## Programs by Campus

### Bloomington

#### Statistics

##### Courses

- STAT-S 501 Statistical Methods I: Introduction to Statistics (3 cr.) P: One undergraduate course in statistics. This course takes a systematic approach to the exposition of the general linear model — focusing on correlation, simple linear and multiple regression. Students are introduced to the use of statistical analysis software. The first third of the course consists of a review of statistics, data analysis tools, significance tests, and confidence intervals. Students learn how to think creatively about the use of statistical methods in their own research.

- STAT-S 503 Statistical Methods II: Generalized Linear Models and Categorical Data (3 cr.) P: STAT S501 or one undergraduate course in statistics. This course takes a systematic approach to the exposition of the general linear model — focusing on categorical data. Of primary concern will be models for which the response variable is categorical. Such models include probit, logit, ordered logit, and Poisson regression, among others. Students learn how to think creatively about the use of statistical methods in their own research.

- STAT-S 520 Introduction to Statistics (3 cr.) P: MATH M212, M301, M303, or the equivalent. Basic concepts of data analysis and statistical inference, applied to 1-sample and 2-sample location problems, the analysis of variance, and linear regression. Probability models and statistical methods applied to practical situations and actual data sets from various disciplines. Elementary statistical theory, including the plug-in principle, maximum likelihood, and the method of least squares.

- STAT-S 610 Introduction to Statistical Computing (3 cr.) Introduction to R from a software engineering perspective and an introduction to algorithms commonly used in applied statistics. Optimization algorithms including gradient descent, stochastic gradient descent, the EM algorithm, and topics in convex optimization. Stochastic algorithms including rejection sampling, Metropolis-Hastings, and Gibbs sampling.

- STAT-S 611 Applied Statistical Computing (3 cr.) P: STAT S520 or equivalent or consent of instructor. This course will be an introduction to statistical computing using R and C/C++. It will mainly focus on writing code for solving statistical problems. We will also cover a number of algorithms used in modern statistical computation, with emphasis in stochastic simulation methods.

- STAT-S 612 Reproducible Results and the Workflow of Data Analysis (3 cr.) P: Graduate level class in regression modeling. This course presents methods for producing statistical analyses that are reproducible. Topics include creating datasets containing metadata, using script files that allow results to be replicated, methods to organize and preserve files, approaches to documenting research, and ways to maintain the provenance of statistical results.

- STAT-S 621 Fundamentals of Statistical Methods and Theory I (3cr.) P: MATH-M 301 or M303 or equivalent; MATH-M 311 or equivalent; and STAT-S520 or equivalent; or permission of instructor. Part 1 of a 2-semester sequence on fundamental concepts, principles, and techniques of probabilistic/statistical inference. Random variables and probability distributions, expectation, limit laws, parametric vs nonparametric inference, Bayesian vs frequentist inference, point estimation, hypothesis testing, confidence sets, simulation.

- STAT-S 625 Nonparametric Theory and Data Analysis (3 cr.) P: Two statistics courses at the graduate level, or consent of instructor. Survey of methods for statistical inference that do not rely on parametric probability models. Statistical functionals, bootstrapping, empirical likelihood. Nonparametric density and curve estimation. Rank and permutation tests.

- STAT-S 626 Bayesian Theory and Data Analysis (3 cr.) P: Two statistics courses at the graduate level, or consent of instructor. Introduction to the theory and practice of Bayesian inference. Prior and posterior probability distributions. Data collection, model formulation, computation, model checking, sensitivity analysis.

- STAT-S 631 Applied Linear Models I (3 cr.) P: STAT S320 and MATH M301 or M303 or S303 (or equivalent courses), or consent of instructor. Part I of a 2-semester sequence on linear models, emphasizing linear regression and the analysis of variance, including topics from the design of experiments and culminating in the general linear model.

- STAT-S 632 Applied Linear Models II (3 cr.) P: STAT S631, or consent of instructor. Part II of a 2-semester sequence on linear models, emphasizing linear regression and the analysis of variance, including topics from the design of experiments and culminating in the general linear model.

- STAT-S 637 Categorical Data Analysis (3 cr.) P: Two statistics courses at the graduate level, or consent of instructor. The analysis of cross classified categorical data. Loglinear models; regression models in which the response variable is binary, ordinal, nominal, or discrete. Logit, probit, multinomial logit models; logistic and Poisson regression. Equivalent to EDUC Y637.

- STAT-S 639 Multilevel Models (3 cr.) P: Two statistics courses at the graduate level, or consent of instructor. Introduction to the general multilevel model with an emphasis on applications. Discussion of hierarchical linear models, and generalizations to nonlinear models. How such models are conceptualized, parameters estimated and interpreted. Model fit via software. Major emphasis throughout the course will be on how to choose an appropriate model and computational techniques. Equivalent to EDUC Y639.

- STAT-S 640 Multivariate Data Analysis (3 cr.) P: Two statistics courses at the graduate level, or consent of instructor. Elementary treatment of multivariate normal distributions, classical inferential techniques for multivariate normal data, including Hotelling’s T² and MANOVA. Discussion of analytic techniques such as principal component analysis, canonical correlation analysis, discriminant analysis, and factor analysis. Equivalent to PSY P654.

- STAT-S 645 Covariance Structure Analysis (3 cr.) P: Two statistics courses at the graduate level, or consent of instructor. Path analysis. Introduction to multivariate multiple regression, confirmatory factor analysis, and latent variables. Structural equation models with and without latent variables. Mean-structure and multi-group analysis. Equivalent to EDUC Y645.

