Department of Statistics
332 YOST HALL
Phone 368-6941; Fax 368-0252
Joe Sedransk
Statistics links mathematics to other disciplines to understand uncertainty and probability in the abstract and in the context of actual applications to science, medicine, actuarial science, social science, management science, business, engineering, and to contemporary life. As technology brings advances, the statistical theory and methodology required to do them justice becomes more challenging: higher dimensional, dynamic, or computer-intensive. The field of statistics is rapidly expanding to meet the three facets of these challenges: the underlying mathematical theory, the data analysis methodology, and the interdisciplinary collaborations and new fields of application.
Joseph Sedransk, Ph.D. (Harvard University)
Professor and Chair
Bayesian inference, Sample survey theory, methodology and applications, Theory of sampling from finite populations, Inference for partially missing data
Paula FitzGibbon, M.S. (Miami University)
Instructor
Jiming Jiang, Ph.D. (University of California at Berkeley)
Assistant Professor
Asymptotic theory for restricted maximum likelihood estimation, Generalized linear models
Nell Sedransk, Ph.D. (Iowa State University)
Professor
Topologic foundations for statistical inference, Bayesian design and inference, Spatial statistics, Inference for complex systems
Jiayang Sun, Ph.D. (Stanford University)
Associate professor
Methodologies of statistical computing and modern data analysis
Wojbor Woyczynski, Ph.D. (Wroclaw University, Poland)
Professor
Stochastic models, Probability, Random fields, Boundary problems, Time series, Dynamics of chaotic processes, Diffusion, Turbulence, Shock theory
Raymond Neff, Sc.D. (Harvard University)
Adjunct Professor; Vice President for Information Services
Mary H. Regier, Ph.D. (University of California at Berkeley)
Adjunct Professor
Students in statistics begin with a foundation in mathematics, then add statistical theory plus intensive modern data analysis and a concentration in a field of each student's choice where statistics is used. The goal is to develop an appreciation of each facet of the discipline and a mastery of technical skills. This prepares students to enter a growing profession with opportunities in the academic, governmental, actuarial, and industrial spheres.
For the undergraduate student looking toward graduate school, the course of study within these guidelines easily incorporates additional mathematics in preparation for the more abstract mathematical level of graduate courses.
The more specialized option in actuarial science expands the basic program in statistics to incorporate topics from operations research and numerical analysis which are fundamental to actuarial theory and computation. This actuarial option includes the coursework necessary to prepare for the first 100 credits of professional actuarial examinations (administered by the Society of Actuaries).
All undergraduate majors begin with a foundation in mathematics and a core of courses in mathematical statistics, courses in statistical methodology and courses in modern data analysis. Each student's program is individualized by the choice of an applied field of concentration according to the student's own talents and interests and by the choice of appropriate STAT electives which may be drawn from offerings by the Statistics Department and from suitable offerings by other departments at CWRU. The Senior Project option also allows students either to work in a research setting or to participate in interdisciplinary collaboration or in industrial consulting along with a statistics faculty member.
The B.A. degree offers flexibility and the chance to pursue a wider range of interests. It also offers the possibility of expanding the interdisciplinary aspect of the program to complete the requirements for majors in two fields. Some examples of particularly attractive double majors combine statistics with computer science, biology (molecular, organismal or ecology), psychology, economics, accounting, management science.
The B.S. degree adds a laboratory science requirement. For students seriously interested in basic science, a natural science is the logical choice as a focus for the application, and the B.S. degree is the logical choice of program.
The B.S. degree in statistics requires a minimum of 124 hours, including at least 68 hours of approved coursework, including 27 hours in statistics, the remainder in related disciplines and a substantive field of application, to satisfy the following requirements:
(1) MATH 121, 122, 223, 224, and 201 or equivalent;
(2) CMPS 131 or ECMP 251 or approved alternate; plus additional higher numbered course in computation from CMPS or ECMP offerings or EPBI 414 or EPBI 420;
(3) STAT 325 and 326, STAT 345 and 346;
(4) At least 15 hours of courses in statistical methodology to be chosen from statistics courses numbered 300 and higher offered by the Statistics Department, or approved courses in statistical methodology or probability taught in biostatistics, computer science, economics, mathematics, operations research, systems engineering, etc. At least 6 hours must be in STAT courses; 243 and STAT 244 may be counted;
(5) Two approved courses (or more) numbered 300 or above in an approved discipline outside statistics;
(6) A combined total of 12 hours (or more) in ASTR, BIOL, CHEM, GEOL, PHYS which may be counted toward a major in that field including at least one of PHYS 121 and 122, CHEM 105 and 106 plus 113, CHEM 107 and 108 plus 113, BIOL 110 and 210 plus 211, BIOL 110 and 220 plus 221.
Students are strongly encouraged to include advanced expository or technical writing courses in their programs.
