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SDS 380C. Statistical Methods I

SDS 380D. Statistical Methods II

SDS 381. Mathematical Methods for Statistical Analysis

SDS 382. Introduction to Probability and Statistics

SDS 183K. Data Analysis Applications

SDS 383C. Statistical Modeling I

SDS 383D. Statistical Modeling II

SDS 384: Topics in Statistics and Probability

SDS 385. Topics in Applied Statistics

SDS 386C. Probabilistic Graphical Models

SDS 386D. Monte Carlo Methods in Statistics

SDS 387. Linear Models

SDS 388. Consulting Seminar

SDS 389. Time Series and Dynamic Models

SDS 292. Intro to Scientific Programming

SDS 392M. Computational Economics

SDS 393C. Numerical Analysis: Linear Algebra

SDS 393D. Numerical Analysis: Interpolation, Approximation, Quadrature, and Differential Equations

SDS 394. Scientific and Technical Computing

SDS 394C. Parallel Computing

SDS 394D. Distributed and Grid Computing for Scientists and Engineers

SDS 394E. Visualization and Data Analysis

SDS 395. Advanced Topics in Scientific Computation

SDS 398T. Supervised Teaching in Statistics and Computation

An introduction to the fundamental concepts and methods of statistics. The course will cover topics ranging from descriptive statistics, sampling distributions, confidence intervals, and hypothesis testing. Topics could include simple and multiple linear regression, Analysis of Variance, and Categorical Analysis. Use of statistical software is emphasized. Prerequisite: Graduate standing.

A continuation of SDS 380C: Statistical Methods I. The course presents an overview of advanced statistical modeling topics. Topics may include random and mixed effects models, time series analysis, survival analysis, Bayesian methods, and multivariate analysis of variance. Use of statistical software is emphasized. Prerequisite: Graduate standing, and Statistics and Data Sciences 380C or the equivalent.

Introduction to mathematical concepts and methods essential for multivariate statistical analysis. Topics include basic matrix algebra, eigenvalues and eigenvector, quadratic forms, vector and matrix differentiation, unconstrained optimization, constrained optimization, and applications in multivariate statistical analysis. Prerequisite: Graduate standing and one course in statistics.

Expectation and variance of random variables, conditional probability and independence, sampling distributions, point estimation, confidence intervals, hypothesis tests, and other topics. Prerequisite: Graduate standing, and M408D or M408L.

Introduction to core applied statistical modeling ideas from a probabilistic, Bayesian perspective. Topics include: (i) Exploratory Data Analysis; (ii) Programming and Graphics in R; (iii) Bayesian Probability Models; (iv) Intro to the Gibbs Sampler; (v) Applied Regression Analysis; (vi) The “Normal-means” problem; and (vii) Hierarchical Models. Prerequisite: Graduate standing.

In this course, students will learn to describe real-world systems using structured probabilistic models that incorporate multiple layers of uncertainty. Major topics to be covered include: (i) theory of the multivariate normal distribution; (ii) mixture models; (iii) introduction to nonparametric Bayesian analysis; (iv) advanced hierarchical models and latent-variable models; (v) Generalized Linear Models; and (vi) advanced topics in linear and nonlinear regression. Examples will be taken from a wide variety of applied fields in the physical, social, and biological sciences. Prerequisite: Graduate standing.

Introduction to the use of statistical or mathematical applications for data analysis. Two hours per week for eight weeks. May be repeated for credit when the topics vary. Offered on the credit/no credit basis only. Prerequisite: Graduate standing.
Topic 1: SPSS
Topic 2: SAS
Topic 3: STATA
Topic 4: Selected Topics

Concepts of probability and mathematical statistics with applications in data analysis and research. May be repeated for credit when the topics vary. Prerequisite: Graduate standing, and Statistics and Data Sciences 382, Mathematics 362K and 378K, or consent of instructor.

**Topic 1: Applied Probability.** Basic probability theory, combinatorial analysis of random phenomena, conditional probability and independence, parametric families of distributions, expectation, distribution of functions of random variables, limit theorems.

