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# Statistics Course Descriptions

STOR 151-BASIC CONCEPTS OF STATISTICS AND DATA ANALYSIS I-
Prerequistite: MATH 110 (or exemption). Elementary introduction  to statistical reasoning, including sampling, elementary probability, statistical inference, and data analysis. STOR 151 may not be taken for credit by students who have a credit for ECON 400 or PSYC 210. (3)

STOR 155-INTRODUCTION TO STATISTICS -
Prerequisite: MATH 110 (or exemption). Data analysis; correlation and regression; sampling and experimental design; basic probability (random variables, expected values, normal and binomial distributions); hypothesis testing and confidence intervals for means, proportions, and regression parameters; use of spreadsheet software. (3)

STOR 358- SAMPLE SURVEY METHODOLOGY (BIOS 664) -
Prerequisite: STOR 456 or equivalent. Principles and methods associated with survey sampling, including simple random sampling, stratified sampling and cluster sampling. Questionnaire design, problems of nonresponse, sources of nonsampling errors. Design, execution, and analysis of an actual survey.  Spring.  Kalsbeek. (3)

STOR 435- INTRODUCTION TO PROBABILITY (MATH 535) -
Prerequisites: Working knowledge of MATH 231-233. Introduction to the mathematical theory of probability.  Probability models for random experiments.   Basic properties of probability measures.  Conditional probability and independence.  Discrete random variables: hypergeometric, binomial, geometric, negative binomial, and Poisson.  Continuous random variables: uniform, exponential, Gaussian, Cauchy and gamma.  Jointly distributed random variables. Definition and basic properties of expectations, variances, covariances and correlations.  Basic inequalities for probabilities and expectations.  Laws of large numbers and the central limit theorem.  Fall and Spring.  Budhiraja, Nobel. (3)

STOR 455-STATISTICAL METHODS I -
Prerequisite: STOR 155 or equivalent. Some familiarity with matrix algebra recommended, but not required. This course presents regression analysis and related techniques, and is recommended for students throughout the natural and social sciences who are interested in applying regression analysis in their research and/or understanding the statistical concepts underlying the methodology. The topics include simple and multiple linear regression, matrix representation of the regression model, statistical inferences for regression model, diagnostics and remedies for multicollinearity, outlier and influential cases, polynomial regression and interaction regression models, model selection, weighted least square procedure for unequal error variances, and ANOVA model and test. Statistical software SAS will be used throughout the course to demonstrate how to apply the techniques on real data. The main purposes of this courses is to let students know how to use regression methods properly in data analysis and lay the foundation for more advanced studies in statistics. Fall. Hannig. (3)

STOR 456- STATISTICAL METHODS II -
Prerequisite: STOR 455. The focus of this course is on analysis of time series data, that is, data recorded in time. Such data arise in a wide range of areas including Environmental Sciences, Economics, Business and Finance, Actuarial Sciences, Social Sciences. The topics of the course include estimation and elimination of trend and seasonal components, stationary time series, ARMA models, spectral analysis, modeling and forecasting of time series. Some statistical software will be used throughout the course to demonstrate how to apply the techniques on real time series data. Spring. Shen, Pipiras, Smith. (3)

STOR 555- MATHEMATICAL STATISTICS -
Prerequisite: STOR 435 or equivalent. Derivation and analysis of point estimators using decision theory, including the methods of Bayes and minimax estimation, maximum likelihood, method of moments, and unbiased estimation. Confidence intervals. Hypothesis testing, including Bayesian methods, multiple hypotheses, the Neyman-Pearson Lemma, simple and composite hypotheses, likelihood ratio tests, Type I and Type II errors, power calculations. Uses of and relationships between the families of standard probability models, including the Normal, Gamma, Chi-Squared, Student's T, Uniform, Beta, Binomial, Negative Binomial, Poisson, Hypergeometric, and Cauchy distributions, as well as the Poisson Process and the Bernoulli Process. Fall only.  Carlstein, Kelly. (3)

STOR 634- MEASURE AND INTEGRATION -
Prerequisite: Real analysis. An introduction to measure-theoretic probability.  Definition and properties of abstract and Lebesgue measures.  Definition and properties of the Lebesgue integral: monotone and dominated convergence theorems.  Lp spaces.  Moment and probability inequalities.  Signed measures: Lebesgue decomposition, Jordan-Hahn decomposition, Radon-Nikodym theorem. Product measures and Fubini-Tonelli theorems.  Kolmogorov's consistency theorem.  Independence, Borel-Cantelli lemmas, and Kolmogorov's zero-one law. Fall. Leadbetter, Pipiras, Budhiraja. (3).

STOR  635- PROBABILITY-
Prerequisite: STOR 634 or permission of instructor.  Convergence of random series.  The strong laws of large numbers. Conditional expectations.  Discrete parameter martingales: convergence, stopping times, and optional sampling theorems.  Uniform integrability.  Weak convergence: characteristic functions and the central limit theorem.  Elements of large deviations.  The ergodic theorem.  Spring. Leadbetter, Pipiras, Budhiraja. (3)

STOR 641- STOCHASTIC PROCESSES
Prerequisites: STOR 435 and permission of instructor. Discrete Markov chains; Continuous Markov chains: Poisson, birth-death, etc.; Stationary processes. Fall. Ziya, Kulkarni. (3).