The B.A. degree in statistics requires a minimum of 120 hours, including at least 56 hours of approved coursework, including 27 hours in statistics, the remainder in related disciplines and a substantive field of application, to satisfy the following requirements:
(1) MATH 121, 122, 223, 224, and 201 or equivalent;
(2) CMPS 131 or ECMP 251 or approved alternate; plus additional higher numbered course in computation from CMPS or ECMP offerings or EPBI 414 or EPBI 420;
(3) STAT 325 and 326, STAT 345 and 346;
(4) At least 15 hours of courses in statistical methodology to be chosen from statistics courses numbered 300 and higher offered by the Statistics Department, or approved courses in statistical methodology or probability taught in biostatistics, computer science, economics, mathematics, operations research, systems engineering, etc. At least 6 hours must be in STAT courses; 243 and STAT 244 may be counted;
(5) Two approved courses (or more) numbered 300 or above in an approved discipline outside statistics.
Students are strongly encouraged to include advanced expository or technical writing courses in their programs.
Students may pursue a B.A. with double major in statistics and a related field from within the College of Arts and Sciences. In this case, the substantive field requirement (No. 5 above) is waived.
The actuarial program leading to a either a B.A. or a B.S. in statistics requires 30 hours in statistics and actuarial studies and must satisfy the requirements for the appropriate degree program with the following modifications of requirements (4) and (5):
(4) At least 12 hours of courses in statistical methodology to be chosen from statistics courses numbered 300 and higher offered by the Statistics Department, or approved courses in statistical methodology or probability taught in biostatistics, computer science, economics, mathematics, operations research, systems engineering, etc. At least 6 hours must be in STAT courses; STAT 243 and STAT 244 may be counted;
(5) MATH 431, OPRE 401, STAT 317.
Students ordinarily can expect to be prepared to take Actuarial Exams for at least 100 credits in the Society of Actuaries prior to graduation.
A minor in statistics requires a minimum of 15 hours of approved coursework in statistics. The minor must satisfy the requirements below and must include a minimum of 9 credits in courses from the Statistics Department offerings.
(1) STAT 243 and 244 or STAT 345 and 346 or other approved sequence
(2) STAT 208 or STAT 312 or STAT 313 or STAT 332 or STAT 333 or STAT 325
(3) Two approved elective courses in statistics numbered 300 or above.
The combined bachelor-master degrees in statistics require a minimum of 21 hours beyond the bachelor's degree requirements. In total, 42 hours must be in statistics, including an M.S. thesis or M.S. research project, with the remainder (either 41 or 26 hours for B.S. or B.A., respectively) in approved coursework in related disciplines and a field of application. In addition to the B.S. or B.A. requirements, a combined degree program must include:
(1) STAT 455 and three semesters of STAT 491;
(2) M.S. research project (STAT 621) or M.S. Thesis (STAT 651);
(3) At least 6 additional hours of courses in statistical theory and methodology (making a total of 21 hours including at least 4 STAT courses numbered 400 or higher) to be chosen from from Statistics Department offerings numbered 300 and higher, or approved courses in statistical methodology or probability taught in biostatistics, computer science, economics, mathematics, operations research, systems engineering, etc.
Students are strongly encouraged to include advanced expository or technical writing courses in their programs.
The department offers programs leading to the Master of Science and to the Doctor of Philosophy degrees. Graduate assistantships both with teaching responsibilities and with research duties are available to qualified applicants.
The dual core of the M.S. program is mathematical statistics and modern data analysis. Expanding from this core, students develop technical facility in a variety of statistical methodologies. This breadth of competence is designed to equip graduates to go beyond the appropriate choice of method for implementation and to be able to adapt these techniques and to construct new methods to meet the specific objectives and constraints of new situations.
The M.S. degree in statistics requires a minimum of 30 hours of approved coursework in statistics and related disciplines and an M.S. research project or a thesis. Each student's program is developed in consultation with the Director of Graduate Studies or a senior faculty mentor and must satisfy the following requirements:
(1) STAT 425 and 426;
(2) STAT 445 and 446;
(3) STAT 455;
(4) STAT 495 (3 credits); with M.S. project option (STAT 621) in (5) below, STAT 491 (3 credits) may be substituted for STAT 495;
(5) M. S. research project (STAT 621) or M.S. Thesis (STAT 651);
(6) A minimum of 12 hours of approved graduate level statistics electives including at least 2 STAT courses numbered 400 or higher plus other elective courses in statistical methodology or probability taught in biometry, computer science, economics, mathematics, operations research, systems engineering, etc.
The goals of this program are to give each student a balanced view of statistical theory and the application of statistics in practice or in substantive research and at the same time to have the student develop a broad competence in statistical methodology. The required core coursework reflects this balance. The first two requirements are for full-year sequences in data analysis and theory; and the third develops the theory underlying linear modeling. The requirement for applications of statistics can be satisfied either through intensive participation in the Consulting Forum or through an M.S. research project. Graduate students are also required to participate in a forum or seminar to gain experience in written and oral presentation. The remainder of each student's program is individualized to address the more specialized statistical demands of the selected field of concentration or the focus of multidisciplinary work.