**Topic 2: Mathematical Statistics I.** The first semester of a two-semester course covering the general theory of mathematical statistics. The two-semester course covers distributions of functions of random variables, properties of a random sample, principles of data reduction, overview of hierarchical models, decision theory, Bayesian statistics, and theoretical results relevant to point estimation, interval estimation, and hypothesis testing.

**Topic 3: Mathematical Statistics II.** A continuation of Statistics and Scientific Computation 384 (Topic 2). Additional prerequisite: Statistics and Data Sciences 384 (Topic 2).

**Topic 4: Regression Analysis.** Simple and multiple linear regression, inference in regression, prediction of new observations, diagnostics and remedial measures, transformations, model building. Emphasis will be on both understanding the theory and applying theory to analyze real data.

**Topic 5: Multivariate Statistical Analysis.** Introduction to the general multivariate linear model: a selection of techniques including principle components, factor analysis, and discriminant analysis.

**Topic 6: Design and Analysis of Experiments.** Design and analysis of experiments, including one-way and two-way layouts; components of variance; factorial experiments; balanced incomplete block designs; crossed and nested classifications; fixed, random, and mixed models; split plot designs.

**Topic 7: Bayesian Statistical Methods.** Fundamentals of Bayesian inference in single and multi-parameter models for inference and decision making, including simulation of posterior distributions, Markov chain Monte Carlo methods, hierarchical models, and empirical Bayes models.

**Topic 8: Time Series Analysis.** Introduction to statistical time series analysis: ARIMA and more general models, forecasting, spectral analysis, and time domain regression. Model identification, estimation of parameters, and diagnostic checking are included. Additional Prerequisite: Statistics and Data Sciences 384 (Topic 3) and consent of instructor.

**Topic 9: Computational Statistics.** A course in modern computationally-intensive statistical methods including simulation, optimization methods, Monte Carlo integration, maximum likelihood / EM parameter estimation, Markov chain Monte Carlo methods, resampling methods, non-parametric density estimation.

**Topic 10: Stochastic Processes.** Concepts and techniques of stochastic processes with an emphasis on the nature of change of variables with respect to time. Characterization, structural properties and inference are covered.

Theories, models and methods for the analysis of quantitative data. With consent of the graduate advisor, may be repeated for credit when the topics vary. Prerequisite: Graduate standing, and Statistics and Data Sciences 380 or 382 or consent of instructor.

**Topic 1: Experimental Design.** Principles, construction and analysis of experimental designs. Includes one-way classification, randomized blocks, Latin squares, factorial and nested designs. Fixed and random effects, multiple comparisons, and analysis of covariance. Additional prerequisite: Statistical Methods I or its equivalent.

**Topic 2: Applied Regression.** Simple and multiple linear regression, residual analysis, transformations, model building with real data, testing models. Additional prerequisite: Experimental Design or its equivalent.

**Topic 3: Applied Multivariate Methods.** A practical introduction to the analysis of multivariate data as applied to examples from the social sciences. Multivariate linear model, principal components and factor analysis, discriminant analysis, clustering and canonical correlation. Additional prerequisite: Applied Regression or its equivalent.

**Topic 4: Analysis of Categorical Data.** Methods for analyzing categorical data. Topics include categorical explanatory variables within the General Linear Model; models of association among categorical variables; models in which the response variable is categorical or is a count. Logical similarities across methods will be emphasized.

**Topic 5: Structural Equation Modeling.** Introduction to the basic concepts, methods and computing tools of structural equation modeling. Emphasis will be placed on developing a working familiarity with some of the common statistical procedures, coupled with their application through the use of statistical software. Additional prerequisite: Applied Regression or its equivalent.

**Topic 6: Hierarchical Linear Models.** Introduction to multilevel data structures, model building and testing, effect size, fixed and random effects, missing data and model assumptions, logistic HLM, statistical power, and design planning. Additional prerequisite: Applied Regression or its equivalent.

**Topic 7: Survey Sampling and Methodology.** Survey planning, execution and analysis. Principles of survey research, including sampling, measurement; questionnaire construction and distribution; response effects; validity and reliability; scaling data sources; data reduction and analysis.

