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Course Criteria
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3.00 Credits
Statistical consulting skills needed to deal with clients, formulate statistical models, explain analyses, use standard statistical computer packages, and write reports in language understandable to the client.
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3.00 Credits
Methods for sampling the environment and subsequent analysis of resulting data are considered. Emphasis is placed on design-based analysis and spatial data analysis. Special topics include environmental variables, environmental toxicology, and long-term trend detection.
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3.00 Credits
Algorithms for computer generation of discrete and continuous univariate and multivariate random variates. Finite population sampling algorithms. Poisson processes. Variance reduction techniques. Analysis of simulated data.
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3.00 Credits
A continuation of Computing Techniques in Statistics I. Resampling methods. Markov-chain simulation techniques. Numerical integration. Optimization techniques. Data augmentation methods. Selected topics in advanced statistical computation.
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3.00 Credits
Common statistical and genetic models appropriate for analyzing genetic data, especially DNA sequence data. Emphasis on fitting models, estimating parameters, and making inferences based on genetic data.
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3.00 Credits
Measurable spaces and measures, Lebesgue-Stieljes measure, independence, almost sure and in probability convergence, integration in probability spaces, product measures, absolute continuity of measures, weak law of large numbers, strong law of large numbers, weak convergence.
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3.00 Credits
Central limit theorem and Lindeberg-Feller theorem, stable laws, infinitely divisible laws, conditional expectations, Martingales, almost sure convergence for martingales, uniform integability, Markov chains, Brownian motion, Skorokhod's representation and Donsker's theorem.
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3.00 Credits
Methods for constructing and analyzing designed experiments are considered. Concepts of experimental unit, randomization, blocking, replication, and orthogonal contrasts are introduced. Designs include completely randomized design, randomized complete block design, Latin squares design, split-plot design, repeated measures design, and factorial and fractional factorial designs.
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3.00 Credits
Relevant matrix theory, multivariate random vectors, exact and asymptotic distributions, multivariate normal distribution (MVN), Q-Q plots, sampling from MVN and inference for population mean vector, covariance matrix, correlation matrix, MANOVA, principal component analysis, factor analysis, discriminant analysis and classification and clustering.
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3.00 Credits
Statistical modeling using nonlinear regression is considered. Topics include fixed-effects nonlinear regression models, nonlinear least squares, computational methods and practical matters, growth models, and compartmental models. Nonlinear mixed-effects models are discussed, including model interpretation, estimation and inference. Examples will be drawn from forestry, pharmaceutical sciences, and other fields.
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