Graduate Courses for Statistics and Probability (STAT)

Schedule of Classes: Fall | Winter | Spring | Summer
(Only current and next semester available)

STAT 400 Applied Probability and Statistics I (3 credits)
Prerequisite: MATH141. Not acceptable toward graduate degrees in STAT, AMSC, or MATH. Credit will be granted for only one of the following: BMGT231, ENEE324 or STAT400. These courses are not interchangeable. Consult your program requirements or advisor for what is acceptable toward your program of study.
Random variables, standard distributions, moments, law of large numbers and central limit theorem. Sampling methods, estimation of parameters, testing of hypotheses.

STAT 401 Applied Probability and Statistics II (3 credits)
Prerequisite: STAT400 (Not acceptable toward graduate degrees in STAT, AMSC, or MATH).
Point estimation - unbiased and consistent estimators. Interval estimation. Minimum variance and maximum likelihood estimators. Testing of hypotheses. Regression, correlation and analysis of variance. Sampling distributions. Elements of non-parametric methods.

STAT 405 Stochastic Models for Queues and Networks (3 credits)
Prerequisite: STAT400 or ENEE324. Credit will be granted for only one of the following: BMGT435 or STAT405.
Review of probability and random variables. Generating functions. Poisson and renewal processes. Single server queues with random customer arrivals. Markov models, balance equations. Examples of queuing networks. Applications to computer and communications networks.

STAT 410 Introduction to Probability Theory (3 credits)
Prerequisite: MATH240 and MATH241. Also offered as SURV410. Credit will be granted for only one of the following: STAT410 or SURV410.
Probability and its properties. Random variables and distribution functions in one and several dimensions. Moments. Characteristic functions. Limit theorems.

STAT 420 Introduction to Statistics (3 credits)
Prerequisite: STAT410 or SURV410. Also offered as SURV420. Credit will be granted for only one of the following: STAT420 or SURV420.
Point estimation, sufficiency, completeness, Cramer-Rao inequality, maximum likelihood. Confidence intervals for parameters of normal distribution. Hypothesis testing, most powerful tests, likelihood ratio tests. Chi-square tests, analysis of variance, regression, correlation. Nonparametric methods.

STAT 430 Introduction to Statistical Computing with SAS (3 credits)
Prerequisite: STAT400 or permission of instructor.
Descriptive and inferential statistics. SAS software: numerical and graphical data summaries; merging, sorting and splitting data sets. Least squares, regression, graphics and informal diagnostics, interpreting results. Categorical data, lifetime data, time series. Applications to engineering, life science, business and social science.

STAT 440 Sampling Theory (3 credits)
Prerequisite: STAT401 or STAT420. Also offered as SURV440. Credit will be granted for only one of the following: STAT440 or SURV440.
Simple random sampling. Sampling for proportions. Estimation of sample size. Sampling with varying probabilities. Sampling: stratified, systematic, cluster, double, sequential, incomplete.

STAT 464 Introduction to Biostatistics (3 credits)
Prerequisite: One semester of calculus. Not acceptable for credit towards degrees in mathematics or statistics. Junior standing.
Probabilistic models. Sampling. Some applications of probability in genetics. Experimental designs. Estimation of effects of treatments. Comparative experiments. Fisher-Irwin test. Wilcoxon tests for paired comparisons.

STAT 470 Actuarial Mathematics (3 credits)
Prerequisite: Calculus through MATH240 and MATH241. Recommended: STAT400.
Major mathematical ideas involved in calculation of life insurance premiums, including compound interest and present valuation of future income streams; probability distribution and expected values derived from life tables; the interpolation of probability distributions from values estimated at one-year multiples; the 'Law of Large Numbers' describing the regular probabilistic behavior of large populations of independent individuals; and the detailed calculation of expected present values arising in insurance problems.

STAT 498 Selected Topics in Statistics (1-6 credits)
Prerequisite: permission of department. Repeatable to 16 credits.
Topics of special interest to advanced undergraduate students will be offered occasionally under the general guidance of the MATH/STAT major committee. Students register for reading in statistics under this number.

