What follows is the list of courses offered by the School of Statistics. For further details contact:

• Prof. C. Bingham: Undergraduate Advisor (kb@umn.edu), or
  
• Prof. G. Oehlert: Director of Graduate Studies (gary@stat.umn.edu).
  

1xxx. Courses intended primarily for lower division students.
1001

3xxx. Courses intended primarily for upper division students. These courses count toward a Statistics undergraduate degree.
3011 , 3021 , 3022

4xxx. Courses intended primarily for advanced undergraduates. These courses count toward a Statistics undergraduate degree. Graduate students may enroll in these courses, and, with the permission of the advisor and department may count them as part of graduate degree work.
4101 , 4102 , 4893

5xxx. Courses intended primarily for graduate students. Advanced undergraduates may enroll in these courses, and may count them toward an undergraduate degree. All of these courses count toward Statistics graduate minors, and all except 5021 count toward Statistics graduate degrees.
5021 , 5031 , 5041 , 5101 , 5102 , 5201 , 5302 , 5303 , 5401 , 5421 , 5601 , 5931-2, 5993

8xxx. Courses intended for graduate students. All of these courses count toward Statistics graduate degrees and minors. Undergraduates, in unusual circumstances, may enroll in such courses.
8061-2 , 8101-2 , 8111-2 , 8121 , 8131 , 8141 , 8151 , 8171 , 8201 , 8311 , 8313 , 8321 , 8321 , 8401 , 8411 , 8421 , 8501 , 8511 , 8666 , 8701 , 8711 , 8721 , 8801 , 8900 , 8931-2 , 8992

STAT 1001. INTRODUCTION TO THE IDEAS OF STATISTICS.
(3 cr.; prereq. QP-High school algebra, SP-High school algebra)
Controlled vs. observational studies; presentation and description of data; chance variation; correlation and causality; confidence intervals; statistical tests.

STAT 3011. INTRODUCTION TO STATISTICAL ANALYSIS.
(4 cr.; QP-2 years of high school math; SP-2 years of high school math. No credit given if credit has been received for STAT 5021.)
Describing data & relationships; discrete & continuous random variables, sampling distributions; confidence intervals; 1- and 2-sample significance tests; comparisons; count data; simple linear regression; 1-way ANOVA.

STAT 3021. INTRODUCTION TO PROBABILITY AND STATISTICS.
(3 cr.; prereq. QP-Differential and integral calculus; SP-MATH 1272)
Elementary probability and probability distributions; sampling and elements of statistical inference; regression.

STAT 3022. DATA ANALYSIS.
(4 cr.; prereq. QP-3011 or 3091; SP-3011 or 3021)
Further topics in regression and ANOVA; nonparametric methods; model selection & verification; writing statistical reports; use of statistical software; additional selected topics.

STAT 4101. THEORY OF STATISTICS I.
(4 cr.; prereq. QP-MATH 1252; SP-MATH 1272)
Random variables and distributions; generating functions; standard distribution families; data summaries; sampling distributions; likelihood and sufficiency.

STAT 4102. THEORY OF STATISTICS II.
(4 cr.; prereq.QP-5121; SP-4101. No credit if credit was received for STAT 5102.)
Estimation; significance tests; distribution free methods; power; application to regression, analysis of variance, and analysis of count data.

STAT 4893. SENIOR PAPER.
(1 cr.; prereq. QP-Stat major; SP-Stat major.)
Satisfies senior project requirement for CLA majors. Directed study. Paper on specialized area, a consulting project, or original computer program.

STAT 5021. STATISTICAL ANALYSIS.
(4 cr.; prereq. QP-college algebra or #; SP-3011; college algebra or #; Stat course recommended)
Intensive version of STAT 3011 for graduate students needing statistics as a research technique. Descriptive statistics; elementary probability; estimation; one- and two- sample tests; contingency tables; correlation; linear and multiple regression; ANOVA.

STAT 5031. STATISTICAL METHODS FOR QUALITY IMPROVEMENT.
(4 cr.;prereq QP-3012 or 3091 or 5021 or 5122 or 5132 or 5152, MATH 1252; SP-3021 or 4102 or 5021 or 5102 or 8102, MATH 1272)
Statistical quality improvement is important in many areas. Its original applications centered in Shewhart's work on assembly-line manufacturing, and on military specifications for acceptable products. Today, it is applied far outside these areas, in health care, finance and education to mention just three.

