Techniques of experimentation based on statistical principles with application to quality improvement and other fields. Full and fractional factorial designs for factors at two levels; dispersion effects; related topics.

Basic probability and statistics with applications and examples in engineering. Elementary probability, random variables and their distribution, random processes, statistical inference, linear regression, correlation and basic design of experiments with application to quality assurance, reliability, and life testing. May not be taken concurrently with or after STAT 513, STAT 515, or STAT 516. Not for C.A.S., M.A.S., or Ph.D credit in Statistics.

Probability and independence; discrete and continuous random variables; joint, marginal, and conditional densities; moment generating functions; laws of large numbers; binomial, Poisson, gamma, univariate and bivariate normal distributions.

Functions of random variables, order statistics, sampling distributions, central limit theorem, quality of estimators, interval estimation, sufficient statistics, minimum-variance unbiased estimator, maximum likelihood, large-sample theory, introduction to hypothesis testing.

Hypothesis testing, Neyman-Pearson lemma, likelihood ratio tests, power, the theory of linear models including multiple linear regression and ANOVA, the Chi-square goodness-of-fit test, Chi-square inference for contingency tables, Bayesian inference, and advanced topics including survival analysis (only if time permits).

Applications and principles of elementary probability, essential discrete and continuous probability distributions, sampling distributions, estimation, and hypothesis testing. Inference for means, variances, proportions, one-way ANOVA, simple linear regression, and contingency tables. Statistical packages such as SAS or R. May not be taken concurrently with or after STAT 509, STAT 513, or STAT 516. Not for CAS, MAS, MS, or PhD credit in Statistics.

Applications and principles of linear models. Simple and multiple linear regression, analysis of variance for basic designs, multiple comparisons, random effects, and analysis of covariance. Statistical packages such as SAS. Not for CAS, MAS, MS, or PhD credit in Statistics.

Theory and applications of advanced statistical models. Includes implementation and assessment of generalized linear, nonlinear and nonparametric regression, mixed effect, repeated measures, multivariate regression, and spatial models.

Applications and principles of nonparametric statistics. Classical rank-based methods, and selected categorical data analysis and modern nonparametric methods. Statistical packages such as R.

Techniques of statistical sampling in finite populations with applications in the analysis of sample survey data. Topics include simple random sampling for means and proportions, stratified sampling, cluster sampling, ratio estimates, and two-stage sampling.

Time series analysis and forecasting using the multiple regression and Box-Jenkins approaches.

An introduction to stochastic processes, including conditional probability, Markov chains, Poisson processes, and Brownian motion. Incorporates simulation and applications to actuarial science.

Probability spaces. Random variables. Mean and variance. Geometric Brownian Motion and stock price dynamics. Interest rates and present value analysis. Pricing via arbitrage arguments. Options pricing and the Black-Scholes formula.

Convex sets. Separating Hyperplane Theorem. Fundamental Theorem of Asset Pricing. Risk and expected return. Minimum variance portfolios. Capital Asset Pricing Model. Martingales and options pricing. Optimization models and dynamic programming.

Statistical procedures for process control including CUSUM and Shewhart Control Charts, and lot-acceptance sampling.

Statistical analysis of environmental data. Review of multiple regression and ANOVA, nonlinear regression models and generalized linear models, analyses for temporally and spatially correlated data, and methods of environmental sampling.

Introduction to fundamentals of multivariate statistics and data mining. Principal components and factor analysis; multidimensional scaling and cluster analysis; MANOVA and discriminant analysis; decision trees; and support vector machines. Use of appropriate software.

Theory and application of machine learning. Current mainstream programming libraries such as in Python, and implementation of regression, clustering, principal components, and linear discriminant analysis. Detailed coverage of methods such as random forests, support vector machines, and k-nearest neighbors. Introduction to neural networks.

Principles of Bayesian statistics, including: one- and multi-sample analyses; Bayesian linear models; Monte Carlo approaches; prior elicitation; hypothesis testing and model selection; hierarchical models; selected advanced models; statistical packages such as WinBUGS and R.

An introduction to statistical packages such as R and SAS with special focus on data management and computing procedures such as Monte Carlo simulation.

Advanced programming techniques in SAS, including database management, macro language, and efficient programming practices.

Techniques for data visualization and graphics including interactive graphics, data wrangling and cleaning, data ethics, database querying and administration.

Normative approaches to uncertainty in artificial intelligence. Probabilistic and causal modeling with Bayesian networks and influence diagrams. Applications in decision analysis and support. Algorithms for probability update in graphical models.

Foundational techniques and tools required for data science and big data analytics. Concepts, principles, and techniques applicable to any technology and industry for establishing a baseline that can be enhanced by future study.

This course focuses on quantitative knowledge for interdisciplinary applications in genetics as well as hands-on experience in analyzing genetic data. In this course, students will have programming exercises in using analysis tools to conduct genome-wide analysis, annotation, and interpretation of genetic data using R/Bioconductor packages.

Introduction to statistics for elementary, middle, and high school teachers. The fundamentals of data collection, descriptive statistics, probability, and inference with special focus on methods of teaching statistical reasoning. For M.A.T. (excluding mathematics) / M.Ed. / M.T. and nondegree credit only.

Course content varies and will be announced in the schedule of courses by title.

Introduction to data collection, descriptive statistics, and statistical inference with examples from hospitality, retail, sport, and entertainment management. Focus on selecting, implementing, and interpreting the appropriate statistical methods using software such as Excel and SPSS. Not for minor or degree credit in Mathematics or Statistics. Does not prepare students for STAT 516, STAT 518, STAT 519 or STAT 525.