Each student may choose either the applied research project or the thesis option depending on individual interests. In either case the student can expect to work with a faculty mentor in undertaking a significant task which will culminate in polished written and oral presentations; in many cases the work will be suitable for presentation at professional society meetings or publishable in a substantive literature. A student coming to school from a position as professional statistician might choose a statistical problem arising in the workplace as the basis for an M.S. research project. A student intending to continue graduate work toward a Ph.D. might choose an M.S. research project to explore the intimate relationship of statistics to substantive fields. Alternatively, either student might choose the thesis option to tailor methodology to a new setting or to make a first essay at mathematical statistical research.
The focus of the doctoral program is on research and the plan of study emphasizes the theory of statistics so that graduates from this program will be able both to extend the theoretical basis for statistics and to bring statistical thought to scientific research in other fields. The objective of preparing students to collaborate in interdisciplinary work demands the breadth as well, so advanced knowledge of a substantive field and participation in the collaborative experience are also integral to the program.
Students planning to enter the doctoral program in statistics should obtain information from the departmental office. Plans of study are prepared individually by the graduate student and a faculty advisor to develop the talents and interests of each student.
Note: Credit given for only one (1) of APPL STAT courses, including:
STAT 312, STAT 313, STAT 332, STAT 333, STAT 412, STAT 433, STAT 385, STAT 485.
STAT 201, Basic Statistics for Social and Life Sciences I, 3
Designed for undergraduates in the social sciences and life sciences who need to use statistical techniques in their fields. Descriptive statistics, probability models, sampling distributions. Point and confidence interval estimation, hypothesis testing. Elementary regression with accompanying efficient computing procedures and statistical software. Use of SPSS. Not for credit toward major or minor in Statistics.
STAT 207, Statistics for Business and Management Science I, 3
Organizing and summarizing data. Mean, variance, moments. Elementary probability, conditional probability. Commonly encountered distributions including binomial, Poisson, uniform, exponential, normal distributions. Central limit theorem. Sample quantities, empirical distributions. Reference distributions (chi-square, z-, t-, F-distributions). Point and interval estimation; hypothesis tests. Use of SPSS. Note: For credit after any APPL STAT course.
STAT 208, Statistics for Business and Management Science II, 3
Analysis of variance. Simple linear regression and correlation; multiple linear regression. Analysis of contingency table date, goodness-of- fit tests. Nonparametric methods including sign, Wilcoxon, Kruskal-Wallis and runs tests. Introduction to time series analysis and forecasting. Decision theory with application to quality control. Use of SPSS in applications.
Prerequisite: STAT 207 or STAT 285
STAT 243, Statistical Theory with Application I, 3
Introduction to fundamental concepts of statistics through examples including design of an observational study, industrial simulation. Randomness, distribution functions, conditional probabilities exemplified in real applications. Derivation of common discrete distributions. Expectation operator. Statistics as random variables, point and interval estimation. Maximum likelihood estimators. Properties of estimators.
Prerequisite: MATH 122 or MATH 126
STAT 244, Statistical Theory with Application II, 3
Extension of inferences to continuous-valued random variables. Common continuous-valued distributions. Expectation operator. Maximum likelihood estimators for the continuous case. Simple linear, multiple and polynomial regression. Properties of regression estimators when errors are Gaussian. Regression diagnostics. Class or student projects gathering real data or generating simulated data, fitting models and analyzing residuals from fit.
Prerequisite: STAT 243 and MATH 122 or MATH 126
STAT 301, Basic Statistics for Social and Life Sciences II, 3
(Continuation of STAT 201) Basic theory of design of experiments, analysis of variance and multiple linear regression. Analysis of discrete data in contingency tables, sensitivity and specificity, odds ratios. Tests of goodness of fit. Taught in case-based format with individual and/or collaborative student projects. Not for credit toward undergraduate major or minor in Statistics nor for credit toward any graduate degree in Statistics.
Prerequisite: STAT 201
STAT 312, Basic Statistics for Engineering and Physical Sciences , 3
For advanced undergraduate students in engineering, physical sciences, life sciences. Comprehensive introduction to probability models and statistical methods of analyzing data with the object of formulating statistical models and choosing appropriate methods for inference from experimental and observational data and for testing the model's validity. Balanced approach with equal emphasis on probability, fundamental concepts of statistics, point and interval estimation, hypothesis testing, regression modeling. Note: Credit given for only one (1) of APPL STAT courses.
Prerequisite: MATH 122
STAT 313, Statistics for Experimenters, 3
For advanced undergraduates in engineering, physical sciences, life sciences. Comprehensive introduction to probability models and statistical methods of analyzing data. General objective is to train students in formulating statistical models, in choosing appropriate methods for inference from experimental and observational data and to test the validity of these models.
Focus on practicalities of inference from experimental data. Inference for curve and surface fitting to real data sets. Designs for experiments and simulations. Student generation of experimental data and application of statistical methods for analysis. Critique of model; use of regression diagnostics to analyze errors. Note: Credit given for only one (1) of APPL STAT courses.
Prerequisite: MATH 122 or equivalent.