STAT 600 Probability Theory I (3 credits)
Prerequisite: STAT 410.
Probability space, classes of events, construction of probability measures. Random variables, convergence theorems, images of measures. Independence. Expectation and moments, Lebesque integration, spaces, Radon-Nikodym and LP theorem, singular and absolutely continuous measures. Conditional expectations, existence of regular distributions, applications. Probabilities on product spaces, Fubini theorem, Kolmogorov extension theorem, Tulcea product theorem.

STAT 601 Probability Theory II (3 credits)
Prerequisite: STAT 600.
Characteristic functions. Bochner's representation theorem. Helly's theorems and Levy's inversion formula. Applications of residue theorem. Infinitely divisible distributions. Kolmogorov's three-series theorem. Law of the iterated logarithm. Arc sine Law. Central limit theorems (Lindeberg-Feller theorem). Weak and strong laws of large numbers. Martingale convergence theorems (for sequences).

STAT 610 Stochastic Processes I (3 credits)
Prerequisites: STAT 600; and STAT 601, or equivalent. Recommended: STAT 650, MATH 630.
General classes of stochastic processes, finite-dimensional distributions, random elements of function spaces. Sample continuity and measurability. Gaussian processes, covariance functions, Brownian motion construction and properties. Weak convergence theory for probability measures on spaces of (continuous) functions. Markov processes with continuous time-parameter: transition functions, semigroups and infinitesimal generators.

STAT 650 Applied Stochastic Processes (3 credits)
Prerequisite: STAT 410 or MATH 410 with one semester of probability.
Basic concepts of stochastic processes. Renewal processes and random walks, fluctuation theory. Stationary processes, spectral analysis. Markov chains and processes (discrete and continuous parameters.) Birth and death processes, diffusion processes. Applications from theories of queuing, storage, inventory, epidemics, noise, prediction and others.

STAT 658 Advanced Applied Stochastic Processes II (3 credits)
Prerequisites: STAT 650 plus a graduate course in analysis, or permission of instructor. Recommended: STAT 600, STAT 601, STAT 610. Repeatable to 6 credits if content differs.
Advanced topics in applied stochastic processes, rotating among the headings of queueing theory, population proceses, and regenerative phenomena. Course includes disucssion of stochastic models and fields of application, Markov process theory including calculation and characterization of stationary distributions and diffusion approximations, renewal theory and Wiener-Hopf factorization theory.

STAT 687 Minicourse Series in the Mathematical Sciences (1 credits)
Also offered as AMSC 687 and MATH 687. Credit will be granted for only one of the following: AMSC 687, MATH 687 or STAT 687.
This series will consist of up to sixteen 3-lecture presentations covering a broad range of topics in the mathematical sciences. Each minicourse is intended to be self-contained and accessible to first year graduate students and advanced undergraduates. The goal of each minicourse is to present an active research area or significant result and the necessary vocabulary and perspective for students to appreciate it. The goal of the Minicourse Series is to broaden a student's awareness of the mathematical sciences and to inform them of research directions.

STAT 689 Research Interactions in Statistics (1-3 credits)
Prerequisite: consent of instructor. Repeatable to 06 credits if content differs.
The students participate in a vertically integrated (undergraduate, graduate and/or postdoctoral, faculty) research group. Format varies, but includes regular meetings, readings and presentations of material. See graduate program's online syllabus or contact the graduate program director for more information.

STAT 698 Selected Topics in Probability (1-4 credits)

STAT 700 Mathematical Statistics I (3 credits)
Prerequisite: STAT 410 or equivalent.
Sampling distributions including noncentral chi-squared, t, F. Exponential families, completeness. Sufficiency, factorization, likelihood ratio. Decision theory, Bayesian methods, minimax principle. Point estimation. Lehmann-Scheffe and Cramer-Rao theorems. Set estimation.

