# STAT - Statistics

## STAT5 Statistics

Introduction to statistical methods/reasoning, including descriptive methods, data-gathering (experimental design and sample surveys), probability, interval estimation, significance tests, one- and two-sample problems, categorical data analysis, correlation and regression. Emphasis on applications to the natural and social sciences. Students cannot receive credit for this course if they have already received credit for course 7. (Formerly AMS 5.)

5

## STAT7 Statistical Methods for the Biological, Environmental, and Health Sciences

Case-study-based introduction to statistical methods as practiced in the biological, environmental, and health sciences. Descriptive methods, experimental design, probability, interval estimation, hypothesis testing, one- and two-sample problems, power and sample size calculations, simple correlation and simple linear regression, one-way analysis of variance, categorical data analysis. (Formerly AMS 7.)

5

## STAT7L Statistical Methods for the Biological, Environmental, and Health Sciences Laboratory

Computer-based laboratory course in which students gain hands-on experience in analysis of data sets arising from statistical problem-solving in the biological, environmental, and health sciences. Descriptive methods, interval estimation, hypothesis testing, one-and two-sample problems, correlation and regression, one-way analysis of variance, categorical data analysis. (Formerly AMS 7L.)

2

## STAT80A Gambling and Gaming

Games of chance and strategy motivated early developments in probability, statistics, and decision theory. Course uses popular games to introduce students to these concepts, which underpin recent scientific developments in economics, genetics, ecology, and physics. (Formerly AMS 80A.)

5

## STAT80B Data Visualization

Introduces the use of complex-data graphical representations to extract information from data. Topics include: summary statistics, boxplots, histograms, dotplots, scatterplots, bubble plots, and map-creation, as well as visualization of trees and hierarchies, networks and graphs, and text. (Formerly AMS 80B.)

5

## STAT108 Linear Regression

Covers simple linear regression, multiple regression, and analysis of variance models. Students learn to use the software package R to perform the analysis, and to construct a clear technical report on their analysis, readable by either scientists or nontechnical audiences. (Formerly AMS 156.)

5

## STAT131 Introduction to Probability Theory

Introduction to probability theory and its applications. Combinatorial analysis, axioms of probability and independence, random variables (discrete and continuous), joint probability distributions, properties of expectation, Central Limit Theorem, Law of Large Numbers, Markov chains. Students cannot receive credit for this course and course 203 and Computer Engineering 107. (Formerly AMS 131.)

5

## STAT132 Classical and Bayesian Inference

Introduction to statistical inference at a calculus-based level: maximum likelihood estimation, sufficient statistics, distributions of estimators, confidence intervals, hypothesis testing, and Bayesian inference. (Formerly AMS 132.)

5

## STAT198 Independent Study or Research

Students submit petition to sponsoring agency.

5

## STAT198F Independent Study or Research

Students submit petition to sponsoring agency.

2

## STAT200 Research and Teaching in Statistics

Focuses on basic teaching techniques for teaching assistants, including responsibilities and rights, leading discussion or lab sessions, presentation techniques, maintaining class records, and grading. Examines research and professional training, including use of library, technical writing, giving seminar and conference talks, and ethical issues in science and engineering.

3

## STAT202 Linear Models in SAS

Case study-based course teaches statistical linear modeling using the SAS software package. Teaches generalized linear models; linear regression; analysis of variance/covariance; analysis of data with random effects and repeated measures. (Formerly AMS 202.)

5

## STAT203 Introduction to Probability Theory

Introduces probability theory and its applications. Requires a multivariate calculus background, but has no measure theoretic content. Topics include: combinatorial analysis; axioms of probability; random variables (discrete and continuous); joint probability distributions; expectation and higher moments; central limit theorem; law of large numbers; and Markov chains. Students cannot receive credit for this course and course 131 or Computer Engineering 107. (Formerly AMS 203.)

5

## STAT204 Introduction to Statistical Data Analysis

Presents tools for exploratory data analysis (EDA) and statistical modeling in R. Topics include numerical and graphical tools for EDA, linear and logistic regression, ANOVA, PCA, and tools for acquiring and storing large data. No R knowledge is required. Enrollment is restricted to graduate students and by permission of instructor. (Formerly AMS 204.)