STAT 317, Theory of Interest and Life Contingencies, 3
Mathematical formulation for calculation of compound interest, present and accumulated values of single investments and of portfolios. Life table analysis for simple and multiple decrement functions. Life and special annuities; life insurance and reserves for life insurance. Statistical issues for prediction from actuarial models. Problem solving using actual insurance record data. Topics covered include areas examined in the American Society of Actuaries examination over ASA courses 150 and 160.
Prerequisite: MATH 223 and STAT 346 or STAT 446 or STAT 382
STAT 325, Data Analysis I, 3
Basic exploratory data analysis for univariate response with single or multiple covariates. Graphical methods and data summarization, model-fitting using S-plus computing language. Linear, polynomial, and multiple linear regression. Emphasis on data projection onto low-dimensional subspaces, on model selection criteria and on diagnostics to assess goodness of fit. Techniques include transformation, smoothing, median polish, robust/resistant methods. Case studies, and analysis of individual data sets. Knowledge of regression required.
Prerequisite: MATH 201 and EPBI 214 or EPBI 220 or equivalent
STAT 326, Data Analysis II, 3
Extensions of exploratory data analysis and modeling to multivariate response observations and to non-Gaussian data. Singular value decomposition and projection, principal components, factor analysis and latent structure analysis, clustering techniques, cross-validation, E-M algorithm, recursive partitioning algorithms. Introduction to generalized linear modeling. Case studies of complex data sets with multiple objectives for analysis.
Prerequisite: STAT 325
STAT 332, Statistics for Signal Processing, 3
For advanced undergraduate students in engineering, physical sciences, life sciences. Introduction to probability models and statistical methods. Emphasis on probability as relative frequencies. Derivation of conditional probabilities and memoryless channels. Joint distributions of random variables, transformations, autocorrelation, series of irregular observations, stationarity. Random harmonic signals with noise, random phase and/or random amplitude. Modulation and averaging properties. Transmission through linear filters. Power spectra, ARMA processes and forecasting. Note: Credit given for only one (1) of APPL STAT courses.
Prerequisite: MATH 122
STAT 333, Uncertainty in Engineering and Science, 3
Phenomena of uncertainty appear in engineering and science for various reasons and can be modeled in different ways. The course integrates the mainstream ideas in statistical data analysis with models of uncertain phenomena stemming from three distinct viewpoints: algorithm / computational complexity; classical probability theory; and chaotic behaviour of nonlinear systems. Descriptive statistics, estimation procedures and hypothesis testing (uncluding design of experiments). Mathematica notebooks and simulations will be used. Note: Credit given for only one (1) of APPL STAT courses.
Prerequisite: MATH 122
STAT 345, Theoretical Statistics I, 3
Topics provide the background for statistical inference. Random variables; distribution and density functions; transformations, expectation. Common univariate distributions. Multiple random variables; joint, marginal and conditional distributions; hierarchical models, covariance. Distributions of sample quantities, distributions of sums of random variables, distributions of order statistics. Methods of statistical inference.
Prerequisite: MATH 122 or MATH 223
STAT 346, Theoretical Statistics II, 3
Point estimation: maximum likelihood, moment, Bayes' and invariant estimators. Methods of evaluating estimators including mean squared error, consistency, "best" unbiased and sufficiency. Hypothesis testing; likelihood ratio, invariant, Bayes' and union-intersection tests. Properties of tests including power function, bias, invariance and locally most powerful tests. Interval estimation by inversion of test statistics, use of pivotal quantities. Bayes' and invariant intervals. Multivariate distributions and joint estimation of parameters.
Prerequisite: STAT 345 or STAT 381
STAT 391, Statistics Student Seminar, 1
Seminar run collaboratively by students to investigate an area of current research, the topic chosen each semester. All students participate in presentation of material each semester. Recommended for all students majoring in statistics in their senior year. Emphasis on written and oral presentation of statistical summaries, reports and projects.
Prerequisite: Statistics major or minor, and nine credits of approved Statistics courses, 240 or above.
STAT 395, Senior Project in Statistics, 3
An individual project done under faculty supervision involving the investigation and statistical analysis of a real problem encountered in university research or an industrial setting. Written report.
Prerequisite: Permission of instructor required.
STAT 412, Statistics for Design and Analysis in Engineering and Science, 3
For graduate students in engineering, physical sciences, life sciences embarking on research. Comprehensive introduction to probability models focused on statistical methods of planning experiments and analyzing data. Discrete and continuous random variables; joint, marginal and conditional distributions of several random variables. Descriptive statistics and their distributions. Point and interval estimation. Design and inference for curve and surface fitting. Extensive use of standard statistical software. Note: Credit given for only one (1) of APPL STAT courses.
Prerequisite: MATH 122
STAT 413, Reliability and Calibration, 3
Failure distributions related to life testing; extreme value distributions and their hazard functions. Static reliability of series, parallel and mixed systems. Coherent systems and system reliability approximations. Dynamic reliability models. Linear estimation, maximum likelihood, EM estimation, estimation from censored data. Calibration procedures. Distributions from uncalibrated processes, optimization of calibration procedures. Examples from industrial research and production processes.
