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Course Criteria
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3.00 Credits
An advanced mathematical treatment of analytical and algorithmic aspects of finite dimensional nonlinear programming. Including an examination of structure and effectiveness of computational methods for unconstrained and constrained minimization. Special attention directed toward current research and recent developments in the field.
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3.00 Credits
Least squares estimation and hypothesis testing procedures for linear models. Consideration of regression, analysis of variance and covariance in a unified manner. Emphasis on use of the computer to apply these techniques to experimental (including unequal cell sizes) and survey situations.
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3.00 Credits
Review of completely randomized, randomized complete block and Latin square designs and basic concepts in the techniques of experimental design. Designs and analysis methods in factorial experiments, confounded factorials, response surface methodology, change-over design, split-plot experiments and incomplete block designs. Examples used to illustrate application and analysis of these designs.
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3.00 Credits
Statistical methods for analyzing life-testing data and accessing system reliability. Grouped and time-censored data, order statistics. Classical and Bayesian inference for univariate and multivariate exponential, Weibull, lognormal and gamma distributions. Experimental designs and sampling plans for accelerated testing and burn-in procedures. Taguchi's reliability improvement philosophy. Field performance and software reliability analysis.
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3.00 Credits
Principles for interpretation and design of sample surveys. Estimator biases, variances and comparative costs. Simple random sample, cluster sample, ratio estimation, stratification, varying probabilities of selection. Multi-stage, systematic and double sampling. Response errors.
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3.00 Credits
Analysis of discrete data, illustrated with genetic data on morphological characters allozymes, restriction fragment length polymorphisms and DNA sequences. Maximum likelihood estimation, including iterative procedures. Numerical resampling. Development of statistical techniques for characterizing genetic disequilibrium and diversity. Measures of population structure and genetic distance. Construction of phylogenetic trees. Finding alignments and similarities between DNA sequences. Locating genes with markers.
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4.00 Credits
Analysis of decision problems involving risk and uncertainty. Modeling decision process; Bayesian probability analysis, use of information, and subjective probability; utility theory and multiattribute utility assessment; dynamics of interacting with decision makers and subject matter specialists; decision trees, influence diagrams and other tools to assist in modeling decision problems. Laboratory develops skill in implementing methodology.
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3.00 Credits
An introduction to use of statistical methods for analyzing and forecasting data observed over time. Trigonometric regression, periodogram/spectral analysis. Smoothing. Autoregressive moving average models. Regression with autocorrelated errors. Linear filters and bivariate spectral analysis. Stress on methods and applications; software implementations described and used in assignments.
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3.00 Credits
An introduction to use of multivariate statistical methods in analysis of data collected in experiments and surveys. Topics covered including multivariate analysis of variance, discriminant analysis, canonical correlation analysis and principal components analysis. Emphasis upon use of a computer to perform multivariate statistical analysis calculations.
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3.00 Credits
Statistics methods for analysis of multivariate data, focusing on data collected in form of repeated measurements. Multivariate normal distribution, Hotelling's T2, multivariate analysis of variance, repeated measures analysis of variance, growth curve models, mixed effects models. Methods for analyzing multivariate data in form of counts, categorical data and binary data, emphasizing recent approaches in statistical literature.
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