**Topic 8: Introduction to Bayesian Methods.** A practical introduction to Bayesian statistical inference, with an emphasis on applications in behavioral and measurement research. Examination of how Bayesian statistical inference differs from classical inference in the context of simple statistical procedures and models, such as hypothesis testing, ANOVA and regression. Additional prerequisite: Applied Regression or its equivalent.

**Topic 9: Longitudinal Data Analysis.** Applications of models to data collected at successive points in time. Multilevel models for change, random coefficient models; latent growth curve models; models for nonlinear growth. Applications of models to event-occurrence data. Discrete-time and continuous-time event history models.

**Topic 10: Modern Statistical Methods.** An introduction to conducting statistical analysis using modern resampling methods of bootstrapping and Monte Carlo simulation. Equal emphasis will be placed on theoretical understanding and application.

**Topic 11: Mathematical Statistics for Applications.** Introduction to the basic concepts of probability and mathematical statistics for doctoral degree students who plan to use statistical methods in their research but do not need a highly mathematical development of the subject. Topics include probability distributions and estimation theory and hypothesis testing techniques. Additional prerequisite: A calculus course covering integration and differentiation.

**Topic 12: Meta-Analysis.** An introduction to statistics used to synthesize statistical results from a set of studies. Course content can include calculation of different effect sizes, calculating pooled estimates using fixed and random effects models, testing moderating variables using fixed and mixed effects models, test of heterogeneity of effect sizes, assessing and correcting publication bias. Additional prerequisite: Applied Regression (Topic 2) or the equivalent.

**Topic 13: Factor Analysis.** An introduction to exploratory and confirmatory factor analysis. Exploratory factor analysis section's content can include review of matrix algebra and vector geometry, principal components and principle axis factoring, factor rotation methods. Confirmatory factor analysis section's content includes single- and multiple-factor, multi-sample models, multitrait-multimethod and latent means modeling. For both methods, experience will be provided in writing up and critiquing others' studies. Additional prerequisite: Applied Regression (Topic 2) or the equivalent.

**Topic 14: Maximum-Likelihood Statistics.** Introduction to the likelihood theory of statistical inference. Topics include probability distributions, estimation theory, and applications of the MLE to models with categorical or limited dependent variables, event count models, event history models, models for time-series cross-section data, and models for hierarchical data.

**Topic 15: Survival Analysis/DurationModeling.** This course will focus on the statistical methods related to the analysis of survival or time to event data. Survival analysis, hazard modeling, has applications in several fields, such as studying time till death (medical or biological), length of unemployment (economics), a felon's time to parole (criminology), duration of first marriage (sociology), and reliability and failure time analysis (engineering). The class will focus on practical applications. Some of the topics covered in the course will include descriptive statistics, such as Kaplan-Meier estimators, semiparametric and parametric regression models, model development and assessing model adequacy.

**Topic 16: Selected Topics.**

An introduction to statistical learning methods, exploring both the computational and statistical aspects of data analysis. Topics include numerical linear algebra, convex optimization techniques, basics of stochastic simulation, nonparametric methods, kernel methods, graphical models, decision tress and data re-sampling. Prerequisites: Graduate standing.

This course focuses on stochastic simulation for Bayesian inference. The main focus is for students to develop a solid understanding of MCMC methods and the underlying theoretical framework. Topics include: (i) Markov chains; (ii) Intro to MC integration; (iii) Gibbs Sampler; (iv) Metropolis-Hastings algorithms; (v) Slice sampling; and (vi) Sequential Monte Carlo. Prerequisites: Graduate standing, knowledge of mathematical statistics as well as basic coding skills (R, Matlab, or Stata).

This course focuses on the practical application of the projection approach to linear models. The course will begin with a review of essential linear algebra concepts including vector spaces, basis, linear transformations, norms, orthogonal projections, and simple matrix algebra. It continues by presenting the theory of linear models from a projection-based perspective. Still on the projection framework, Bayesian ideas will be introduced. Additional topics include: (i) Analysis of Variance; (ii) Generalized Linear Models; and (iii) Variable Selection Techniques. Prerequisites: Graduate standing, knowledge of mathematical statistics at a graduate level and linear algebra at an advanced undergraduate level is required as well as basic coding skills (R, Matlab, or Stata).