Prerequisite: STAT 244 or any APPL STAT Course.
STAT 414, Industrial Statistics, 3
Introduces researchers and engineers to statistical methods used to solve problems related to the collection and analysis of data. Case studies illustrate which techniques are applicable and how they are used. Derivations of sampling distributions. Includes one, two, and K-sample test and estimation procedures and methods of multiple comparisons.
Prerequisite: STAT 244 or any APPL STAT Course.
STAT 417, Theory of Interest and Life Contingencies, 3
For graduate students interested in actuarial science. Mathematical formulation for calculation of compound interest, present and accumulated values of single investments and of portfolios. Life table analysis for simple and multiple decrement functions. Life and special annuities; life insurance and reserves for life insurance. Statistical issues for prediction from actuarial models. Problem solving using actual insurance record data. Topics covered include areas examined in the American Society of Actuaries examination over ASA courses 150 and 160. Additional work is expected from graduate students.
Prerequisite: MATH 223 and STAT 346 or STAT 446 or STAT 382 or STAT 482
STAT 425, Data Analysis I, 3
Basic exploratory data analysis for univariate response with single or multiple covariates. Graphical methods and data summarization model-fitting using S-plus computing language. Linear, polynomial, and multiple linear regression. Emphasis on data projection onto low-dimensional subspaces, on model selection criteria and on diagnostics to assess goodness of fit. Techniques include transformation, smoothing, median polish, robust/resistant methods. Case studies, and analysis of individual data sets. Knowledge of regression required.
Prerequisite: MATH 201 and EPBI 414 or EPBI 420 or equivalent
STAT 426, Data Analysis II, 3
Extensions of exploratory data analysis and modeling to multivariate response observations and to non-Gaussian data. Singular value decomposition and projection, principal components, factor analysis and latent structure analysis, clustering techniques, cross-validation, E-M algorithm, recursive partitioning algorithms. Introduction to generalized linear modeling. Case studies of complex data sets with multiple objectives for analysis.
Prerequisite: STAT 425
STAT 427, Statistical Computing, 3
Numerical methods for statistical problems: numerical optimization, design and execution of simulation studies using Monte Carlo methods; Markov chain Monte Carlo methods (including Gibbs sampling). Comparative evaluation of statistical algorithms, computation and/or approximation of distribution functions. Introduction to statistical graphics. Predominant use of statistical language S.
Prerequisite: STAT 345 or STAT 445, and STAT 325 or STAT 425
STAT 433, Uncertainty in Engineering and Science, 3
notebooks and simulations will be used. Note: Credit given for only one (1) of APPL STAT courses.
Prerequisite: MATH 223 or MATH 122
STAT 437, Stochastic Modeling of Scientific Data, 3
Introduction to stochastic modeling of data. Emphasis on models and statistical analysis of data with a significant temporal and/or spatial structure. Markovian and semi-Markovian models, point processes, point cluster models, queuing models, likelihood methods, estimating equations. Note: Restricted to declared graduate and undergraduate majors and minors in Statistics and Biostatistics only.
Prerequisite: STAT 343 or STAT 443 (preferred); alternatively one of any APPL STAT course.
STAT 445, Theoretical Statistics I, 3
Topics provide the background for statistical inference. Random variables; distribution and density functions; transformations, expectation. Common univariate distributions. Multiple random variables; joint, marginal and conditional distributions; hierarchical models, covariance. Distributions of sample quantities: distributions of sums of random variables, distributions of order statistics. Methods of statistical inference. Graduate students are responsible for mathematical derivations, and full proofs of principal theorems. Introductory Statistics course above 240 required.
Prerequisite: MATH 223
STAT 446, Theoretical Statistics II, 3
Point estimation: maximum likelihood, moment, Bayes' and invariant estimators. Methods of evaluating estimators including mean squared error, consistency, "best" unbiased and sufficiency. Hypothesis testing; likelihood ratio, invariant, Bayes' and union-intersection tests. Properties of tests including power function, bias, invariance and locally most powerful tests. Interval estimation by inversion of test statistics, use of pivotal quantities. Bayes' and invariant intervals. Multivariate distributions and joint estimation of parameters. Graduate students are responsible for mathematical derivations and full proofs of principal theorems.
Prerequisite: STAT 445 or STAT 481
STAT 448, Bayesian Theory with Applications, 3
Principles of Bayesian theory, methodology and applications. Methods for forming prior distributions using conjugate families, reference priors and empirically-based priors. Derivation of posterior and predictive distributions and their moments. Properties when common distributions such as binomial, normal or other exponential family distributions are used. Hierarchical models. Computational techniques including Markov chain Monte Carlo and importance sampling. Extensive use of applications to illustrate concepts and methodology.
Prerequisite: STAT 445 or STAT 481
STAT 453, Time Series, Wavelets I, 3
Stationary discrete-time and continuous-time models. Search for hidden periodicities in data. Fast Fourier transform; smoothing and filtering; spectra and periodograms. Multiple series; cross spectra and cross periodograms. Prediction problems. Time-frequency localization and the uncertainty principle, windowed Fourier transforms. Introduction to wavelet and multiresolution analysis.