5

## STAT205 Introduction to Classical Statistical Learning

Introduction to classical statistical inference. Topic include: random variables and distributions; types of convergence; central limit theorems; maximum likelihood estimation; Newton-Raphson, Fisher scoring, Expectation-Maximization, and stochastic gradient algorithms; confidence intervals; hypothesis testing; ridge regression, lasso, and elastic net.

5

## STAT205B Intermediate Classical Inference

Statistical inference from a frequentist point of view. Properties of random samples; convergence concepts applied to point estimators; principles of statistical inference; obtaining and evaluating point estimators with particular attention to maximum likelihood estimates and their properties; obtaining and evaluating interval estimators; and hypothesis testing methods and their properties. (Formerly AMS 205B.)

5

## STAT206 Applied Bayesian Statistics

Introduces Bayesian statistical modeling from a practitioner's perspective. Covers basic concepts (e.g., prior-posterior updating, Bayes factors, conjugacy, hierarchical modeling, shrinkage, etc.), computational tools (Markov chain Monte Carlo, Laplace approximations), and Bayesian inference for some specific models widely used in the literature (linear and generalized linear mixed models). (Formerly AMS 206.)

5

## STAT206B Intermediate Bayesian Inference

Bayesian statistical methods for inference and prediction including: estimation; model selection and prediction; exchangeability; prior, likelihood, posterior, and predictive distributions; coherence and calibration; conjugate analysis; Markov Chain Monte Carlo methods for simulation-based computation; hierarchical modeling; Bayesian model diagnostics, model selection, and sensitivity analysis. (Formerly AMS 206B.)

5

## STAT207 Intermediate Bayesian Statistical Modeling

Hierarchical modeling, linear models (regression and analysis of variance) from the Bayesian point of view, intermediate Markov chain Monte Carlo methods, generalized linear models, multivariate models, mixture models, hidden Markov models. (Formerly AMS 207.)

5

## STAT208 Linear Statistical Models

Theory, methods, and applications of linear statistical models. Review of simple correlation and simple linear regression. Multiple and partial correlation and multiple linear regression. Analysis of variance and covariance. Linear model diagnostics and model selection. Case studies drawn from natural, social, and medical sciences. Course 205 strongly recommended as a prerequisite. Undergraduates are encouraged to take this class with permission of instructor. (Formerly AMS 256.)

5

## STAT209 Generalized Linear Models

Theory, methods, and applications of generalized linear statistical models; review of linear models; binomial models for binary responses (including logistical regression and probit models); log-linear models for categorical data analysis; and Poisson models for count data. Case studies drawn from social, engineering, and life sciences. (Formerly AMS 274.)

5

## STAT222 Bayesian Nonparametric Methods

Theory, methods, and applications of Bayesian nonparametric modeling. Prior probability models for spaces of functions. Dirichlet processes. Polya trees. Nonparametric mixtures. Models for regression, survival analysis, categorical data analysis, and spatial statistics. Examples drawn from social, engineering, and life sciences. (Formerly AMS 241.)

5

## STAT223 Time Series Analysis

Graduate level introductory course on time series data and models in the time and frequency domains: descriptive time series methods; the periodogram; basic theory of stationary processes; linear filters; spectral analysis; time series analysis for repeated measurements; ARIMA models; introduction to Bayesian spectral analysis; Bayesian learning, forecasting, and smoothing; introduction to Bayesian Dynamic Linear Models (DLMs); DLM mathematical structure; DLMs for trends and seasonal patterns; and autoregression and time series regression models. (Formerly AMS 223.)

5

## STAT224 Bayesian Survival Analysis and Clinical Design

Introduction to Bayesian statistical methods for survival analysis and clinical trial design: parametric and semiparametric models for survival data, frailty models, cure rate models, the design of clinical studies in phase I/II/III. (Formerly AMS 276.)

5

## STAT225 Multivariate Statistical Methods

Introduction to statistical methods for analyzing data sets in which two or more variables play the role of outcome or response. Descriptive methods for multivariate data. Matrix algebra and random vectors. The multivariate normal distribution. Likelihood and Bayesian inferences about multivariate mean vectors. Analysis of covariance structure: principle components, factor analysis. Discriminant, classification and cluster analysis. (Formerly AMS 225.)

5

## STAT226 Spatial Statistics

Introduction to the analysis of spatial data: theory of correlation structures and variograms; kriging and Gaussian processes; Markov random fields; fitting models to data; computational techniques; frequentist and Bayesian approaches. (Formerly AMS 245.)

