Courses numbered between 36-701 and 36-740 are at the Master's level, those between 36-751 and 36-799 represent Ph.D.-level core courses, and those between 36-800 and 36-899 are Ph.D.-level elective courses.

36-701 Perspectives on Statistics 6 units

Students are introduced to the faculty and their interests, the field of statistics, and the facilities at Carnegie Mellon. Each faculty member gives at least one elementary lecture on some topic of his or her choice. In the past, topics have included: the field of statistics and its history, large-scale sample surveys, survival analysis, subjective probability, time series, robustness, multivariate analysis, psychiatric statistics, experimental design, consulting, decision-making, probability models, statistics and the law, and comparative inference. Students are also given information about the libraries at Carnegie Mellon and current bibliographic tools. In addition, students are instructed in the use of the Departmental and University computational facilities and available statistical program packages.

36-703 Intermediate Probability 12 units

The basic definitions of probability and topics such as conditional probability, conditional expectation, and multivariate change of variables are reviewed. Different modes of convergence of random variables are defined and are used to present the laws of large numbers and the central limit theorem. Discrete-time Markov chains and the Poisson process are introduced and discussed in detail. Additional topics covered include birth and death processes, continuous-time Markov chains, and elementary renewal processes. Material is presented at the level of Ross, Introduction to Probability Models, 4th ed.

36-705 Intermediate Statistics 12 units

Some elementary concepts of statistics are reviewed, and the concepts of sufficiency, likelihood, and information are introduced. Several methods of estimation, such as maximum likelihood estimation and Bayes estimation, are studied, and some approaches to comparing different estimation procedures are discussed. The theories of subjective probability and utility are presented and are then used to formulate statistical decision problems. Methods for finding and characterizing optimal decisions are considered. Material is presented at the level of Bickel and Doksum, Mathematical Statistics and DeGroot, Optimal Statistical Decisions.

36-707 Regression Analysis 12 units

This is a course in data analysis using mutiple linear regression. Topics covered include simple linear regression, ordinary least squares and weighted least squares, the geometry of least squares, quadratic forms, F tests and ANOVA tables, residuals, outlier detection, and identification of influential observations, polynomial and dummy variable techniques, and variable selection methods. Essential background in linear algebra is reviewed where necessary. When time permits other topics such as nonlinear regression and robust estimation will be discussed.

36-708 Linear Models and Experimental Design 12 units

This is a course in experimental design and the analysis of experimental data using linear models. The first part of the course covers theoretical background: the multivariate normal distribution, distribution of quadratic forms, principles of analysis of variance, and the Bayesian approach to linear models. The second part concerns basic experimental designs: latin squares, factorial designs, fractional factorials, and nested designs. In the final component of the course, random effects and mixed models, repeated measures, and longitudinal analysis are discussed.

36-711 Statistical Computing 6 units

This course introduces students to a range of computational techniques that are important to statistics. The topics covered include numerical linear algebra, simulation, numerical optimization, graphical techniques, and the use of statistical packages and programming libraries.

36-715 Applied Stochastic Processes 6 units

This course is a continuation of Intermediate Probability, 36-703. Topics are drawn from renewal theory, queueing, networks, branching processes, reliability theory, and martingales.

36-720 Discrete Multivariate Analysis 6 units

Theory of maximum likelihood in exponential families developed in Intermediate Statistics, 36-705, is applied to the analysis of binary and categorical data. Logistic regression and loglinear models are introduced, and students gain experience in using statistical program packages and interpreting results.

36-722 Continuous Multivariate Analysis 6 units

This course covers the multivariate normal distributions and its marginal, conditional and sampling distributions. Other topics include Hotelling's T-squared, MANOVA, discriminant analysis, and principal components. The data analytic portions of the class use standard statistical packages.

36-724 Applied Bayesian Methods 6 units

This course is an introduction to practical Bayesian methodology. The use of conjugate families, introduced in Intermediate Statistics, 36-705, is discussed. Building on techniques in Statistical Computing, 36-711, methods for calculating posterior distributions are presented, as is the concept of hierarchical model. The emphasis throughout is on the application of Bayesian thinking to problems in data analysis.