Prerequisite: STAT 333 or STAT 346 or STAT 412 or STAT 433 or STAT 446
STAT 455, Linear Models, 3
Theory of least squares estimation, interval estimation and tests for models with normally distributed errors. Regression on dummy variables, analysis of variance and covariance. Variance components models. Model diagnostics. Robust regression. Large sample theory for mixed models.
Prerequisite: MATH 201 and STAT 346 or STAT 446 or STAT 382
STAT 466, Theory and Methods of Experimental Design, 3
(also listed as EPBI 446). Experimental design for polynomial regression models and for multi-factor models. Theory for construction of increased efficiency designs including fractional factorials, Latin squares. Designs for response surfaces. GOSSETT-generated optimal designs for nonstandard problems. Knowledge of regression required.
Prerequisite: STAT 425
STAT 468, Sampling from Finite Populations: Theory and Applications, 3
(also listed as EPBI 447). Introduction to the theory and methodology of sampling from finite populations. Simple random, stratified random, systematic and multistage cluster sampling. Linear, ratio and regression estimators. Methodology for handling missing data, inference for small geographical areas or for small subpopulations, inference for quantiles. Application to large-scale personal interview and telephone surveys.
Prerequisite: STAT 343 or STAT 345 or STAT 445 or STAT 381
STAT 471, Special Topics in Statistics, 1-3
Topics in specialized areas of statistical theory and methodology, with emphasis on recent advances in theory and development of new methodology. Topics may change from year to year. Number of credit hours for the class will be predetermined each semester based on the material to be presented.
Consent of the instructor required.
STAT 476, Advances in Statistics and Modeling, 1-3
Topics in specialized areas of statistics and stochastic modeling, with emphasis on recent advances in theory and formulation of models. Investigation of new areas of application for statistical or stochastic models. Topics may change from year to year. Number of credit hours for the class will be predetermined each semester based on the material to be presented.
Consent of the instructor required.
STAT 491, Graduate Student Seminar, 1-2
Seminar run collaboratively by graduate students to investigate an area of current research, the topic chosen each semester. All graduate students participate in presentation of material each semester. Satisfies requirement for every full-time graduate student to enroll in a participatory seminar every semester while registered in any graduate degree program.
Graduate standing required.
STAT 495A, Consulting Forum, 1
Faculty and/or graduate students present collaborative research in case-study format. New requests for statistical assistance illustrate the consultation process. Graduate students assist faculty in the application of statistical modeling and methodology to research problems in substantive areas. Topics include ethical issues in collaborative research and in presentation of expert statistical testimony. Guest lecturers include statisticians working in industry and in consulting firms.
STAT 495B, Consulting Forum, 3
Faculty and/or graduate students present collaborative research in case-study format. New requests for statistical assistance illustrate the consultation process. Graduate students assist faculty in the application of statistical modeling and methodology to research problems in substantive areas. Topics include ethical issues in collaborative research and in presentation of expert statistical testimony. Guest lecturers include statisticians working in industry and in consulting firms. Consent of the instructor required.
Prerequisite: STAT 325 or STAT 425.
STAT 525, Advanced Techniques in Data Analysis, 3
Topics drawn from resampling methods (including bootstrapping), nonparametric curve and surface fitting, kernel density estimation, projection pursuit, approaches to model uncertainty, models for repeated measures and structural-functional models, statistical inference for non-statistical mathematical models of large systems.
Prerequisite: STAT 425
STAT 527, Advanced Statistical Computing, 3
Topics drawn from data types and data structures, numerical stability and errors in computer calculation, constrained optimization, computer graphics and graphical diagnostics for statistics, visualization of high dimensional data, curve and surface - fitting. Predominant use of statistical language S.
Prerequisite: STAT 427
STAT 537, Advanced Stochastic Modeling of Scientific Data I, 3
Spatial statistics. Theory and techniques for spatial or spatial-temporal relationships in high dimensional data, point pattern analysis, estimation of spatial covariance either stationary or non-stationary in space, applications to environmental sciences. Characterizations and solutions for mapping problems, for image reconstruction, for analysis of fractal spatial-temporal processes with particular application to environmental sciences.
Prerequisite: STAT 437 and STAT 446 or STAT 482
STAT 538, Advanced Stochastic Modeling of Scientific Data II, 3
Foundations of discrete and continuous-time dynamical systems. Complexity of nonlinear dynamical systems. Descriptive statistics of dynamical systems, invariant densities and their estimation. Ergodic properties, space and time-averaging. Chaotic behavior. Fractals as a signature of chaos. Statistical estimation of fractal dimension. Asymptotic fluctuations in dynamical systems. Statistical problems in physical sciences; statistical hydrodynamics. Statistical problems for hydrological, atmospheric and oceanic models. Theoretical foundations of simulation of random phenomena.