STAT 5041. BAYESIAN DECISION MAKING.
(3 cr.; prereq QP-5122 or 5132 or 5152; SP-4101 or 5021 or 5101 or #)
Axioms for subjective probability and utility. Optimal statistical decision making. Sequential decisions and decision trees. Introduction to backward induction. Bayesian data analysis.

STAT 5101. THEORY OF STATISTICS I.
(4 cr.; prereq. QP-MATH 3252, no credit if credit was received for STAT 5121 or STAT 5122; SP-MATH 2263)
No credit if credit was received for STAT 4101 or MATH 5651. Same as MATH 5651. Logical development of probability and some basic issues in Statistics. Probability spaces, random variables and their distributions and expected values, law of large numbers and central limit theorem, generating functions, sampling, sufficiency, and estimation.

STAT 5102. THEORY OF STATISTICS II.
(4 cr.; SP-5101 or MATH 5651, no credit if credit was received for 4102)
Estimation, test of hypotheses, size and power; categorical data; contingency tables; multivariate normal distribution; linear models; decision theory.

STAT 5201. SAMPLING METHODOLOGY IN FINITE POPULATIONS.
(3 cr.; prereq. QP-3091 or 5021 or 5121 or #; SP-3011 or 3021 or 5021 or #)
Simple random, systematic, stratified, and unequal probability sampling ratio and model based estimation; single stage, multistage and adaptive cluster sampling; spatial sampling.

STAT 5302. APPLIED REGRESSION ANALYSIS.
(4 cr.; prereq. QP-3012 or 5021 or 5133 or 5153, no credit if credit was received for 5161; SP-3022 or 5021 or 4102 or 5102 or #)
Simple, multiple, and polynomial regression. Estimation, testing, and prediction. Use of graphics in regression. Stepwise and other numerical methods; weighted least squares; nonlinear models; response surfaces. Experimental research and applications.

STAT 5303. DESIGNING EXPERIMENTS.
(4 cr.; prereq. QP-3012 or 5021 or 4102 or 5133 or 5153 or #, no credit if credit was received for 5163; SP-3022 or 4102 or 5021 or 5102 or #)
Analysis of variance, multiple comparisons, variance-stabilizing transformations, contrasts, construction and analysis of complete and incomplete block designs, fractional factorial designs, confounding, split plots, and response surface design.

STAT 5401. APPLIED MULTIVARIATE METHODS.
(3 cr.; prereq. QP-5302 or 5133 or 5153; SP-5302 or 8102 or #)
Bivariate and multivariate distributions. Multivariate normal distributions. Analysis of multivariate linear models, including Hotellings's T-squared, multivariate analysis of variance (MANOVA), multivariate analysis of covariance (MANCOVA), and regression with multivariate dependent variable. Repeated measures, growth curve and profile analysis. Canonical correlation analysis. Principle components and factor analysis. Discrimination, classification and clustering.

STAT 5421. ANALYSIS OF CATEGORICAL DATA.
(3 cr.; prereq. QP-3012 or 5021 or 5133 or #, no credit if credit was received for 5162; SP-5302 or 8102 or #)
Varieties of categorical data, cross-classifications, and contingency tables. Tests for independence. Combining 2x2 tables. Multidimensional tables and log linear models, maximum-likelihood estimation and tests for goodness of fit. Logistic regression, generalized linear models and multinomial response models.

STAT 5601. NONPARAMETRIC METHODS.
(3 cr.; prereq. QP-5021 or 5122 or 5132 or 5152 or #; SP-3022 or 5021 or 5102 or #)
Order statistics, classical rank based procedures (e.g. Wilcoxon, Kruskal-Wallis), goodness of fit. May include some of these topics: smoothing, bootstrap, generalized linear models.

STAT 5931-2. TOPICS IN STATISTICS.
(3 cr.; prereq. SP- #)
Topics vary according to students need and available staff.

STAT 5993. TUTORIAL COURSE.
(1-3 cr.; prereq. SP- #)
Study in areas not covered by regular offerings. Directed study.

STAT 8061-2. APPLIED STATISTICAL METHODS.
(4+4 cr.; prereq. graduate standing in Statistics or #)
Regression with one and many predictors; graphics; model building and assessment; diagnostics; outliers; nonlinear regression; generalized linear models; logistic and Poisson regression; two way and higher dimensional contingency tables; design of experiments; randomization; completely randomized designs; ANOVA; contrasts; multiple comparisons; factorial and fractional factorial designs; complete and incomplete block designs; covariates; confounding; split plots; random effects; response surface and mixture designs.