STOR 654- STATISTICAL THEORY I -
Prerequisite: Real analysis or advanced calculus and intermediate undergraduate probability.  An introduction to non-asymptotic statistical inference.  Basic inequalities for probabilities and expectations: Markov, Chebyshev, Jensen, and Cauchy-Schwartz.  Basic decision theory.  Sufficiency, minimal sufficiency, ancillarity and completeness.  Point estimation: method of moments, maximum likelihood, and information inequalities.  Hypothesis testing: likelihood ratio tests, Neyman-Pearson theory.  Confidence intervals: inverting test statistics, pivotal quantities, optimality properties. Fall. Nobel, Hannig. (3)

STOR 655- STATISTICAL THEORY II -
Prerequisite: STOR 654 or equivalent. Continuation of STOR 654.  An introduction to asymptotic statistical inference. Basic multivariate analysis: covariance and expectation, multinormal and non-central chi-squared distributions, linear and quadratic forms.  Convergence in distribution and probability.  Asymptotic statistical inference: consistency, asymptotic normality, efficiency, asymptotic distribution of likelihood ratio tests, chi-squared goodness of fit tests, Wald tests and related confidence intervals.  Spring.  Ji, Hannig. (3)

STOR 664- APPLIED STATISTICS I -
Prerequisite: STOR 555 or permission of the instructor. Strong background in multivariate calculus and linear algebra is required for this course. This course presents in-depth regression analysis and related techniques. Both theoretical development and computational implementation of the techniques will be presented. The topics include simple and multiple linear regression; matrix representation of the regression model and solution; the geometric approach to least squares theory; the ANOVA table; confidence and prediction intervals; hypothesis tests; diagnostics for influential observations and model assumptions such as normality; diagnostics for model selection (multicollinearity, variable selection, transformations such as log, Box-Cox, etc.). Selected additional topics depending on time and instructor: weighted and generalized least squares, nonlinear regression, and analysis of designed experiments (one-way and two-way analysis of variance, factorial designs). Computing environments: R, SAS, MATLAB (varies depending on instructor). Fall. Carlstein, Liu, Smith. (3)

STOR 665- APPLIED STATISTICS II -
Prerequisite: STOR 664 or permission of the instructor. Analysis of variance (ANOVA), including nested and crossed models, and multiple comparisons.  GLM basics, including exponential families, link functions, likelihood, quasi-likelihood, conditional likelihood, iterative reweighted least squares, EM algorithm, and diagnostic techniques.  Linear mixed model (LMM) basics including variance components, prediction of random effects; various estimation techniques based on ANOVA, maximum likelihood and restricted maximum likelihood. Selected additional topics depending on time and instructor: generalized estimating equations (GEE), generalized LMM, longitudinal data and various nonlinear models. Spring. Shen. (3)

STOR 754- TIME SERIES AND MULTIVARIATE ANALYSIS -
Prerequisite: STOR 435. Time Series: Exploratory and graphical analysis; Time domain analysis and ARMA models; Fourier analysis: FFT, periodogram, smoothing; State space analysis: Kalman filter, dynamic models. Multivariate: Principal components, canonical correlation; Classification, clustering; Dimension reduction: projection pursuit, alternating conditional sliced inverse regression. Spring. Leadbetter, Smith, Sen. (3)

Prerequisites: STOR 635 and 655. This is a theoretical course covering more advanced topics in asymptotic statistics.  General theory of moment, M- and L-Estimators.  Bayes procedures.  U-statistics, rank and sign tests.  Asymptotic properties of likelihood and chi-squared statistics.  Uniform laws of large numbers.  Empirical processes. Nobel. (3)

STOR 765- CONSULTING -
Prerequisite: permission of instructor. Projects are assigned by the instructor. Typically these projects relate to requests for statistical consulting assistance from outside the Department. The class meets once per week over an academic year for a total of three credit hours. Fall and Spring. Marron. (3 credits for one year)

STOR 756- DESIGN AND ROBUSTNESS -
Corequisite, Statistics 165. Design: Classical designs (BIB, Latin square, fractional factorial, industrial designs, Taguchi; Optimal designs: D-optimality, etc.; Sequential designs: sequential probability ratio test, Stein 2-stage. Robust methods: M-, L-, R-estimates, breakdown, influence curves; bootstrap, jackknife, cross-validation. (3)

STOR 757- BAYESIAN STATISTICS AND GENERALIZED LINEAR MODELS -
Corequisites: STOR 664 and 655, or permission of the instructor. Bayes factors; Empirical Bayes, formulation, Stein effect; Classical: EM, Laird-Ware; Hierarchical: prior, MCMC. GLM specific models: Binomial regression, polytomous regression, Cox proportional hazard, log linear.  Hannig, Smith. (3)

STOR 851- SEQUENTIAL ANALYSIS -
Prerequisites: STOR 635 and 655. Hypothesis testing and estimation when the sample size depends on the observations. Sequential probability ratio tests. Sequential design of experiments. Optimal stopping. Stochastic approximation. (3).