Prerequisite: STAT 437
STAT 545, Advanced Theory of Statistics I, 3
A systematic development of advanced statistical theory. Background concepts. Limits, order comparisons, convergence. Sample moments, quantiles and other statistics. Transformations. Characterization of distribution functions and characteristic functions. Normal and other approximations to distributions. Quadratic forms and other functions of asymptotically normal statistics. Asymptotic properties of statistics including asymptotic efficiency, consistency. Admissibility, sufficiency and ancillarity. Nuisance parameters, parameter orthogonality. Distribution theory in nuisance parameters.
Prerequisite: STAT 446 or STAT 482
STAT 546, Advanced Theory of Statistics II, 3
Estimation: maximum likelihood, minimax, Bayes', empirical Bayes', and James-Stein estimators. Entropy and information. U-statistics and their distributions. Von Mises differentiable statistical functions, M, L, R-estimators. Confidence intervals and regions. Simple and weighted empirical processes. Convergence and distributions for empirical processes.
Prerequisite: STAT 545
STAT 547, Advanced Theory of Statistics III, 3
Development of empirical process theory with application to censored data with random, fixed or arbitrary censoring mechanism. Characterization of quantile processes, spacings and large deviations as empirical processes. Asymptotic results for nonparametric regression, bootstrap and other resampling estimators.
Prerequisite: STAT 546
STAT 553, Time Series and Wavelets II, 3
Advanced topics in time series including nonstationary series, nonlinear models. In-depth development and application of wavelet theory. Wavelets as computational tool. Extensive use of computing to illustrate and investigate modeling with wavelets.
Prerequisite: STAT 453 and STAT 456 or MATH 491
STAT 555, Generalized Linear Models, 3
Generalization from linear statistical models to discrete responses and other non-Gaussian cases. Theory for binomial proportions and logits, Poisson counts and loglinear models, multinomial response models, models of survival data. Analysis of deviance, model checking. Conditional, marginal and quasi-likelihood methods. Inverse linear models. Generalized linear mixed models.
Prerequisite: STAT 455 or STAT 483
STAT 571, Advanced Topics in Statistics, 1-3
For advanced graduate students. Topics in specialized areas of statistical theory and methodology, with emphasis on recent advances in theory, developments of new methodology and definition of new research questions. Topics may change from year to year. Number of credit hours for the class will be predetermined each semester based on the material to be presented.
Consent of the instructor required.
STAT 576, Advanced Topics in Modeling, 1-3
Advanced topics in specialized areas of statistics and stochastic modeling designed to define new research directions drawing on recent advances in theory and model formulation. Focus on statistical issues arising in the application of statistical or stochastic models to new substantive research efforts. Topics may change from year to year. Number of credit hours for the class will be predetermined each semester based on the material to be presented.
Consent of the instructor required.
STAT 591, Statistical Research Seminar, 1-3
Seminar to prepare and explore current research topics presented by faculty and invited statistics colloquium speakers. Graduate students lecture on background material for colloquia using recent publications. Following each colloquium, students lead discussion and clarify further the contributions of the research. Newer students are paired with senior students; colloquium assignments coincide with students' research interests insofar as possible. Attendance at statistics colloquia is required. Satisfies requirement for every full-time graduate student to enroll in a participatory seminar every semester while registered in any graduate degree program. Number of credit hours will be determined by prior agreement with the instructor and depends on the extent of the student's responsibility.
Consent of the instructor required.
STAT 601, Reading and Research, 1-3
Individual study and/or project work. Permission of instructor required.
STAT 621, M.S. Research Project, 1-9
Completion of statistical design and/or analysis of a research project in a substantive field which requires substantial and/or nonstandard statistical techniques and which leads to results suitable for publication. Written project report must present the context of the research, justify the statistical methodology used, draw appropriate inferences and interpret these inferences in both statistical and substantive scientific terms. Oral presentation of research project may be given in either graduate student seminar or consulting forum. Permission of instructor required.
STAT 651, Thesis M.S., 1-36
(Credit as arranged) May be used as alternative to STAT 621 (M.S. Research Project) in fulfillment of requirements for M.S. degree in Statistics. Permission of instructor required.
STAT 701, Dissertation Ph.D., 1-36
(Credit as arranged) Permission of instructor required.