STAT 8101-2. THEORY OF STATISTICS I, II.
(3+3 cr.; prereq. graduate standing in Statistics or #)
8101:: Probability, transformations, expectation, univariate and multivariate distributions, central limit theorem, sampling and sampling distributions, sufficiency, likelihood. 8102:: Point and interval estimation, maximum likelihood, delta method, hypothesis testing, decision theory, analysis of variance, regression.

STAT 8111-2. MATHEMATICAL STATISTICS I, II.
(3+3 cr.; prereq. 5102 or 8102 or #; real analysis, matrix algebra)
8111: Review of probability theory, basic inequalities, characteristic functions and exchangeability. Multivariate normal distribution. Exponential family. Decision theory, admissibility and Bayes rules. 8112: Statistical inference, estimation and hypothesis testing. Convergence and relationship between modes of convergence. Asymptotics of maximum likelihood estimators, distribution functions, quantiles. Delta method.

STAT 8121. THEORY OF INFERENCE.
(3 cr.; prereq. 8112, MATH 8657 or #)
Topics may vary according to interest of instructors and students. Possible topics include conditional distributions and sufficiency, theory of estimation, comparison of various theories of statistical inference; Neyman-Pearson theory of hypothesis testing and its extensions, confidence regions, invariance, nonparametric and sequential inference, likelihood inference, Bayesian inference.

STAT 8131. PREDICTIVE INFERENCE.
(3 cr.; prereq. 8112 or equivalent)
Both traditional frequentis and other nontraditional predictive approaches will be discussed. Then, Bayesian predictive methods will be introduced with a brief discussion of the purpose for which data are to be used. A theoretical apparatus is then delineated. This is exemplified using a variety of common statistical paradigms. Areas from model selection, comparisons and allocation, perturbation analysis and control will also be discussed.

STAT 8141. PROBABILITY ASSESSMENT.
(3 cr.; prereq. 5102 or 8102)
Probability as a language of uncertainty for quantifying and communicating expert opinion and for use as Bayesian prior distributions. Methods for elicitation and construction of subjective probabilities. De Finetti coherence, predictive elicitation, fitting subjective-probability models, scoring rules, calibration of probabilities, heuristics and psychological distortions, computer aided elicitation, combining opinions, use of experts.

STAT 8151. STATISTICAL DECISION THEORY
(3 cr.; prereq. 8112, MATH 8656)
Comparison of inferential methods in statistics, including risk comparison, minimaxity, admissibility and related topics. Wald's formulation of decision is used as a basis. Formal and proper Bayes rules are discussed and compared with frequentist inferences. Topics may vary depending on instructor.

STAT 8171. SEQUENTIAL ANALYSIS
(3 cr.prereq. 8112)
Walds's sequential probability ratio test and modifications. Sequential decision theory. Martingales. Sequential estimation, design, and hypothesis testing. Recent developments.

STAT 8201. TOPICS IN SAMPLING.
(3 cr.; prereq 8102)
Introduction to sampling theeory; Stratified sampling, Ratio estimators, Cluster sampling, Double sampling, Superpopulation theory, Bayesian methods, multiple imputation and nonresponse.

STAT 8311. LINEAR MODELS.
(4cr.; prereq. linear algebra, 5102 or 8102 or #)
General linear model theory from a coordinate-free geometric approach. distribution theory,anova tables, testing,confidence statements,mixed models, covariance structures,variance components estimation.

STAT 8312. LINEAR AND NONLINEAR REGRESSION.
(3 cr.; prereq. 8311)
Nonlinear regression: asymptotic theory, Bates-Watts curvatures, bootstrap, errors in the predictors, exponential family nonlinear models, leverage and super leverage, model assessment, parameter plots, partially nonlinear models, projected residuals, transform-both-sides methodology, Wald versus likelihood inference. Topics in linear and generalized linear models as they relate to issues involving nonlinearity: CERES plots, diagnostics, local influence analysis, residuals, semi-parametric models, model assessment.

STAT 8313. TOPICS IN EXPERIMENTAL DESIGN.
(3 cr.; prereq. 8311)
Design of experiments, optimal design, Bayes design, nonlinear design, algorithms for computing designs, sample size, recent developments.

STAT 8321. REGRESSION GRAPHICS.
(3 cr.; prereq. 8311)
Foundations of regression graphics: dimension-reduction subspaces, existence theorems for central dimension reduction subspaces, basic theorems for graphical regression and inverse regression graphics, Li-Duan Lemma, structural dimension of a regression. Inferring about central dimension reduction subspaces by using 3D plots, graphical regression, inverse regression graphics, net-effect plots, principal Hessian directions, scatterplot matrices, sliced inverse regression. Special emphasis on graphics for survival analysis and regressions with a binary response variable. Graphics for model assessment.

