# Courses

#### STAT 100. Statistical Literacy in the Age of Information.

This course is intended for majors in non-quantitative fields. Focus will be on the development of an awareness of statistics at the conceptual and interpretative level, in the context of everyday life. Data awareness and quality, sampling, scientific investigation, decision making, and the study of relationships are included. Emphasis will be on the development of critical thinking through in-class experiments and activities, discussions, analyses of real data sets, written reports, and collaborative learning. Computing activities will be included where appropriate; no previous computing experience required.
(3 credit hours) Offered: Fall, Spring.
Pr.: MATH 100. Cannot be taken for credit if credit has been received for any other statistics course.

#### STAT 325. Introduction to Statistics.

A basic first course in probability and statistics; frequency distributions; averages and measures of variation; probability; simple confidence intervals and tests of significance appropriate to binomial and normal populations; correlation and regression, including confidence intervals and tests of significance for bivariate populations.
(3 credit hours) Offered: Fall, Spring, Summer.
Pr.: MATH 100.

#### STAT 340. Biometrics I.

A basic first course in probability and statistics with textbook, examples, and problems aimed toward the biological sciences. Frequency distributions, averages, measures of variation, probability, confidence intervals; tests of significance appropriate to binomial, multinomial, Poisson, and normal sampling; simple regression and correlation.
(3 credit hours) Offered: Fall, Spring.
Pr.: MATH 100. Cannot be taken for credit if credit has been received for STAT 325, or 350.

#### STAT 341. Biometrics II.

Analysis and interpretation of biological data using analysis of variance, analysis of covariance, and multiple regression. Negative binomial distribution and its applications.
(3 credit hours) Offered: Spring.
Pr.: STAT 325, 340, or 350.

#### STAT 350. Business and Economic Statistics I.

A basic first course in probability and statistics with textbook, examples, and problems pointed toward business administration and economics. Frequency distributions, averages, index numbers, time series, measures of variation, probability, confidence intervals, tests of significance appropriate to binomial, multinomial, Poisson, and normal sampling; simple regression and correlation.
(3 credit hours) Offered: Fall, Spring, Summer.
Pr.: MATH 100. Cannot be taken for credit if credit has been received for STAT 325, or 340.

#### STAT 351. Business and Economic Statistics II.

Continuation of STAT 350 including study of index numbers, time series, business cycles, seasonal variation, multiple regression and correlation, forecasting; some nonparametric methods applicable in business and economic studies.
(3 credit hours) Offered: Fall, Spring, Summer.
Pr.: STAT 325, 340, or 350.

#### STAT 399. Honors Seminar in Statistics.

Selected topics. May be used to satisfy quantitative requirements for BS degree. Open only to students in the honors program.
(3 credit hours)

#### STAT 410. Probabilistic Systems Modeling.

Descriptive statistics and graphical methods; basic probability; probability distributions; several random variable; Poisson processes; computer simulation of random phenomena; confidence interval estimation; hypothesis testing.
(3 credit hours) Offered: Spring.
Pr.: MATH 221 and CIS 300.

#### STAT 490. Statistics for Engineers.

First course in statistics with examples and problems toward engineering. Distributions, means, measures of variation, confidence intervals, graphical display of data, simple regression and correlation, philosophy of experimentation. Must be taken conc. with a laboratory course in engineering which uses statistics.
(1 credit hour) Offered: Fall, Spring.

#### STAT 499. Honors Project.

Open only to Arts and Science students who are active members of the University Honors Program.
(3 credit hours) Offered: Fall, Spring, Summer.

#### STAT 510. Introductory Probability and Statistics I.

Descriptive statistics, probability concepts and laws, sample spaces; random variables; binomial, uniform, normal, and Poisson; two-dimensional variates; expected values; confidence intervals; binomial parameter, median, normal mean, and variance; testing simple hypotheses using CIs and X2 goodness of fit. Numerous applications.
(3 credit hours) Offered: Fall, Spring.
Pr.: MATH 221.

#### STAT 511. Introductory Probability and Statistics II.

Law of Large Numbers, Chebycheff's Inequality; continuation of study of continuous variates; uniform, exponential, gamma, and beta distribution; Central Limit Theorem; distributions from normal sampling; introduction to statistical inference.
(3 credit hours) Offered: Spring.
Pr.: STAT 510.

