Offered as EPBI 481 and STAT 445.

**STAT 446. Theoretical Statistics II (3)**

Point estimation: maximum likelihood, moment estimators. Methods of evaluating estimators including mean squared error, consistency, “best” unbiased and sufficiency. Hypothesis testing; likelihood ratio and union-intersection tests. Properties of tests including power function, bias. Interval estimation by inversion of test statistics, use of pivotal quantities. Application to regression. Graduate students are responsible for mathematical derivations, and full proofs of principal theorems. Recommended preparation: MATH 223 or STAT 445.

Offered as EPBI 482 and STAT 446.

**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. Recommended preparation: STAT 445.

**STAT 453. Time Series and 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.

Prereq: STAT 333 or STAT 346 or STAT 433 or STAT 446 or permission of department.

**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. Analysis of longitudinal data.

Prereq: MATH 201 and STAT 346 or STAT 446

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. Recommended preparation: Graduate standing.

**STAT 495A. Consulting Forum (1–3)**

This course unifies what students have learned in their course work to apply their knowledge in consulting. It recognizes the fact that the essence of the statistical profession is continuing interaction with practitioners in the sciences, engineering, medicine, economics, etc. The course presents the views of prominent experts in the field as obtained from the literature and other sources. The responsibilities of the consultant and the client are discussed. Sample consulting problems are presented and strategies for solving them are provided.

Prereq: STAT 325 or STAT 425.

**STAT 495B. Consulting Forum With Practicum (3)**

This course is designed to provide a hands-on experience with statistical consulting under the guidance of the instructor. It will include discussion of practical aspects of consulting such as the entrepreneurial nature of this activity. The students will become involved in actual consulting projects generated in a collaborative environment. Statistical problems, together with their substantive background, will be presented by individuals from the private sector (e.g., from industry) and/or Case Western Reserve faculty and students. Selected problems will be addressed in a collaborative fashion; i.e., by a team involving graduate students from the Statistics Department, the course instructor, and scientists. Some of these problems may lead to collaborative research or entrepreneurial ventures.

Prereq: STAT 495A, STAT 325, or STAT 425 or consent of department.

**STAT 525. Advanced Data Analysis (3)**

Topics drawn from resampling methods (including bootstrapping), MCMC (Gibbs sampling), nonparametric curve and surface fitting, kernel density estimation, projection pursuit, mixture models, time series (time permitting), approaches to model uncertainty, models for repeated measures and structural-functional models, statistical inference for large systems, modern data analysis techniques. Recommended preparation: STAT 426 or permission of department.

**STAT 538. Stochastic Models: Diffusive Phenomena and Stochastic Differential Equations (3)**

Foundation of discrete and continuous time stochastic dynamical systems. Descriptive statistics. Correlational and spectral methods for stationary processes. Ergodic properties, space and time averaging. Stochastic dynamics of diffusive type, Brownian, and Levy processes and their fractal structure. Statistical problems in physical sciences. Statistical hydrodynamics. Simulation of random phenomena. Recommended preparation: STAT 312 or equivalent.

**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. Recommended preparation: STAT 446.

**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. Recommended preparation: STAT 545.

**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 for survival data. Analysis of deviance, model checking. Conditional, marginal and quasi-likelihood methods. Inverse linear models. Generalized linear mixed models. Recommended preparation: STAT 455.

**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.

**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.

**STAT 601. Reading and Research (1–9)**

Individual study and/or project work.

**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.

**STAT 651. Thesis M.S. (1–18)**

(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.

**STAT 701. Dissertation Ph.D. (1–18)**

(Credit as arranged.)

Prereq: Predoctoral research consent or advanced to Ph.D. candidacy milestone.