[IAI Code: M1902] First course in probability and statistics at a precalculus level; emphasizes basic concepts, including descriptive statistics, elementary probability, estimation, and hypothesis testing in both nonparametric and normal models. Credit is not given toward graduation for: Credit is not given for both STAT 100 and any one of the following: ECON 202, PSYC 235, or SOC 485. Prerequisite: MATH 112.
Data Science Discovery is the intersection of statistics, computation, and real-world relevance. As a project-driven course, students perform hands-on-analysis of real-world datasets to analyze and discover the impact of the data. Throughout each experience, students reflect on the social issues surrounding data analysis such as privacy and design. Same as CS 107 and IS 107.
See course schedule for topics. Approved for Letter and S/U grading. May be repeated if topics vary.
Survey of statistical concepts, data analysis, designed and observational studies and statistical models. Statistical computing using a statistical package such as R or a spreadsheet. Topics to be covered include data summary and visualization, study design, elementary probability, categorical data, comparative experiments, multiple linear regression, analysis of variance, statistical inferences and model diagnostics. May be taken as a first statistics course for quantitatively oriented students, or as a second course to follow a basic concepts course. Credit is not given for both STAT 200 and STAT 212.
Explores the data science pipeline from hypothesis formulation, to data collection and management, to analysis and reporting. Topics include data collection, preprocessing and checking for missing data, data summary and visualization, random sampling and probability models, estimating parameters, uncertainty quantification, hypothesis testing, multiple linear and logistic regression modeling, classification, and machine learning approaches for high dimensional data analysis. Students will learn how to implement the methods using Python programming and Git version control. Prerequisite: STAT 107.
Application of statistical reasoning and statistical methodology to biology. Topics include descriptive statistics, graphical methods, experimental design, probability, statistical inference and regression. In addition, techniques of statistical computing are covered. Credit is not given for both STAT 212 and STAT 200.
Statisticians must be savvy in programming methods useful to the wide variety of analysis that they will be expected to perform. This course provides the foundation for writing and packaging statistical algorithms through the creation of functions and object oriented programming. Fundamental programming techniques and considerations will be emphasized. Students will also create dynamic reports that encapsulate their implemented algorithms. Students must have access to a computer on which they can install software. Prerequisite: One of STAT 107, STAT 200, or STAT 212.
May be repeated to a maximum of 8 hours. Prerequisite: Consent of instructor.
May be repeated to a maximum of 8 hours. Prerequisite: Consent of instructor.
Introduction to mathematical statistics that develops probability as needed; includes the calculus of probability, random variables, expectation, distribution functions, central limit theorem, point estimation, confidence intervals, and hypothesis testing. Offers a basic one-term introduction to statistics and also prepares students for STAT 410 and STAT 425. Same as MATH 463. 4 undergraduate hours. 4 graduate hours. Prerequisite: MATH 231. Not intended for first-time freshmen.
Continuation of STAT 408. Examines parametric point and interval estimation, including maximum likelihood estimation, sufficiency, completeness, and Bayesian estimation; hypothesis testing; linear models; regression and correlation. Same as ASRM 402. 4 undergraduate hours. 4 graduate hours. Credit is not given for both STAT 409 and STAT 410. Prerequisite: STAT 408.
Continuation of STAT 400. Includes moment-generating functions, transformations of random variables, normal sampling theory, sufficiency, best estimators, maximum likelihood estimators, confidence intervals, most powerful tests, unbiased tests, and chi-square tests. Same as MATH 464. 3 undergraduate hours. 4 graduate hours. Credit is not given for both STAT 410 and STAT 409. Prerequisite: MATH 241 and STAT 400.
Systematic, calculus-based coverage of the more widely used methods of applied statistics, including simple and multiple regression, correlation, analysis of variance and covariance, multiple comparisons, goodness of fit tests, contingency tables, nonparametric procedures, and power of tests; emphasizes when and why various tests are appropriate and how they are used. Same as ASRM 450. 3 undergraduate hours. 4 graduate hours. Prerequisite: STAT 408 or STAT 400; MATH 231 or equivalent; knowledge of basic matrix manipulations; or consent of instructor.
This is the foundation for advanced statistical modeling with a focus on multiple strategies for analyzing data. The course explores linear regression, least squares estimates, F-tests, analysis of residuals, regression diagnostics, transformations, model building, generalized and weighted least squares, PCA, A/B testing, randomization tests, ANOVA, random effects, mixed effects, and longitudinal data. Statistical computing is an integral part of the course. 3 undergraduate hours. 4 graduate hours. Prerequisite: STAT 400; MATH 257 or MATH 415. Concurrent Enrollment in STAT 410 is preferred.
