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: MATH 131 with a grade of C or better, or MATH 141 or
equivalent. 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 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: STAT410.
Probability space; distribution functions and densities; Poissson limit
theoreom; de Moivre-Laplace theorem; measure-theoretic definition of
expectation; classification of measures on R; convergence of random
variables; Radon-Nikodym theorem;LP spaces; conditional probabilities;
independence of events, sigma-algebras and random variables; Bayes' theo
rem; pi-systems and Dynkin systems; discrete Markov chains; random
walks; gambler's ruin problem; Markov chains on a general phase space;
Borel-cantelli lemmas; Kolmogorov inequality; three series theorem; laws
of large numbers.
STAT 601 Probability Theory II (3 credits)
Prerequisite: STAT 600.
Weak convergence of measures; characteristic functions; Central Limit
Theorem and local limit theorem; stable laws; Kolmogorov consistency
theorem (without proof); conditional expectations and martingales;
optimal stopping theorem; convergence of martingales; Brownian motion;
Markov processes and families; stochastic integral and Ito formula.
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 AMSC687 and MATH687. Credit will be granted for only one
of the following: AMSC687, MATH687 or STAT687.
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 STAT798C.
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 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)