A thorough study of the topics covered on the AP Statistics Examination. A non-calculus-based introduction, including descriptive and inferential one- and two-variable statistics, and emphasizing activities illustrating statistical thinking. Current secondary high school teacher certification in mathematics. For I.M.A./M.A.T. (excluding mathematics)/M.Ed./M.T. and nondegree credit only. Restricted to graduate students.

Introduction to probability and the concepts of estimation and hypothesis testing for use in experimental, social, and professional sciences. One and two-sample analyses, nonparametric tests, contingency tables, sample surveys, simple linear regression, various statistical packages. Not to be used for M.S. or Ph.D. credit in statistics or mathematics. Not to be used for M.S. or Ph.D. credit in statistics or mathematics.

Continuation of STAT 700. Simple linear regression, correlation, multiple regression, fixed and random effects analysis of variance, analysis of covariance, experimental designs, some multivariate methods, various statistical packages. Not to be used for M.S. or Ph.D. credit in statistics or mathematics.

Fundamental theory of statistics and how it applies to industrial problems. Topics include probability, random variables and vectors and their distributions, sampling theory, point and interval estimators, and application to the theory of reliability, regression, process control and quality issues. Not to be used for M.S. or Ph.D. credit in statistics.

Continuation of STAT 702. Topics include discussion of theoretical properties of point estimators and tests of hypotheses, elements of statistical tests, the Neyman-Pearson Lemma, UMP tests, likelihood ratio and other types of tests, and Bayes procedures in the decision process. Not to be used for M.S. or Ph.D. credit in statistics.

Primarily for graduate students in statistics and the mathematical sciences. Probability concepts, inferences for normal parameters, regression, correlation, use of computer statistical packages.

Continuation of STAT 704. Analysis of variance (fixed and random effects), analysis of covariance, experimental design, model building, other applied topics, and use of computer statistical packages.

Specialized experimental design: 2n and 3n factorials; fractional replication; confounding; incomplete block designs, including split-plot, split-block, and Latin square designs; general principles of design.

Statistical methods for environmental and ecological sciences, including nonlinear regression, generalized linear models, spatial analyses/kriging, temporal analyses, meta-analysis, quantitative risk assessment.

Theoretical underpinnings of environmetrics. Spatial statistics, temporal and longitudinal analysis, hierarchical modeling, and Bayesian inferences for environmental data.

Sample spaces, probability and conditional probability, independence, random variables, expectation, distribution theory, sampling distributions, laws of large numbers and asymptotic theory, order statistics, and estimation.

Further development of estimation theory and tests of hypotheses, including an introduction to Bayes estimation, sufficiency, minimum variance principles, uniformly most powerful and likelihood ratio tests, and sequential probability ratio tests.

A study of the general linear statistical model and the linear hypothesis. Topics include the multivariate normal distribution, distributions of quadratic forms, and parameter estimation and hypothesis testing for full-rank models, regression models, and less than full-rank models.

Inference for general nonlinear parametric statistical models for univariate and multivariate response; linear and quadratic estimating equations; models for covariance structure; effects of model misspecification and robustness.

Special topics in probability theory and stochastic processes not offered in other courses.

Special topics in statistics not offered in other courses.

Stochastic properties, identification, estimation, and forecasting methods for stationary and nonstationary time series models.

Theory of stochastic processes, including branching processes, discrete and continuous time Markov chains, renewal theory, point processes, and Brownian motion.

A survey of the theory and applications of the fundamental techniques for analyzing multivariate data.

A survey of current algorithms and software for solving fundamental problems of statistical computing with emphasis on computer generation of random variates.

Methods for fitting (regression) response surfaces and interpreting them subject to random error. Includes designs and industrial process optimization methods.

The various statistical and probability models in reliability and life testing and inference procedures for such models, including life distributions, parametric and nonparametric inference methods, hazard and failure rate functions, plotting methods, analysis of mixtures, censoring.

Advanced methods for analysis of discrete data. Higher-order contingency tables, log-linear and other generalized linear models. Multivariate methods for matched pairs and longitudinal data.

Modern methods for the analysis of repeated measures, correlated outcomes, and longitudinal data, including repeated measures ANOVA, generalized linear models, random effects, and generalized estimating equations.

Statistical theory and applications extending regression and analysis of variance to non-normal data. Encompasses logistic and other binary regressions, log-linear models, and gamma regression models.

Statistical models for item response theory, Rasch and other models for binary and polytomous data, and applications. Use of statistical software.

An exposure to the techniques of statistical consulting through discussion and analysis of actual statistical problems which occur in fields of application.

Experiences in actual statistical consulting settings; participation and critiques.

CL: 2020.

Probability spaces, random variables and distributions, expectations, characteristic functions, laws of large numbers, and the central limit theorem.

More about distributions, limit theorems, Poisson approximations, conditioning, martingales, and random walks.

The advanced theory of statistical inference, including the theory for likelihood construction for different types of data and models, algorithms for maximizing likelihood, likelihood-based inference, M-estimation and likelihood-based inference in the presence of model misspecification, Jackknife and bootstrap.

This course covers basic issues and principles of statistical decision theory including theory on Bayesian decision rules, minimax analysis, invariance principle, and sequential analysis.

Modes of convergence, limit theorems, and the asymptopic properties of estimators and tests.

The general theory of nonparametric statistics, including order statistic theory, theory of ranks, U-statistics in nonparametric estimation and testing, linear rank statistics and their application to location and scale problems, goodness-of-fit, and other distribution-free procedures.

For doctoral candidates.

CL: 2020.

For doctoral candidates.