#### STAT 610. Introduction to Mathematical Statistics I

Development of axiomatic probability; univariate and multivariate random variables and their probability distribution functions; conditional distributions and independent random variables; methods of transformation for distributions of functions of random variables; convergence in distribution and probability.
(3 credit hours) Offered: Fall
Pr.: MATH 222

#### STAT 611 - Introduction to Mathematical Statistics II

Estimation of probability distribution parameters by maximum likelihood, Bayesian and bootstrap methods; minimum variance unbiased estimation based on sufficient statistics; mean squared error and consistency of estimators; confidence interval estimation; statistical tests of hypotheses by likelihood ratios; most powerful tests; distribution-free inference; applications to regression models and categorical data.
(3 credit hours) Offered: Spring
Pr.: STAT 610

#### STAT 701. Fundamental Methods of Biostatistics.

A course emphasizing concepts and practice of statistical data analysis for health sciences. Basic techniques of descriptive and inferential statistical methods applied to health related surveys and designed experiments. Populations and samples, parameters and statistics; sampling distributions for hypothesis testing and confidence intervals for means and proportions involving one sample, paired samples and multiple independent samples; odds ratios, risk ratios, simple linear regression. Use of statistical software to facilitate the collection, manipulation, analysis and interpretation of health related data.
(3 credit hours) Offered: Fall, Spring, Summer.
Pr.: Junior standing and equivalent of college algebra or with instructor permission

#### STAT 703. Introduction to Statistical Methods for the Sciences.

Statistical concepts and methods basic to experimental research in the natural sciences; hypothetical populations; estimation of parameters; confidence intervals; parametric and nonparametric tests of hypotheses; linear regression; correlation; one-way analysis of variance; t-test; chi-square test.
(3 credit hours) Offered: Fall, Spring, Summer.
Pr.: Junior standing and equivalent of college algebra or with instructor permission.

#### STAT 705. Regression and Analysis of Variance.

Simple and multiple linear regression, analysis of covariance, correlation analysis, one-, two- and three-way analysis of variance; multiple comparisons; applications including use of computers; blocking and random effects.
(3 credit hours) Offered: Fall, Spring, Summer.
Pr.: One previous statistics course.

#### STAT 706. Basic Elements of Statistical Theory.

The mathematical representation of frequency distributions, their properties, and the theory of estimation and hypothesis testing. Elementary mathematical functions illustrate theory.
(3 credit hours) Offered: Fall.
Pr.: MATH 205, 210, or 220 and STAT 325 or equiv.

#### STAT 710. Sample Survey Methods.

Design, conduct, and interpretation of sample surveys.
(3 credit hours) Offered: Fall, in even years.
Pr.: STAT 510 or 770.

#### STAT 713. Applied Linear Statistical Models.

Matrix-based regression and analysis of variance procedures at a mathematical level appropriate for a first-year graduate statistics major. Topics include simple linear regression, linear models in matrix form, multiple linear regression, model building and diagnostics, analysis of covariance, multiple comparison methods, contrasts, multifactor studies, blocking, subsampling, and split-plot designs.
(3 credit hours) Offered: Fall.
Pr.: Prior knowledge of matrix or linear algebra and one prior course in statistics. A student may not receive credit for both STAT 705 and STAT 713.

#### STAT 716. Nonparametric Statistics.

Hypothesis testing when form of population sampled is unknown: rank, sign, chi-square, and slippage tests; Kolmogorov and Smirnov type tests; confidence intervals and bands.
(3 credit hours) Offered: Fall, in odd years.
Pr.: STAT 705 or 713.

#### STAT 717. Categorical Data Analysis.

Analysis of categorical count and proportion data. Topics include tests of association in two-way tables; measures of association; Cochran-Mantel-Haenzel tests for 3-way tables; generalized linear models; logistic regression; loglinear models.
(3 credit hours) Offered: Spring.
Pr.: STAT 705 or STAT 713.

#### STAT 720. Design of Experiments.

Planning experiments so as to minimize error variance and avoid bias; Latin squares; split-plot designs; switch-back or reversal designs; incomplete block designs; efficiency.
(3 credit hours) Offered: Spring, Summer.
Pr.: STAT 705 or STAT 713.

#### STAT 722. Experimental Designs for Product Development and Quality Improvement.

A study of statistically designed experiments which have proven to be useful in product development and quality improvement. Topics include randomization, blocking, factorial treatment structures, factional factorial designs, screening designs, and response surface methods.
(3 credit hours) Offered: Fall.
Pr.: STAT 511 or STAT 705 or STAT 713.

#### STAT 725. Introduction to SAS Computing.

Topics may include basic environment and syntax, reading and importing data from files, data manipulation basic graphics, and built-in and user-defined functions.
(1 credit hour) Offered: Fall.
Pr.: One graduate-level course in statistics.