36-726 Statistical Practice 6 units

Students are taught how to structure a consulting session, elicit and diagnose a problem, manage a project, and report an analysis. The class will participate in meetings with industrial and academic clients.

36-728 Time Series Analysis I 6 units

Basic concepts in the representation of time series in the time domain are presented, such as stationarity, invertibility, the memory function, autoregressive moving average models, and the forecasting function. The mathematics of difference equations is reviewed. Methods for building AR, MA and ARMA models are discussed. The course also introduces state space models and the Kalman filter. Real-world data are used as illustrative examples.

36-730 Time Series Analysis II 6 units

This course continues the study of time series in the time domain covering topics such as nonstationarity, seasonal models, and exact likelihood estimation. The course also begins the study of time series in the frequency domain and introduces spectral analysis. Other topics covered may include regression models with time series error, seasonal adjustment (signal extraction), intervention analysis, outlier detection, and stochastic control.

36-732 Topics in Biostatistics 6 units

This course considers statistical methods for the analysis of data arising from biomedical research. Topics will be drawn from the areas of bioassay, clinical trials, case-control studies, survival analysis, and the analysis of longitudinal data.

36-734 Survey Sampling 6 units

This course is an introduction to the basic concepts of survey sampling: simple random sampling, stratification, systematic sampling, clustering and subsampling.

36-753 Probability Theory and Stochastic Processes I 12 units per semester
36-754 Probability Theory and Stochastic Processes II

The first semester of this course presents the essential elements of measure and integration theory, an axiomatic development of probability theory, random variables, distribution functions, characteristics functions, and modes of convergence. During the second semester, laws of large numbers, the central limit problem, large deviations, conditional expectation, and martingale theory will be covered. Special topics such as Brownian motion, Markov processes and stationary processes will be covered as time permits. Typical texts for this course are Chung, A Course in Probability Theory, 2nd ed., and Royden, Real Analysis.

36-755 Advanced Statistical Theory I 12 units per semester
36-756 Advanced Statistical Theory II

This course involves intensive study of the fundamental topics in statistical theory: sufficient statistics, estimation, hypothesis testing, exchangeability, invariance, posterior distributions, decision theory, large sample theory, and optimality criteria.

36-757 Advanced Data Analysis 12 units per semester
36-758 Advanced Data Analysis

Analysis of selected data sets, exemplifying a variety of methodologies, is a focus of this course. It builds on the M.S. level methodological courses, which focus on techniques, and instead focuses on the process of analysis. New methodologies are introduced as needed.

36-760 Linear Statistical Models 6 units

This course covers the theory of linear models. Topics include distribution theory of the normal linear model, random and fixed effects models, Bayesian and hierarchical models, generalized linear models, and the coordinate-free approach to linear models.

36-761 Advanced Statistical Computing 12 units

Topics are drawn from: computer representation of numbers, fixed and floating point arithmetic, errors in computer calculations and numerical stability, data types and data structures, general methods for approximating percentage points of probability distributions and some specific examples, methods of computational linear algebra with a particular emphasis on methods that are useful in regression analysis, stepwise regression techniques, methods of constrained and unconstrained optimization, and robust estimation calculations.

36-806 Comparative Statistical Inference 12 units

There are several distinct approaches to statistics associated with Neyman and Pearson, Fisher, Jeffreys, and Savage. The goal of this course is to compare critically the alternative schools of thought so that students gain an appreciation of the arguments put forward and the consequences of adopting each point of view.

36-811 Nonparametric Statistical Inference 12 units

This course surveys classical and modern nonparametrics. The classical portion describes distribution-free procedures such as the Kolmogorov-Smirnov test and Kendall's tau and introduces permutation tests, U statistics and asymptotic relative efficiency. Modern topics include the bootstrap, influence functions, robust statistics, ACE, CART and partially ranked data.