| Year 1: | MATH 121 | MATH 122 |
| | CMPS 131 | GER: Arts and Humanities |
| | ENGL 150 | GER: Science |
| | GER: Science | GER: Social Sciences |
| | GER: Social Sciences | Free Elective |
| | Physical Education Requirement | Physical Education Requirement |
| | Total: 16 hours | Total: 16 hours |
|
| Year 2: | MATH 223 | MATH 224 |
| | STAT 243 | MATH 201 |
| | GER: Arts and Humanities | STAT 244 |
| | GER: Social Sciences | GER: Arts and Humanities |
| | Free Elective | GER: Global and Cultural Diversity |
| | Total: 15 hours | Total: 15 hours |
|
| Year 3: | STAT 345 | STAT 346 |
| | EPBI 420 | STAT Elective |
| | Substantive Field Requirement | Substantive Field Requirement |
| GER: Arts and Humanities | Free Elective |
| | Science Requirement | Science Requirement |
| | Total: 15 hours | Total: 15 hours |
|
| Year 4: | STAT 325 | STAT 326 |
| | STAT Elective | STAT 395 |
| | STAT 391 | STAT 391 |
| | Free Elective | Free Elective |
| | Free Elective | Free Elective |
| | Free Elective | Free Elective |
| | Total: 16 hours | Total: 16 hours |
| Year 1: | MATH 121 | MATH 122 |
| CMPS 131 | GER: Arts and Humanities |
| | ENGL 150 | GER: Science |
| | GER: Science | GER: Social Sciences |
| | GER: Social Science | Free Elective |
| | Physical Education Requirement | Physical Education Requirement |
| | Total: 16 hours | Total: 16 hours |
|
|
| Year 2: | MATH 223 | MATH 224 |
| | STAT 243 | MATH 201 |
| | GER: Arts and Humanities | STAT 244 |
| | GER: Social Sciences | GER: Arts and Humanities |
| | Free Elective | GER: Global and Cultural Diversity |
| | Total: 15 hours | Total: 15 hours |
|
| Year 3: | STAT 345 | STAT 346 |
| EPBI 420 | STAT Elective |
| | Substantive Field Requirement | Substantive Field Requirement |
| | GER: Arts and Humanities | Free Elective |
| | Free Elective | Free Elective |
| | Total: 15 hours | Total: 15 hours |
|
| Year 4: | STAT 325 | STAT 326 |
| | STAT Elective | STAT 395 |
| Free Elective | STAT 391 |
| | Free Elective | Free Elective |
| | Free Elective | Free Elective |
| | Total: 15 hours | Total: 13 hours |
| Year 1: | MATH 121 | MATH 122 |
| | CMPS 131 | GER: Arts and Humanities |
| | ENGL 150 | GER: Science |
| | GER: Science | GER: Social Sciences |
| | GER: Social Sciences | Free Elective |
| | Physical Education Requirement | Physical Education Requirement |
| | Total: 16 hours | Total: 16 hours |
|
| Year 2: | MATH 223 | MATH 224 |
| | STAT 243 | MATH 201 |
| | GER: Arts and Humanities | STAT 244 |
| | GER: Social Sciences | GER: Arts and Humanities |
| Free Elective | GER: Global and Cultural Diversity |
| | Total: 15 hours | Total: 15 hours |
|
| Year 3: | STAT 345 | STAT 346 |
| | EPBI 420 | STAT 317 |
| OPRE 401 | STAT Elective |
| | GER: Arts and Humanities | Free Elective |
| | Free Elective | Free Elective |
| Total: 15 hours | Total: 15 hours |
|
| Year 4: | STAT 325 | STAT 326 |
| | STAT Elective | STAT 395 |
| | MATH 431 | STAT 391 |
| | Free Elective | Free Elective |
| Free Elective | Free Elective |
| Total: 15 hours | Total: 13 hours |
| Year 1: | MATH 121 | MATH 122 |
| ECMP 251 | GER: Arts and Humanities |
| ENGL 150 | GER: Science |
| GER: Science | GER: Social Sciences |
| | GER: Social Sciences | Free Elective |
| Physical Education Requirement | Physical Education Requirement |
| Total: 16 hours | Total: 16 hours |
|
| Year 2: | MATH 223 | MATH 224 |
| STAT 333 (or 243) | MATH 201 |
| GER: Arts and Humanities | STAT 343 (or 244) | |
| GER: Social Science | GER: Arts and Humanities |
| Science Requirement | Science Requirement |
| Total: 15 hours | Total: 15 hours |
|
| Year 3: | STAT 345 | STAT 346 |
| EPBI 420 | STAT Elective |
| Substantive Field Requirement | Substantive Field Requirement |
| GER: Arts and Humanities | GER: Global and Cultural Diversity |
| Free Elective | Free Elective |
| Total: 15 hours | Total: 15 hours |
|
| Year 4: | STAT 425 | STAT 426 |
| STAT Elective | STAT Elective |
| STAT 491 (1) | STAT 491 (1) |
| Free Elective | Free Elective |
| Free Elective | Free Elective |
| Free Elective | Free Elective |
| Total: 16 hours | Total: 16 hours |
|
| Year 5: | STAT 455 | STAT Elective |
| STAT Elective | STAT Elective |
| STAT 491 (1) | STAT 651 |
| Free Elective | STAT 491 (1) |
| Total: 10 hours | STAT 495 (1) |
| | Total: 11 hours |
| Year 1: | STAT 425 | STAT 426 |
| STAT 445 | STAT 446 |
| STAT Elective | STAT Elective |
| STAT 491 (1) | STAT 491 (1) |
| Total: 10 hours | Total: 10 hours |
|
| Year 2: | STAT 455 | STAT Elective (Optional) |
| STAT 495 | STAT Elective (Optional) |
| STAT Elective | STAT 651 |
| | STAT 491 (1) | STAT 491 (1) |
| Total: 10 hours | Total: 4 (-10) hours |
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