5

## STAT229 Advanced Bayesian Computation

Teaches some advanced techniques in Bayesian Computation. Topics include Hamiltonian Monte Carlo; slice sampling; sequential Monte Carlo; assumed density filtering; expectation propagation; stochastic gradient descent; approximate Markov chain Monte Carlo; variational inference; and stochastic variational inference. (Formerly AMS 268.)

5

## STAT243 Stochastic Processes

Includes probabilistic and statistical analysis of random processes, continuous-time Markov chains, hidden Markov models, point processes, Markov random fields, spatial and spatio-temporal processes, and statistical modeling and inference in stochastic processes. Applications to a variety of fields. (Formerly AMS 263.)

5

## STAT244 Bayesian Decision Theory

Explores conceptual and theoretical bases of statistical decision making under uncertainty. Focuses on axiomatic foundations of expected utility, elicitation of subjective probabilities and utilities, and the value of information and modern computational methods for decision problems. (Formerly AMS 221.)

5

## STAT246 Probability Theory with Markov Chains

Introduction to probability theory: probability spaces, expectation as Lebesgue integral, characteristic functions, modes of convergence, conditional probability and expectation, discrete-state Markov chains, stationary distributions, limit theorems, ergodic theorem, continuous-state Markov chains, applications to Markov chain Monte Carlo methods. (Formerly AMS 261.)

5

## STAT266A Data Visualization and Statistical Programming in R

Introduces students to data visualization and statistical programming techniques using the R language. Covers the basics of the language, descriptive statistics, visual analytics, and applied linear regression. Enrollment is by permission of the instructor. (Formerly Applied Math and Statistics 266A and Computer Science 266A.)

3

## STAT266B Advanced Statistical Programming in R

Teaches students already familiar with the R language advanced tools such as interactive graphics, interfacing with low-level languages, package construction, debugging, profiling, and parallel computation. (Formerly Applied Math and Statistics 266B and Computer Science 266B.)

3

## STAT266C Introduction to Data Wrangling

Introduces students to concepts and tools associated with data collection, curation, manipulation, and cleaning including an introduction to relational databases and SQL, regular expressions, API usage, and web scraping using Python. (Formerly Applied Math and Statistics 266C and Computer Science 266C.)

3

## STAT280B Seminars in Statistics

Weekly seminar series covering topics of current research in statistics.

2

## STAT280D Seminar in Bayesian Statistical Methodology

Weekly seminar/discussion group on Bayesian statistical methods, covering both analytical and computational approaches. Participants present research progress and finding in semiformal discussions. Students must present their own research on a regular basis. (Formerly AMS 280D.)

2

## STAT285 Seminar in Career Skills

Seminar in career skills for applied mathematicians and statisticians. Learn about professional activities such as the publication process, grant proposals, and the job market.

2

## STAT291 Advanced Topics in Bayesian Statistics

Advanced study of research topics in the theory, methods, or applications of Bayesian statistics. The specific subject depends on the instructor. Enrollment is restricted to graduate students and by permission of instructor. (Formerly AMS 291.)

3

## STAT296 Masters Project

Independent completion of a masters project under faculty supervision. Students submit petition to sponsoring agency. Enrollment is restricted to graduate students.

2

## STAT297A Independent Study or Research

Independent study or research under faculty supervision. Students submit petition to sponsoring agency. Enrollment is restricted to graduate students.

5

## STAT297B Independent Study or Research

Independent study or research under faculty supervision. Students submit petition to sponsoring agency. Enrollment is restricted to graduate students.

10

## STAT297C Independent Study or Research

Independent study or research under faculty supervision. Students submit petition to sponsoring agency. Enrollment is restricted to graduate students.

15

## STAT297F Independent Study

Independent study or research under faculty supervision. Students submit petition to sponsoring agency. Enrollment is restricted to graduate students.

2

## STAT299A Thesis Research

Thesis research under faculty supervision. Students submit petition to sponsoring agency. Enrollment restricted to graduate students.

5

## STAT299B Thesis Research

Thesis research under faculty supervision. Students submit petition to sponsoring agency. Enrollment restricted to graduate students.

10

## STAT299C Thesis Research

Thesis research under faculty supervision. Students submit petition to sponsoring agency. Enrollment restricted to graduate students.

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