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Course Criteria
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3.00 Credits
PQ: STAT 31200 or consent of instructor. This course is a sequel to STAT 31200. Topics include continuous-time Markov chains, Markov chain Monte Carlo, discrete-time martingales, and Brownian motion and diffusions. The emphasis is on defining the processes and calculating or approximating various related probabilities. The measure theoretic aspects of these processes are not covered rigorously. Spring.
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3.00 Credits
PQ: Consent of instructor. This course covers random sampling methods; stratification, cluster sampling, and ratio estimation; and methods for dealing with non-response and partial response. Autumn.
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3.00 Credits
PQ: STAT 30100 and 30200, or consent of instructor. Primarily intended for second-year graduate students in statistics, this course is also open to students with similar backgrounds in econometrics or finance. Financial data is commonly modeled by diffusion, jump-diffusion, and related models, and it is usually supposed that observation is discrete. This course is concerned with inference in such settings. Spring.
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3.00 Credits
PQ: STAT 24500 or equivalent and linear algebra (STAT 24300 or equivalent). This course introduces the theory, methods, and applications of fitting and interpreting multiple regression models. Topics include the examination of residuals, the transformation of data, strategies and criteria for the selection of a regression equation, nonlinear models, biases due to excluded variables and measurement error, and the use and interpretation of computer package regression programs. The theoretical basis of the methods, the relation to linear algebra, and the effects of violations of assumptions are studied. Techniques discussed are illustrated by examples involving both physical and social sciences data. Autumn.
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3.00 Credits
PQ: STAT 34300. This course introduces the methodology and application of linear models in experimental design. We emphasize the basic principles of experimental design (e.g., blocking, randomization, incomplete layouts). Many of the standard designs (e.g., fractional factorial, incomplete block, split unit designs) are studied within this context. The analysis of these experiments is developed as well, with particular emphasis on the role of fixed and random effects. Additional topics may include response surface analysis, the use of covariates in the analysis of designed experiments, and spatial analysis of field trials. Winter.
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3.00 Credits
PQ: STAT 34300 or consent of instructor. This applied course covers factors, variates, contrasts, and interactions; exponential-family models (i.e., variance function); definition of a generalized linear model (i.e., link functions); specific examples of GLMs; logistic and probit regression; cumulative logistic models; log-linear models and contingency tables; inverse linear models; Quasi-likelihood and least squares; estimating functions; and partially linear models. Spring.
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3.00 Credits
Introductory statistics recommended. Epidemiology is the study of the distribution and determinants of health and disease in human populations. This course introduces the basic principles of epidemiologic study design, analysis, and interpretation, through lectures, assignments, and critical appraisement of both classic and contemporary research articles. The course objectives include: (1) to be able to critically read and understand epidemiologic studies; (2) to be able to calculate and interpret measures of disease occurrence and measures of disease-exposure associations; and (3) to understand the contributions of epidemiology to clinical research, medicine, and public health. Autumn.
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3.00 Credits
PQ: STAT 22400 (=HSTD 32400) or equivalent; or consent of instructor. This course introduces principles and methods for the analysis of time-to-event data. This type of data occurs extensively in both observational and experimental biomedical and public health studies, as well as in industrial applications. While some theoretical statistical detail is given (at the level appropriate for a master's student in statistics), we primarily focus on data analysis. Problems are motivated from an epidemiologic and clinical perspective, concentrating on the analysis of cohort data and time-to-event data from controlled clinical trials. Winter.
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3.00 Credits
PQ: STAT 22600 (=HSTD 32600) or STAT 22400 (=HSTD 32400) or equivalent; and STAT 22700 (=HSTD 32700) or STAT 34700 or equivalent; or consent of instructor. Longitudinal data consist of multiple measures over time on a sample of individuals. This type of data occurs extensively in both observational and experimental biomedical and public health studies, as well as in studies in sociology and applied economics. This course introduces principles and methods for the analysis of longitudinal data. Although some supporting statistical theory is given, we emphasize data analysis and interpretation of models for longitudinal data. Problems are motivated by applications in epidemiology, clinical medicine, health services research, and disease natural history studies. Autumn.
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3.00 Credits
PQ: Consent of instructor. This course covers deformable models for detecting objects in images. Topics include one-dimensional models to identify object contours and boundaries; two-dimensional models for image matching; and sparse models for efficient detection of objects in complex scenes. Mathematical tools needed to define the models and associated algorithms are developed. Applications include detecting contours in medical images, matching brains, and detecting faces in images. Neural network implementations of some of the algorithms are presented, and connections to the functions of the biological visual system are discussed. Y. Amit. Winter.
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