#### STAT 726. Introduction to R Computing.

Topics may include basic environment and syntax, reading and importing data from files, data manipulation basic graphics, and built-in and user-defined functions.
(1 credit hour) Offered: Fall.
Pr.: One graduate-level course in statistics.

#### STAT 727. Statistical Computing/Numerical Methods of Statistics.

Topics may include efficient programming techniques, generating data from non-standard distributions, designing simulation studies, resampling methods, creating and using functions and subroutines, parallel computing in statistics, interfacing lower-level languages (e.g., C, C++, Fortran) with data analysis software (e.g., SAS, R), computational complexity, convergence analysis of algorithms.
(3 credit hours) Offered: Spring.
Pr: STAT 726, and STAT 511 or 771

#### STAT 730. Multivariate Statistical Methods.

Multivariate analysis of variance and covariance; classification and discrimination; principal components and introductory factor analysis; canonical correlation; digital computing procedures applied to data from natural and social sciences.
(3 credit hours) Offered: Spring.
Pr.: STAT 705 or STAT 713.

#### STAT 736. Bioassay.

Direct assays; quantitative dose-response models; parallel line assays; slope ratio assays; experimental designs for bioassay; covariance adjustment; weighted estimates; assays based on quantal responses.
(2 credit hours) Offered: Spring, in odd years.
Pr.: STAT 705 or STAT 713.

#### STAT 745. Statistical Graphics.

Visual display of quantitative information. Statistical graphics topics to include visual perception, basic graphics construction, quantitative univariate to multivariate statistical graphics, trellis displays, introduction to smoothing and graphics, introduction to density estimation and graphics, and categorical graphics. Modern graphics software will be used.
(3 credit hours) Offered: Spring, in even years.
Pr.: STAT 705 or equivalent.

#### STAT 750. Studies in Probability and Statistics

Studies of topics in probability, statistics, experimental design, stochastic processes, or other topics.
(1-4 credit hours) Offered: On demand. May be repeated for credit.
Pr.: Instructor consent.

#### STAT 760. Optimization for Data Science.

Theory and algorithms for linear and nonlinear optimization problems with continuous variables. Elements of convex analysis, first- and second-order optimality methods, duality, and KKT conditions. Algorithms for unconstrained optimization, and linearly and nonlinearly constrained problems. Convergence rate of algorithms. Applications in machine learning, statistics, and related fields (e.g., maximizing likelihood and penalized likelihood functions, MM algorithm, EM algorithms, model selection, sparse PCA). Students are expected to be comfortable with rigorous mathematical arguments.
(3 credit hours) Offered: Spring, even years.
Pr: STAT 511 or 771, and prior knowledge of linear algebra and matrix theory (e.g. MATH 551), and some programming knowledge (e.g. STAT 726)

#### STAT 761. Discrete Optimization & Scalability for Data Science.

Computational complexity, NP-hardness, data as networks, graph theoretic algorithms, exact, approximation and heuristic algorithms, genetic algorithms and online algorithms. Connections to convex and non-convex optimization problems. Applications include problems in statistical machine learning, statistical clustering, design of experiments and observational studies, sampling, and variable selection. Methods may be motivated using data from social networks, search engines, the stock market and elections.
(3 credit hours) Offered: Spring, odd years
Pr: STAT 705 or 713, and STAT 720, and programming knowledge (e.g. STAT 726)

#### STAT 764. Applied Spatio-Temporal Statistics.

Construction and analysis of spatial, time-series, and spatio-temporal data sets. Topics includes data generation using geographic information systems, exploratory data analysis and visualization, and descriptive and dynamic spatio-temporal statistical models. For context, a focus will be on biological or ecological data.
(3 credit hours) Offered: Fall, even years
Pr: STAT 510 or 770, STAT 705 or 713, and STAT 726 or equivalent

#### STAT 766. Applied Data Mining/Machine Learning and Predictive Analytics.

This course addresses the complete process of building analytical tools suitable for learning from data, including automatic online data collection, feature extraction, supervised and unsupervised statistical machine learning methods, evaluation, and report writing. Automatic retrieval of various format online data, including JSON, REST and Streaming API, http(s), html, xml, and databases. Statistical text processing/mining, state of the art top performers of supervised and unsupervised data mining methods, case studies and applications to business, government, social and news media data. Methods include regularized linear and logistic regression, classiﬁcation trees, nearest neighbor methods, support vector machines, Naive Bayes, random forests, boosting/bagging/AdaBoost, clustering, latent Dirichlet allocation, network analysis, and topic modeling models.
(3 credit hours) Offered: Fall, odd years
Pr: STAT 705 or 713 or 717, and prior computer programming proficiency on C, C++, Fortran, R or Python (e.g., CIS 209, STAT 726)