This is a continuation in the study of advanced statistical modeling techniques with a focus on categorical data. The course explores logistic regression, generalized linear models, goodness-of-fit, link functions, count regression, log-linear models, probability models for contingency tables, and ordinal response models. Statistical computing is an integral part of the course. 3 undergraduate hours. 4 graduate hours. Prerequisite: STAT 410; STAT 425.
Examines statistical packages, numerical analysis for linear and nonlinear models, graphics, and random number generation and Monte Carlo methods. Same as CSE 428. 3 undergraduate hours. 4 graduate hours. Prerequisite: STAT 410 or equivalent; knowledge of a programming language.
Studies theory and data analysis for time series; examines auto-regressive moving average model building and statistical techniques; and discusses spectral model building and statistical analysis using windowed periodograms and Fast Fourier Transformations. 3 undergraduate hours. 4 graduate hours. Prerequisite: STAT 410.
Formulation and analysis of mathematical models for random phenomena; extensive involvement with the analysis of real data; and instruction in statistical and computing techniques as needed. 3 undergraduate hours. 4 graduate hours. May be repeated in the same or separate terms if topics vary. Prerequisite: STAT 410; STAT 425. Some topics may require additional prerequisites. Read the section text for each topic.
Introduction to the concepts and methodology of Bayesian statistics, for students with fundamental knowledge of mathematical statistics. Topics include Bayes' rule, prior and posterior distributions, conjugacy, Bayesian point estimates and intervals, Bayesian hypothesis testing, noninformative priors, practical Markov chain Monte Carlo, hierarchical models and model graphs, and more advanced topics as time permits. Implementations in R and specialized simulation software. Same as ASRM 453. 3 undergraduate hours. 4 graduate hours. Prerequisite: STAT 410 and knowledge of R.
Topics in supervised and unsupervised learning are covered, including logistic regression, support vector machines, classification trees and nonparametric regression. Model building and feature selection are discussed for these techniques, with a focus on regularization methods, such as lasso and ridge regression, as well as methods for model selection and assessment using cross validation. Cluster analysis and principal components analysis are introduced as examples of unsupervised learning. Same as ASRM 451. 3 undergraduate hours. 4 graduate hours. Prerequisite: STAT 400, and either STAT 420 or STAT 425.
A stochastic process is a random process that represents the evolution of some system over time. Topics may include discrete-time and continuous-time Markov chains, birth-and-death chains, branching chains, stationary distributions, random walks, Markov pure jump processes, birth-and-death processes, renewal processes, Poisson process, queues, second order processes, Brownian motion (Wiener process), and Ito's lemma. 3 undergraduate hours. 4 graduate hours. Prerequisite: STAT 400 required, STAT 410 preferred, and MATH 225 (or equivalent knowledge of Linear Algebra) highly recommended.
Unsupervised learning is a type of machine learning that deals with finding patterns in data without the use of labeled examples. Two major unsupervised learning techniques, clustering and dimensionality reduction, will be covered with a focus on methods, evaluation metrics, and interpretation of results. The methodologies enable discovery of and inference about hidden insights contained in high-dimensional unlabeled data. Applications on real and artificial datasets are emphasized using programming languages such as Python. 3 undergraduate hours. 4 graduate hours. Prerequisite: STAT 410 and either MATH 415 or MATH 257.
The critical elements of data storage, data cleaning, and data extractions that ultimately lead to data analysis are presented. Includes basic theory and methods of databases, auditing and querying databases, as well as data management and data preparation using standard large-scale statistical software. Students will gain competency in the skills required in storing, cleaning, and managing data, all of which are required prior to data analysis. Same as CSE 440. 3 undergraduate hours. 4 graduate hours. Prerequisite: STAT 400 or STAT 409.
Principles for formulating complex research questions into precise statistical ones, along with selecting, learning, and implementing appropriate statistical procedures to answer those questions. Emphasis is placed on the principles of data analysis rather than the mathematics of specific methods. Topics include the core framework of statistics, surveys of statistical methods, guided data analysis, and effective written and oral communication. 3 undergraduate hours. 4 graduate hours. Prerequisite: STAT 425.