STOR 852- NONPARAMETRIC INFERENCE: RANK-BASED METHODS -
Prerequisites: STOR 635 and 655.  Estimation and testing when the functional form of the population distribution is unknown. Rank, sign, and permutation tests. Optimum nonparametric tests and estimators, including simple multivariate problems. Sen. (3).

STOR 853 - NONPARAMETRIC INFERENCE: SMOOTHING METHODS
Prerequisites: STOR 635 and 655.  Density and regression estimation when no parametric model is assumed. Kernel, spline, and orthogonal series methods. Emphasis on analysis of the smoothing problem and data based smoothing parameter selectors. Marron. (3).

STOR 854 - STATISTICAL LARGE SAMPLE THEORY -
Prerequisites: STOR 635 and 655.  Asymptotically efficient estimators; maximum likelihood estimators. Asymptotically optimal tests; likelihood ratio tests. (3).

STOR 855- SUBSAMPLING TECHNIQUES -
Prerequisite: STOR 655. Basic subsampling concepts: replicates, empirical c.d.f., U-statistics. Subsampling for i.i.d. data: jackknife, typical-values, bootstrap. Subsampling for dependent or nonidentically distributed data: blockwise and other methods. Carlstein. (3).

STOR 831 - ADVANCED PROBABILITY -
Prerequisites: STOR 634 and 635. This is a theoretical course covering selected topics in probability, including: the theory of weak convergence in general spaces, functional central limit theorems, large deviations, concentration inequalities, Poisson approximation, ergodic theory, and stable laws. Budhiraja, Nobel, Pipiras, Leadbetter. (3).

STOR 832- STOCHASTIC PROCESSES -
Prerequisites: STOR 634 and 635. Advanced theoretic course including topics selected from: Foundations of stochastic processes, renewal processes, stationary processes, Markov processes, martingales, point processes. Budhiraja, Pipiras, Leadbetter (3).

STOR 833- TIME SERIES ANALYSIS -
Prerequisites: STOR 754. Analysis of time series data by means of particular models such as autoregressive and moving average schemes. Spectral theory for stationary processes and associated methods for inference. Stationarity testing. Leadbetter, Smith. (3).

STOR 834 - EXTREME VALUE THEORY -
Prerequisites: STOR 634 and 635. Classical asymptotic distributional theory for maxima and order statistics from i.i.d. s equences, including extremal types theorem, domains of attraction, Poisson properties of high level exceedances. Extremal properties of stationary stochastic sequences and continuous time processes. Leadbetter. (3).

STOR 835- POINT PROCESSES -
Prerequisite: STOR 635. Random measures and point processes on general spaces, general Poisson and related processes, regularity, compounding. Point processes on the real line, stationarity and Palm distributions, Palm-Khintchine formulae. Convergence of point processes and related topics. Leadbetter. (3).

STOR 836- STOCHASTIC ANALYSIS -
Prerequisite: STOR 634 and 635, or permission of the instructor. Advanced course covering topics selected from: semimartingale theory, stochastic integrals, homogeneous chaos expansions, stochastic differential equations, Malliavin calculus, infinite dimensional processes, functional central limit theorems, Feynman-Kac formula, Feynman integral. Applications to filtering theory, infinite particle systems, quantum mechanics, and stochastic models in neurophysiology. Budhiraja (3).

STOR 856- MULTIVARIATE ANALYSIS -
Prerequisites: STOR 655 and matrix theory. Multivariate normal distributions. Related distributions. Tests and confidence intervals. Multivariate analysis of variance, covariance, and regression. Association between subsets of a multivariate normal set. Theory of discriminant, canonical, and factor analysis. Sen (3).

STOR 857- NONPARAMETRIC MULTIVARIATE ANALYSIS -
Prerequisite: STOR 852. Nonparametric MANOVA. Large sample properties of the tests and estimates. Robust procedures in general linear models including the growth curves. Nonparametric classification problems. Sen. (3).

STOR 940, 960- SEMINAR IN THEORETICAL STATISTICS -
Prerequisite: STOR 655. (3).

STOR 890, 891- SPECIAL PROBLEMS -
Prerequisite: permission of the instructor. (3).

STOR 930, STAT 950- ADVANCED RESEARCH -
Prerequisite: permission of the instructor. (3).

STOR 970 - Practicum
Students work with other organizations (Industrial/Governmental) to gain practiced experience in Statistics and Operations Research. Students prepare a report based on their experience. (1-15).

STOR 992- MASTER'S ESSAY -
Prerequisite, permission of the student's adviser. Fall and Spring. Staff.  A minimum of 3 credit hours of 992 is required for the M.S. degree.

STOR 994- DOCTORAL DISSERTATION -
Prerequisite, permission of the student's adviser. Fall and spring. Staff. A minimum of 6 credit hours of 694 is required for the PhD degree.

STOR 400- GENERAL REGISTRATION