#### STAT 768. Applied Bayesian Modeling and Prediction.

Bayes rule, principles of Bayesian inference, Bayesian perspective on statistical models, posterior distribution computations using simulations, Markov Chain Monte Carlo (MCMC) (including Gibbs sampling, Metropolis-Hastings algorithm, slice sampler, hybrid forms and alternative algorithms), convergence monitoring and diagnosis, hierarchical models, model checking and model selection, and applications in the sciences using computer software such as R and WinBUGS.
(3 credit hours) Offered: Spring, odd years
Pr: STAT 705 or 713, and STAT 510 or 770

#### STAT 770. Theory of Statistics I.

Probability models, concepts of probability, random discrete variables, moments and moment generating functions, bivariate distributions, continuous random variables, sampling, Central Limit Theorem, characteristic functions. More emphasis on rigor and proofs than in STAT 510 and 511.
(3 credit hours) Offered: Fall.
Pr.: MATH 222.

#### STAT 771. Theory of Statistics II.

Introduction to multivariate distributions; sampling distributions, derivation, and use; estimation of parameters, testing hypothesis; multiple regression and correlation; simple experimental designs; introduction to nonparametric statistics; discrimination.
(3 credit hours) Offered: Spring.
Pr.: STAT 770.

#### STAT 799. Topics in Statistics.

(hours vary) Offered: Fall, Spring, Summer.
Pr.: Consent of instructor.

#### STAT 810. Seminar in Probability and Statistics.

Discussion and lectures on topics in probability and statistics; one seminar talk by each student registered for credit.
(1 credit hour) Offered: Fall, Spring.

#### STAT 818. Theory of Life-Data Analysis.

A study of models and inferential procedures important to life-data analysis. Comparison of estimators (MLE, BLUE, etc.). Pivotal quantities. Design and regression models for non-normal distributions. Analysis of censored data.
(3 credit hours) Offered Fall, in even years.
Pr.: STAT 705 or 713 and STAT 771.

#### STAT 842. Probability for Statistical Inference.

Probability spaces and random elements, distributions, generating and characteristic functions, conditional expectation, convergence modes and stochastic orders, continuous mapping theorems, central limit theory and accuracy, laws of large numbers, asymptotic expansions for approximating functions of random variables and distributions.
(3 credit hours) Offered: Fall.
Pr.: STAT 770 & 771, or equivalent; MATH 633 or equivalent, or concurrent enrollment in MATH 633.

#### STAT 843. Statistical Inference.

Distributions (commonly used univariate and multivariate distributions, including exponential families of distributions and properties), order statistics and distributional properties, (asymptotic) unbiased estimation and the information inequality, likelihood inference for parametric statistical models (including the multi-parameter case, regular and non-regular cases), confidence sets, functional parameters and statistical functionals, density estimation and nonparametric function estimation, permutation methods.
(3 credit hours) Offered: Spring.
Pr.: STAT 842; MATH 634 or equivalent, or concurrent enrollment in MATH 634.

#### STAT 850. Stochastic Processes.

Normal processes and covariance stationary processes; Poisson processes; renewal counting processes; Markov chains; Brownian motion; applications to science and engineering.
(3 credit hours) Offered: Spring, even years.
Pr.: STAT 770.

#### STAT 860. Linear Models I.

Subspaces, projections, and generalized inverses; multivariate normal distribution, distribution of quadratic forms; optimal estimation and hypothesis testing procedures for the general linear model; application to regression models, correlation model.
(3 credit hours) Offered: Fall.
Pr.: STAT 713, 771.

#### STAT 861. Linear Models II.

Continued application of optimal inference procedures for the general linear model to multifactor analysis of variance, experimental design models, analysis of covariance, split-plot models, repeated measures models, mixed models, and variance component models; multiple comparison procedures.
(3 credit hours) Offered: Spring.
Pr.: STAT 860.

#### STAT 870. Analysis of Messy Data.

Design structures; treatment structures; equal and unequal variances; multiple comparisons; unequal subclass numbers; missing cells; interpretation of interaction; variance components; mixed models; split-plot and repeated measures; analysis of covariance; cross-over designs.
(3 credit hours) Offered: Fall.
Pr.: STAT 720.

#### STAT 880. Time Series Analysis.

Autocorrelation function; spectral density; autoregressive integrated moving average processes; seasonal time series; transfer function model; intervention analysis; regression model with time series error.
(3 credit hours) Offered: Fall, in odd years.
Pr.: STAT 713, 771.