STAT 8401. TOPICS IN MULTIVARIATE METHODS.
(3 cr.; prereq. 8311)
Bivariate and multivariate distributions. Multivariate normal distributions. Analysis of multivariate linear models, including Hotellings's T-squared, multivariate analysis of variance (MANOVA), multivariate analysis of covariance (MANCOVA),and regression with multivariate dependent variable. Repeated measures, growth curve and profile analysis. Canonical correlation analysis. Principle components and factor analysis. Discrimination, classification and clustering.

STAT 8411. MULTIVARIATE ANALYSIS.
(3 cr.; prereq. 8112)
Multivariate normal distribution. Inference on the mean, covariance, and correlation and regression coefficients; related sampling distributions such as Hotelling's T-squared and Wishart distributions. Multivariate analysis of variance. Principal components and canonical correlation. Discriminant analysis. Distribution of determinantal roots. Invariance, admissibility, minimax, and other properties of tests and estimates. Large sample distributions. Bayesian analysis.

STAT 8421. THEORY OF CATEGORICAL DATA ANALYSIS.
(3 cr.; prereq. 8062 or #)
Multidimensional cross-classified arrays, sampling models and statistical theory for categorical data. Model selection and simultaneous testing. Logit and multinomial response models. Models for mixed categorical/continuous data. Logistic regression. Analysis of ordered categorical variables. Multiplicative and multiplicative-interaction models. Latent-structure models. Bayesian estimation of cell frequencies. Computing algorithms.

STAT 8501. INTRODUCTION TO STOCHASTIC PROCESSES WITH APPLICATIONS.
(3 cr.; prereq. 5101 or 8101)
Markov chains in discrete and continuous time, renewal processes, Poisson process, Brownian motion, and other stochastic models encountered in applications.

STAT 8511. TIME SERIES ANALYSIS.
(3 cr.; prereq. 5102 or 8102 or #)
Time series as multivariate samples of size 1. Discrete and continuous parameter time series. Stationarity. Autocovariance and autocorrelation. ARIMA models, identification, estimation, diagnostic checking. Other time domain models. Forecasting, seasonal adjustment, time series regressions. Introduction to frequency domain methods.

STAT 8666. DOCTORAL PRE-THESIS CREDITS

STAT 8701. COMPUTATIONAL STATISTICAL METHODS
(3 cr.; prereq 8311, programming experience)
Random variate generation, variance reduction techniques. Robust location estimation and regression, smoothing additive models, regression trees. Programming projectsl basic programming ability and familiarity with standard high-level language (preferably FORTRAN or C) is essential.

STAT 8711. STATISTICAL COMPUTING
(3 cr.; prereq. 8701)
Basic numerical analysis for statisticians. Numerical methods for linear algebra, eigen-analysis, integration, optimization and their statistical applications.

STAT 8721. PROGRAMMING PARADIGMS AND DYNAMIC GRAPHICS IN STATISTICS.
(3 cr.; prereq. 8061-2, 8101-2)
Alternative programming paradigms to traditional procedural programming, including object-oriented programming and functional programming. Applications to the development of dynamic statistical graphs and the representation and use of functional data, such as mean function in a nonlinear regression log likelihoods and prior densities function in a nonlinear regression log likelihoods and prior densities in Bayesian analysis.

STAT 8801. STATISTICAL CONSULTING.
(1 cr.; graduate standing in Statistics or #)
Almost all statistics graduates will work in settings in which at least a part of their work involve consulting to statistics users in other subject areas.
STAT 8801 is required for all Statistics graduate students. The course has two branches. Those taking it for the first time have an in-class course teaching some theory of consulting and problem-solving, meeting skills, aspects of professional practice and behavior, ethics, and continuing education. PhD students taking STAT 8801 again for their remaining consulting requirements see a seminar format including some live consulting sessions, sketches of less familiar statistical methodologies, and expansion on issues covered in the first iteration.

STAT 8900. STUDENT SEMINAR
(1 cr.; prereq. graduate standing in Statistics)
Preparation or presentation of a seminar on statistical topics.

STAT 8931-2. ADVANCED TOPICS IN STATISTICS.
(3 cr.; #)
Topics vary according to student needs and available staff.

STAT 8992. DIRECTED READINGS and RESEARCH.
(1-3cr.; graduate standing in Statistics or #)
Directed studies in areas not covered by regular offerings.