, martingales, stationary processes, ergodic theorem, stationary Gaussian processes, Markov chains, introduction to stochastic processes, Brownian motions. Prerequisite(s): STAT 501. |
| Statistics | STAT | 511 | Advanced Statistical Theory I | 4 hours. | Statistical models, criteria of optimum estimation, large sample theory, optimum tests and confidence intervals, best unbiased tests in exponential families, invariance principle, likelihood ratio tests. Prerequisite(s): STAT 411. |
| Statistics | STAT | 512 | Advanced Statistical Theory II | 4 hours. | Basic concepts in decision theory, prior and posterior distributions, Bayesian decision theory, hierarchical models, robustness, minimax analysis, invariance principle, sequential analysis, completeness. Prerequisite(s): STAT 511. |
| Statistics | STAT | 521 | Linear Statistical Inference | 4 hours. | Estimation and testing in linear models, generalized inverses of matrices, n-dimensional normal distribution, quadratic forms, likelihood ratio tests, best invariant tests, analysis of variance. Prerequisite(s): STAT 411. |
| Statistics | STAT | 522 | Multivariate Statistical Analysis | 4 hours. | Multivariate normal distribution, estimation of mean vector and covariance matrix, T-square statistic, discriminant analysis, general linear hypothesis, principal components, canonical correlations, factor analysis. Prerequisite(s): STAT 521. |
| Statistics | STAT | 531 | Sampling Theory I | 4 hours. | Foundations of survey design and inference for finite populations;the Horvitz-Thompson estimator;simple random, cluster,systematic survey designs;auxiliary size measures in design and inference. Prerequisite(s): STAT 411. |
| Statistics | STAT | 532 | Sampling Theory II | 4 hours. | Uses of auxiliary size measures in survey sampling; cluster sampling; systematic sampling; stratified sampling; superpopulation methods; randomized response methods; resampling; nonresponse; small area estimations. Prerequisite(s): STAT 531. |
| Statistics | STAT | 535 | Optimal Design Theory I | 4 hours. | Gauss-Markov theorem,optimality criteria, optimal designs for 1-way, 2-way elimination of heterogeneity models,repeated measurements, treatment-control ; Equivalence theorem,approximate designs for polynomial regression. Prerequisite(s): STAT 521. |
| Statistics | STAT | 536 | Optimal Design Theory II | 4 hours. | Construction of optimal designs: BIB , Latin square and generalized Youden , repeated measurements , treatment-control studies; construction of factorial designs including orthogonal arrays Prerequisite(s): STAT 535 or consent of the instructor. |
| Statistics | STAT | 571 | Noncooperative Games | 4 hours. | Extensive games. Separation and fixed point theorems. General minimax theorems. Nash equilibria. War duels. Completely mixed games. Games with convex payoff. Stochastic games. Prerequisite(s): STAT 461 or MATH 411. |
| Statistics | STAT | 572 | Cooperative Game Theory | 4 hours. | Utility Theory. Games with side payments, stable sets, core, bargaining sets,Shapley value,Nucleolus. Market games. NTU value. Multilinear extensions, non-atomic games . Prerequisite(s): STAT 571 or consent of the instructor. |
| Statistics | STAT | 591 | Advanced Topics in Statistics, Probability and Operations Research | 4 hours. | Special topics. Topics drawn from areas such as: Data analysis; Bayesion inference; Nonlinear models; Time series; Computer aided design; reliability models; game theory. May be repeated. Prerequisite(s): Approval of the department. |
| Statistics | STAT | 593 | Graduate Student Seminar | 1 hours. | For graduate students who wish to receive credit for participating in a learning seminar whose weekly time commitment is not sufficient for a reading course. This seminar must be sponsored by a faculty member. Satisfactory/Unsatisfactory grading only. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. |
| Statistics | STAT | 595 | Research Seminar | 1 hours. | Current developments in research with presentations by faculty, students, and visitors. Researchers and practitioners from academia, industry and government will present talks on topics of current interest. Satisfactory/Unsatisfactory grading only. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. |
| Statistics | STAT | 596 | Independent Study | 1 TO 4 hours. | Reading course supervised by a faculty member. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the instructor and the department. |
| Statistics | STAT | 598 | Master's Thesis | 0 TO 16 hours. | Research work under the supervision of a faculty member leading to the completion of a master's thesis. Satisfactory/Unsatisfactory grading only. Prerequisite(s): Approval of the department. |
| Statistics | STAT | 599 | Doctoral Thesis Research | 0 TO 16 hours. | Research work under the supervision of a faculty member leading to the completion of a doctoral thesis. Satisfactory/Unsatisfactory grading only. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. |