#### STAT 898. Master's Report.

(2 credit hours) Offered: Fall, Spring, Summer.
Pr.: Consent of instructor.

#### STAT 899. Master's Thesis Research.

(hours vary) Offered: Fall, Spring, Summer.
Pr.: Consent of instructor.

#### STAT 903. Statistical Methods for Spatial Data.

Statistical models and methods for analyzing data that are collected at different spatial locations, and perhaps at different times. Spatial prediction and Kriging for continuous spatial data, along with variogram models and estimation for spatial correlation. Spectral analysis for spatial data. Spatial models for lattice data and inference for lattice models. Models and model fitting for spatial point patterns. Classical approaches as well as newly developed methodological and computational research in spatial statistics will be covered with computer-aided applications.
(3 credit hours) Offered: Spring, odd years.
Pr.: STAT 771, plus one introductory course in statistical computing (e.g. STAT 726 or equivalent background).

#### STAT 904. Resampling Methods.

Application, theory, and computational aspects of resampling methods. Topics include parametric and nonparametric bootstrap methods, the jackknife, and randomization/permutation methods; techniques for estimation, bias correction, confidence intervals, and hypothesis testing; applications to linear and nonlinear models; different test statistics for randomization inferences such as mean differences, rank based statistics, t-statistics, and moderated t-statistics for high-dimensional settings; implementation of methods using statistical software; simulation designs for comparing methods.
(3 credit hours) Offered: Spring, even years.
Pr.: STAT 713, 771.

#### STAT 905. High-Dimensional Data and Statistical Learning.

Statistical methods for the analysis of large scale data. Data mining, supervised and unsupervised statistical learning techniques for prediction and pattern recognition. Methods for model selection, multiple testing control, and estimation in high-dimensions. Applications in various fields, including the sciences and engineering using computer software.
(3 credit hours) Offered: Fall, even years.
Pr.: STAT 713 and 771, plus one introductory course in statistical computing (e.g. STAT 726 or equivalent background).

#### STAT 907. Bayesian Statistical Inference.

Principles of Bayesian inference. Methods of Bayesian data analysis with applications in the sciences. Hierarchical and non-hierarchical models, including linear and generalized linear models. Model checking, Model selection, Model comparison. Bayesian computation including Markov Chain Monte Carlo algorithms. Applications in the sciences utilizing computer software.
(3 credit hors) Offered: Fall, odd years.
Pr.: STAT 720 and 771, plus one introductory course in statistical computing (e.g. STAT 725 or 726 or equivalent background).

#### STAT 940. Advanced Statistical Methods.

Generalized linear models and generalized mixed models. Statistical models based on the exponential family of distributions. Applications to non-normal and discrete data, including binary, Poisson and gamma regression, and log-linear models. Topics include likelihood-based estimation and testing, model-fitting, residual analyses, over-dispersed models, quasi-likelihood, large sample properties, and the use of computer packages. Also, methods for longitudinal repeated measures data that will include inference for continuous and discrete data. Inferential objectives include prediction of response and estimation of correlation/covariance structures. Nonparametric and semiparametric methods covered as time permits.
(3 credit hours) Offered: Fall, even years.
Pr.: STAT 861, plus one introductory course in statistical computing (e.g. STAT 725 or 726 or equivalent background).

#### STAT 941. Advanced Statistical Inference.

Foundations and methods of modern statistical inference including asymptotic theory in parametric models (including local asymptotic normailty and contiguity), efficiency of estimators and tests, Bayes procedures, rank, sign and permutation statistics, U-, M-, L-, R-estimates, chi-square tests, empirical processes and the functional delta method, quantiles and order statistics, inference for nonparametric and semiparametric models.
(3 credit hours) Offered: Spring, even years.
Pr.: STAT 843.

#### STAT 945. Problems in Statistical Consulting.

Principles and practices of statistical consulting. Supervised experience in consultation and consequent research concerning applied statistics and probability associated with on-campus investigations.
(1 credit hour) Offered: Fall, Spring.
Pr.: STAT 720; restricted to majors.

#### STAT 950. Advanced Studies in Probability and Statistics.

Theoretical studies of advanced topics in probability, decision theory, Markov processes, experimental design, stochastic processes, or advanced topics. May be repeated.
(hours vary) Offered: Fall, Spring, Summer.
Pr.: Instructor consent.

#### STAT 999. Research in Statistics.

(hours vary) Offered: Fall, Spring, Summer.
Pr.: Consent of instructor.

(Note: STAT 825 has been replaced with STAT 727.)