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Course Criteria
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3.00 Credits
This course will cover the basics of time series analysis, including autocorrelation, moving averages, autoregressive models, seasonality, forecasting, spectral analysis, Box Jenkins ARIMA models, and transfer function models and multivariate ARIMA models.
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3.00 Credits
This course will begin with a detailed description of maximum likelihood. It will then discuss generalized linear models, including logistic and Poisson regression. Finally various topics in survival analysis will be covered: namely Kaplan-Meier curves and log-rank statistics, Weibull regression, and Cox proportional hazard regression. Examples from medicine and engineering will be given. SAS and S-plus statistical software will be used.
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3.00 Credits
Foundation of Bayesian Statistics, basic theory and several applications including Monte Carlo and Markov Chain Monte Carlo Methods for computing Bayesian inference will be covered. Specific topics include: Foundation of Bayesian Approach, Prior and Posterior distributions; Choice of Priors: subjective and non-subjective or default approaches; Inference using posterior distribution for standard models; and Hierarchical models, and their applications. WinBUGS will be introduced.
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3.00 Credits
Rank-based statistical inference will be covered. Topics include, but are not limited to, the one- and two-sample location problems including the Wilcoxon signed-rank and rank-sum test, Spearman correlation coefficient, one- and two-way Analysis-of-Variance tests, and Kolmogorov-Smirnov test for testing different distributions. In addition, the multiple comparisons issue will be discussed, specifically by comparing several treatments with and without a control treatment. Null distributions of test statistics will be discussed in the small sample and asymptotic cases, with and without ties.
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3.00 Credits
This course will cover the basics of using the SAS and S-plus statistical software. Topics covered include: importing external files, subsetting and merging data files, performing statistical procedures, graphics, matrix calculations, and macros and functions.
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3.00 Credits
The course will cover special topics of statistics that are of interest to students and faculty. Such topics may include those that are not covered in other courses, or extensions of other courses.
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4.00 Credits
The course will cover multivariate normal distribution, distributions of quadratic forms, theory of Analysis of variance as applied to linear regression in full-rank models, estimability and testability in non-full-rank models, and generalized inverse and its use in such models, various types of sums of squares in ANOVA of designed models, associated estimable and testable functions in balanced and unbalanced designs with fixed effects, random effects and mixed effects, and nested and crossed factors. Estimation and testing of fixed effects and variance components using ANOVA Sums of Squares will be covered. SAS will be extensively used to apply these concepts with real data.
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4.00 Credits
The course will cover estimation and testing in mixed models using ML and REML methods, Split Plot designs, repeated measures. The course will also cover topics in Multivariate Statistics, including estimation, test of hypothesis such as Hotelling T-square and MANOVA, Principal components, Factor analysis and, depending on interest Cluster Analysis and Discriminant Analysis.
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4.00 Credits
The course will cover the following topics in depth: Distribution theory, Estimation, Hypotheses testing, Asymptotic behavior of statistics, basics of Bayesian methods, and Decision theory.
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4.00 Credits
Measure theoretic foundations of probability: random variables, expected value (Lebesgue integral). Laws of large numbers, weak convergence. Characteristic functions, central limit theorem. Conditional probability, conditional expectation. Students will be expected to have a strong background in theoretical mathematics or statistics. A good knowledge of multivariable calculus and an introduction to analysis is a must. Advanced Calculus (MATH 6001/6002), Mathematical Statistics (STAT 6021/6022), or equivalent is recommended.
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