Supervised experience in applying statistical or mathematical methods to real problems. Participation in weekly consulting sessions; directed readings in the statistical literature; the ethics of research and consulting; report writing and presentations. May be repeated for credit. Prerequisite: Graduate standing, and consent of instructor.

This course focuses on the general class of state-space models or Dynamic Models. Emphasis will be placed on the implementation and use of the models presented. Applications will focus on the social sciences but an effort will be made to keep students from the physical sciences engaged in the topics. Topics covered include: (i) Dynamic Regression Models; (ii) The Kalman Filter; (iii) Multivariate Time Series Models; (iv) Conditional Variance Models; (v) MCMC algorithms for state-space models; and (vi) Particle Filters. Prerequisite: Graduate standing, and knowledge of mathematical statistics at a graduate level as well as basic coding skills (R, Matlab, or Stata).

Focuses on various mathematical and statistical aspects of data mining. Topics covered include supervised learning (regression, classification, support vector machines) and unsupervised learning (clustering, principal components analysis, dimensionality reduction). The technical tools used in the course draw from linear algebra, multivariate statistics and optimization. Prerequisites: Graduate standing and Mathematics 341 or equivalent.

Introduction to programming using both the C and Fortran (95/2003) languages, with applications to basic scientific problems. Covers common data types and structures, control structures, algorithms, performance measurement, and interoperability. Statistics and Scientific Computation 222 and 292 may not both be counted. Prerequisite: Graduate standing and credit or registration for Mathematics 408C or 408K.

Introduction to the development and solution of economic models of growth, macroeconomic fluctuations, environmental economics, financial economics, general equilibrium models, game theory and industrial economics. The course also includes sections on neural nets, genetic algorithms and agent-based methods and stochastic control theory applied to a variety of economic topics. Prerequisite: Graduate standing.

Same as Computational and Applied Mathematics 383C and Mathematics 383E and Computer Sciences 383C. Survey of numerical methods in linear algebra: floating-point computation, solution of linear equations, least squares problems, algebraic eigenvalue problems. Prerequisite: Graduate standing, either consent of instructor or Mathematics 341 or 340L, and either Mathematics 368K or Computer Sciences 367.

Survey of numerical methods for interpolation, functional approximation, integration, and solution of differential equations. Prerequisite: Graduate standing, either consent of instructor or Mathematics 427K and 365C; and Computational and Applied Mathematics 383C, Computer Sciences 383C, or Mathematics 383E or Statistics and Data Sciences 393C.

Comprehensive introduction to computing techniques and methods applicable to many scientific disciplines and technical applications. Covers computer hardware and operating systems, systems software and tools, code development, numerical methods and math libraries, and basic visualization and data analysis tools.Prerequisite: Graduate standing, and Mathematics 408D or 408M. Prior programming experience is recommended.

Parallel computing principles, architectures, and technologies. Parallel application development, performance, and scalability. Prepares students to formulate and develop parallel algorithms to implement effective applications for parallel computing systems. Three lecture hours a week for one semester. Prerequisite: Graduate standing, and Mathematics 408D or 408M, Mathematics 340L, and prior programming experience using C or Fortran on Unix/Linux systems.

Distributed and grid computing principles and technologies. Covers common modes of grid computing for scientific applications, developing grid enabled applications, future trends in grid computing. Three lecture hours a week for one semester. Prerequisite: Graduate standing, and Mathematics 408D or 408M, Mathematics 340L, and prior programming experience using C or Fortran on Unix/Linux systems.

Scientific visualization principles, practices, and technologies, including remote and collaborative visualization. Introduces statistical analysis, data mining and feature detection. Prerequisite: Graduate standing, Mathematics 408D or 408M, Mathematics 340L, and prior programming experience using C or Fortran on Linux or Unix systems.

Three lecture hours a week for one semester. Topics are announced in the Course Schedule. May be repeated for credit when the topics vary. Prerequisite: Graduate standing; additional prerequisites vary with the topic and are given in the Course Schedule.

Supervised teaching experience; weekly group meetings, individual consultations, and reports. Offered on the credit/no credit basis only. Prerequisite: Graduate standing and appointment as a teaching assistant.