STAT 701 Mathematical Statistics II (3 credits)
Prerequisite: STAT 700 or equivalent.
Testing hypotheses: parametric methods. Neyman-Pearson lemma. Uniformly most powerful tests. Unbiased tests. Locally optimal tests. Large sample theory, asymptotically best procedures. Nonparametric methods, Wilcoxon, Fisher-Yates, median tests. Linear models, analysis of variance, regression and correlation. Sequential analysis.

STAT 705 Computational Statistics (3 credits)
Prerequisite: STAT 420 or STAT 700. Recommended: Some programming experience (any language). Credit will be granted for only one of the following: STAT 705 or STAT 798C. Formerly STAT 798C.
Modern methods of computational statistics and their application to both practical problems and research. S-Plus and SAS programming with emphasis on S-Plus. S-Plus objects and functions, and SAS procedures. Topics include data management and graphics, Monte Carlo and simulation, bootstrapping, numerical optimization in statistics, linear and generalized linear models, nonparametric regression, time series analysis.

STAT 710 Advanced Statistics I (3 credits)
Prerequisite: STAT 421. Recommended corequisite: STAT 600.
Statistical decision theory. Neyman-Pearson lemma and its extensions. Uniformly most powerful test. Monotone likelihood ratio. Exponential families of distributions, concepts of similiarity, and tests with Neyman structure. Unbiased tests and applications to normal families.

STAT 711 Advanced Statistics II (3 credits)
Prerequisite: STAT 710.
Invariance, almost invariance, and applications to rank tests. Invariant set estimation. Linear models with applications to analysis of variance and regression. Elements of asymptotic theory. Minimax principle and Hunt-Stein theorem.

STAT 730 Time Series Analysis (3 credits)
Prerequisites: STAT 700 plus a graduate course in analysis, or permission of instructor. Recommended: STAT 701, STAT 650.
The methodology of probabilistic description and statistical analysis of (primarily stationary) random sequences and processes. Correlation functions, Gaussian processes, Hilbert-space methods including Wold decomposition and spectral representation, periodogram and estimation of spectral densities, parameter estimation and model identification for ARMA processes, linear filtering, Kalman-Bucy filtering, sampling theorems for continuous-time series, multivariate time series.

STAT 740 Linear Statistical Models I (3 credits)
Prerequisite: STAT 420 or STAT 700.
Least squares, general linear models, estimability and Gauss-Markov theorem. Simple and multiple linear regression, analysis of residuals and diagnostics, polynomial models, variable selection. Qualitative predictors, one and two way analysis of variance, multiple comparisons, analysis of covariance. Nonlinear least squares. High-level statistical computer software will be used for data analysis throughout the course.

STAT 741 Linear Statistical Models II (3 credits)
Prerequisite: STAT 740.
Continuation of STAT 740. Multiway layouts, incomplete designs, Latin squares, complete and fractional factorial designs, crossed and nested models. Balanced random effects models, mixed models, repeated measures.General mixed model, computational algorithms, ML and REML estimates. Generalized linear models, logistic and loglinear regression.

STAT 750 Multivariate Analysis (3 credits)
Prerequisite: STAT 420 or STAT 700.
Multivariate normal, Wishart's and Hotelling's distributions. Tests of hypotheses, estimation. Generalized distance, discriminant analysis. Regression and correlation. Multivariate analysis of variance; distribution of test criteria. Principal components, canonical correlations and factor analysis.

STAT 770 Analysis of Categorical Data (3 credits)
Prerequisite: STAT 420 and STAT 430 or permission of department.
Loglinear and logistic models. Single classification, two-way classification; contingency tables; tests of homogeneity and independence models, measures of association, distribution theory. Bayesian methods. Incomplete contingency tables. Square contingency tables - symmetry. Extensions to higher dimensional contingency tables.

STAT 798 Selected Topics in Statistics (1-4 credits)

STAT 799 Master's Thesis Research (1-6 credits)

STAT 898 Pre-Candidacy Research (1-8 credits)

STAT 899 Doctoral Dissertation Research (1-8 credits)