36-812 Sequential Analysis 12 units

This course concerns the analysis of statistical data that are obtained in sequential stages. Topics covered include sequential sampling plans, optimal stopping, sequential estimation and testing, and various problems in the sequential design of experiments such as control theory, inventory theory and clinical trials.

36-813 Asymptotic Theory 12 units

This course provides an overview of various asymptotic techniques. Possible topics include Fisher's principles: consistency, sufficiency, efficiency, information loss, information recovery; Laplace's method; the saddlepoint approximation; asymptotics for robust estimation; asymptotics of resampling schemes.

36-815 Stochastic Processes 12 units

This course is a one semester advanced seminar which presumes knowledge of measure theoretic probability, 36-753, 754. The topics will vary and may be drawn from Brownian motion, stochastic integration, stochastic differential equations, martingales and point processes.

36-820 Advanced Discrete Multivariate Analysis 12 units

This course provides an in-depth look at various topics in categorical data. Possible topics include: large-sample theory, large sparse contingency tables, ordered categories models, model selection in large tables, and exact tests.

36-822 Advanced Multivariate Analysis 12 units

This course presents advanced theory associated with the multivariate normal distribution. Bayesian methods, Wishart and multivariate t distributions, general linear models and hierarchical models, principal components, discriminant analysis, factor analysis, and latent structure models are discussed.

36-824 Topics in Bayesian Statistics 12 units

This course may cover any of several general or specific topics in the theory and/or application of Bayesian methods. Examples include Bayesian analysis of categorical data, Bayesian time series models, general hierarchical models, Bayesian analysis of finite population sample surveys, and Bayesian nonparametric methods.

36-828 Multivariate Time Series 12 units

This course considers several time series jointly. The transfer function and vector autoregressive moving average model are used to model the dynamic relation between processes. Principal component and canonical correlation analyses are employed to reduce the dimensionality and to simplify the underlying structure of processes. Linear dynamic theory and canonical forms are discussed.

36-829 Nonlinear Time Series Analysis 12 units

This course covers the concept of nonlinear dynamic systems, various nonlinear time series models, probabilistic and statistical aspects of nonlinear time series, data analysis in nonlinear time series, and various applications of nonlinear time series. The mathematics of differential equations and diffusion processes will be briefly reviewed. Issues of interest such as marginal distributions, short-term and long-term structures, time reversibility, directionality, nonparametric techniques, numerical methods, and the concept of nonlinearity of a process will be discussed.

36-832 Advanced Biostatistics 12 units

This course considers a number of statistical problems that occur in many fields of application, but arise frequently in biomedical research. The course emphasizes both data-analytical methods and the principles on which they are based. Some topics typically covered are dose-response curves, bioassay, clinical trials, and survival analysis.

36-903, 904 Selected Topics in Probability 12 units

36-905, 906 Selected Topics in Statistics 12 units

36-911 Seminar in Foundations of Statistics 12 units
This seminar offers an opportunity to read and discuss "classic" texts and to investigate their impact on current statistical practice. Topics vary from year to year. Three recent selections were these: A. Wald's contributions to statistical decision theory, with an emphasis on his use of minimax and sequential decision rules, for which the primary text was Statistical Decision Functions; L.J. Savage's theory of personal probability for which the primary text was The Foundations of Statistics; R.A. Fisher's account of varieties of statistical inference, with an emphasis on fiducial probability, for which the primary text was Statistical Methods and Scientific Inference.

36-912 Seminar in Psychiatric Statistics and Biostatistics 12 units

36-913 Workshop in Industrial Statistics 12 units

36-914 Workshop in Computational Statistics 12 units

36-915 Workshop in Bayesian Inference 12 units

36-995 Reading and Research units to be assigned

36-997 Comprehensive Examination for the Degree of Master of Science

36-998 Qualifying Examination for the Degree of Doctor of Philosophy

36-999 Final Public Oral Examination for the Degree of Doctor of Philosophy