This project-based course emphasizes written, visual, and oral communication of statistical results and conclusions. An introduction to statistical consulting is also provided. Additional topics include introductions to statistical methodologies in industry and aspects of careers in statistics. 3 undergraduate hours. 4 graduate hours. Prerequisite: STAT 420 or STAT 425 (completion preferred, but may be taken concurrently) or consent of instructor.
Several of the most widely used techniques of data analysis are discussed with an emphasis on statistical computing. Topics include linear regression, analysis of variance, generalized linear models, and analysis of categorical data. In addition, an introduction to data mining is provided considering classification, model building, decision trees, and cluster analysis. Same as CSE 448. 4 undergraduate hours. 4 graduate hours. Prerequisite: STAT 400 or STAT 409, and credit for or concurrent registration in STAT 410.
Examines current topics and techniques for efficiently and effectively managing and analyzing large-scale data. The course focuses on applications of advanced statistical analysis in data science for massive data sets. Topics include current best practices and technologies for implementation such as parallel and distributed processing, distributed storage techniques, and modern computational frameworks such as cloud computing. 3 undergraduate hours. 4 graduate hours. Prerequisite: (STAT 440 or STAT 447) and (STAT 420 or STAT 425); or permission of the instructor.
Provides a graduate level foundation in fundamental mathematical statistics topics including order statistics, exponential families, sufficiency, Rao-Blackwell theorem, Cramer-Rao lower bound, point estimation, hypothesis testing and interval estimation, likelihood and Bayesian methods, and large-sample asymptotics. Prerequisite: STAT 410.
Provides an advanced introduction to rigorous mathematical foundations of statistical inference, covering topics such as distribution theory, point estimation theory, interval estimation, theory of hypothesis testing, and decision theory. Prerequisite: Familiarity with probability theory and statistics at the level of STAT 410. For Graduate Students Only.
Various topics in computational statistics, such as optimization, Monte Carlo methods, Bayesian computation, and machine learning. Same as CSE 525. May be repeated if topics vary. Prerequisite: STAT 425, STAT 426, and STAT 510 or 511; or consent of instructor.
An advanced introduction to regression analysis with applications to analysing data from disciplines such as biostatistics and economics. The course will introduce classical as well as modern regression methods and goes into the depths of those techniques to understand the motivation, justification, implementation of those methods. An emphasis will be given to understand the statistical properties of those methods along with their practical advantages and limitations. Both theoretical and applied aspects of regression analysis will be discussed. Prerequisite: STAT 410, STAT 510 or STAT 511 (concurrent enrollment is sufficient), and knowledge of R. For Graduate Students Only.
Modern techniques of predictive modeling, classification, and clustering are discussed. Examples of these are linear regression, nonparametric regression, kernel methods, regularization, cluster analysis, classification trees, neural networks, boosting, discrimination, support vector machines, and model selection. Applications are discussed as well as computation and theory. Same as ASRM 551 and CSE 542. Prerequisite: STAT 410 and STAT 425.
Trains students to analyze large complex data using advanced statistical learning methods and algorithms. The main topics in the course include: data exploration and interpretation in data science; large data processing; regularization methods; optimization tools; deep learning; recommender systems; network and graphical models; text mining; and imaging analyses. Students will gain practical skills of data mining and knowledge discovery in various applications such as business, political science, biology and medicine. Prerequisite: STAT 425; STAT 510 or STAT 511.
Measures and probabilities; integration and expectation; convergence theorems and inequalities for integrals and expectations; independence; convergence in probability, almost surely, and mean; Three Series Theorem; laws of large numbers. Prerequisite: MATH 447 or consent of instructor.
A graduate-level introduction to Empirical Process Theory with applications to statistical M estimation, nonparametric regression, and high dimensional statistics. Empirical Process Theory deals with two fundamental questions: the uniform law of large numbers, and the uniform central limit theorems, both of which will be covered. This course provides rigorous training in empirical process for students with a strong background in mathematical statistics. Topics covered are useful for conducting modern theoretical research in statistics and probability. Prerequisite: STAT 511, STAT 575, STAT 553. Restricted to graduate students only.
May be repeated if topics vary. Prerequisite: Consent of instructor.
Directed reading and research. Approved for letter and S/U grading. May be repeated with approval. Prerequisite: Consent of instructor.
Supervised, off-campus experience in a field in which statistical science plays an important role. Approved for letter and S/U grading. Prerequisite: STAT 425 and consent of instructor.