- STAT-S 650 Time Series Analysis (3 cr.) P: Two statistics courses at the graduate level, or consent of instructor. Techniques for analyzing data collected at different points in time. Probability models, forecasting methods, analysis in both time and frequency domains, linear systems, state-space models, intervention analysis, transfer function models and the Kalman filter. Stationary processes, autocorrelations, partial autocorrelations, autoregressive, moving average, and ARMA processes, spectral density of stationary processes, periodograms, estimation of spectral density. Course equivalent to MATH M568.

- STAT-S 655 Longitudinal Data Analysis (3 cr.) P: Two statistics courses at the graduate level, or consent of instructor. Introduction to methods for longitudinal data analysis; repeated measures data. The analysis of change—models for one or more response variables, possibly censored. Association of measurements across time for both continuous and discrete responses. Course is equivalent to EDUC Y655.

- STAT-S 660 Sampling (3 cr.) P: Two statistics courses at the graduate level, or consent of instructor. Design of surveys and analysis of sample survey data. Simple random sampling, ratio and regression estimation, stratified and cluster sampling, complex surveys, nonresponse bias.

- STAT-S 670 Exploratory Data Analysis (3 cr.) P: Two statistics courses at the graduate level, or consent of instructor. Numerical and graphical techniques for summarizing and displaying data. Exploration versus confirmation. Connections with conventional statistical analysis and data mining. Applications to large data sets.

- STAT-S 675 Statistical Learning and High-Dimension Analysis (3 cr.) P: STAT S640, or two statistics courses at the graduate level, or consent of instructor. Dataanalytic methods for exploring the structure of high-dimensional data. Graphical methods, linear and nonlinear dimension reduction techniques, manifold learning. Supervised, semisupervised, and unsupervised learning.

- STAT-S 676 Statistical Learning: Model Selection (3 cr.) P: STAT S675 or consent of instructor. A second semester course in high dimensional data analysis focused on model selection. The course covers the trade-off between model fidelity to the observed data and penalization for model complexity. All methods from the course will be applied to real datasets.

- STAT-S 681 Topics in Applied Statistics (3 cr.) P: Consent of instructor. Careful study of a statistical topic from an applied perspective. May be repeated with different topics.

- STAT-S 682 Topics in Mathematical Statistics (3 cr.) P: Consent of instructor. Careful study of a statistical topic from a theoretical perspective. May be repeated with different topics.

- STAT-S 690 Statistical Consulting (4 cr.) P: Consent of instructor. Development of effective consulting skills, including the conduct of consulting sessions, collaborative problem-solving, using professional resources, and preparing verbal and written reports. Interactions with clients will be coordinated by the Indiana Statistical Consulting Center.

- STAT-S 692 Internship in Statistical Consulting (3 cr.) P: STAT S690 and permission of Director of Graduate Studies. One semester internship at the Indiana Statistical Consulting Center (ISCC). Students work on actual consulting problems under the direct supervision of professional statisticians.

- STAT-S 695 Readings in Statistics (1-3 cr.) P: Consent of instructor. Supervised reading of a topic in statistics. May be repeated with different topics.

- STAT-S 710 Statistical Computing (3 cr.) P: STAT S620, or consent of instructor. Survey of numerical methods in statistics. Matrix factorizations and algorithms for linear regression. Nonlinear optimization, maximum likelihood and nonlinear regression. Pseudorandom number generation and Monte Carlo methods.

- STAT-S 721 Advanced Statistical Theory I (3 cr.) P: S620, some knowledge of elementary measure theory, and/or consent of the instructor. Mathematical introduction to major areas of statistical theory and practice, including statistical models, sufficiency, likelihood inference, estimation and testing, Bayesian inference, decision theory, equivariance, and optimality of test statistics.

- STAT-S 722 Advanced Statistical Theory II (3 cr.) P: S721 or consent of the instructor. A continuation of S721. A mathematical introduction to major areas of statistical theory and practice including multinomial models, canonical linear models, exponential families, asymptotic theory, and general linear models.

- STAT-S 730 Theory of Linear Models (3 cr.) P: STAT S620, or consent of instructor. Theory of the general linear model. Distribution theory, linear hypotheses, the Gauss-Markov theorem, testing and confidence regions. Application to regression and to analysis of variance.

- STAT-S 740 Multivariate Statistical Theory (3 cr.) P: STAT S721 and S722, or consent of the instructor. Multivariate normal distributions. Multivariate linear normal models, estimation and testing. Wishart distributions and models. Inference for the covariance matrix. Eigenvalues, including canonical correlations and principal components/factor analysis.

- STAT-S 771 Advanced Data Analysis I (3 cr.) P: Permission of Director of Graduate Studies. This course introduces Ph.D. students in the Department of Statistics to an in-depth cross-disciplinary research experience, emphasizing the role of statistics in solving scientific, technological, or policy problems. Each student identifies a research project, forms an advisory committee, and provides interim written and oral progress reports throughout the remainder of the semester.

- STAT-S 772 Advanced Data Analysis II (3 cr.) P: STAT-S 771 Second semester of a two-semester sequence. Ph.D. students in the Department of Statistics complete the cross-disciplinary projects they began in STAT-S 771.

- STAT-S 781 Advanced Topics in Applied Statistics (3 cr.) P: Consent of the instructor. Careful study of an advanced statistical topic from an applied perspective. As topics vary, this course may be repeated for credit.

- STAT-S 782 Advanced Topics in Mathematical Statistics (3 cr.) P: Consent of the instructor. Careful study of an advanced statistical topic from a mathematical or theoretical perspective. As topics vary, this course may be repeated for credit.

- STAT-S 785 Seminar on Statistical Theory (3 cr.) P: Ph.D. standing in Department of Statistics. Professional development for Ph.D. students in statistics. Topics in statistical theory will be used to provide students with experience in preparing presentations, posters, referee reports, grant proposals, etc.

- STAT-S 799 Research in Statistics (1-6 cr.) P: Consent of the instructor. Research in statistics.