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Course Criteria
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3.00 Credits
The characteristics of microeconomic data. Limited dependent variable models for cross-sectional microeconomic data: logit/probit models; tobit models; methods for accounting for sample selection; count data models; duration analysis; non-parametricmethods. Panel data models: balanced and unbalanced panels; fixed and random effects; dynamic panel data models; limited dependent variables and panel data analysis.
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3.00 Credits
Expected mean squares, exact and approximate tests of hypotheses for balanced and unbalanced data sets. Fixed, mixed and random models. Randomization theory. Estimation of variance components using regression, MINQUE and general quadratic unbiased estimation theory.
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3.00 Credits
Phylogenetic analyses of nucleotide and protein sequence data. Sequence alignment, phylogeny reconstruction and relevant computer software. Prediction of protein secondary structure, database searching, bioinformatics and related topics. Project required.
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3.00 Credits
Genetic mapping data. Linkage map reconstruction, quantitative genetical models. Statistical methods and computer programs for mapping quantitative trait loci and estimating genetic architecture of quantitative traits.
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3.00 Credits
Computational tools for research in statistics, including applications of numerical linear algebra, optimization and random number generation, using the statistical language R. A project encompassing a simulation experiment will be required.
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3.00 Credits
Construction and analysis of multifactor designs, factorials, fractional factorials, balanced incomplete block designs, Latin squares, orthogonal arrays of strength d and response surface designs. Fractionating mixed level factorials, confounding and blocking techniques, study of robustness of designs to loss of design point.
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3.00 Credits
Inference for general nonlinear parametric statistical models for univariate and multivariate continuous and discrete response, including generalized linear models, nonlinear models with nonconstant variance, and generalized estimating equation procedures for multivariate response, including repeated measurement data. Linear and quadratic estimating equations, models for covariance structure, effects of model misspecification and robustness. Survey of major theoretical results and implementation using standard statistical software.
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3.00 Credits
Migration, mutation, selection, drift, linkage, mating system and other processes bearing on rates of change in population frequencies, means and variances; magnitude and nature of genotypic and nongenotypic variability and their role in alternativeprocedures of plant and animal breeding; experimental and statistical approaches to the analysis of quantitative inheritance.
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3.00 Credits
Role of theory construction and model building in development of experimental science. Historical development of mathematical theories and models for growth of one-species populations (logistic and off-shoots), including considerations of age distributions (matrix models, Leslie and Lopez; continuous theory, renewal equation). Some of the more elementary theories on the growth of organisms (von Bertalanffy and others; allometric theories; cultures grown in a chemostat). Mathematical theories oftwo and more species systems (predator-prey, competition, symbosis; leading up to present-day research) and discussion of some similar models for chemical kinetics. Much emphasis on scrutiny of biological concepts as well as of mathematical structureof models in order to uncover both weak and strong points of models discussed. Mathematical treatment of differential equations in models stressing qualitative and graphical aspects, as well as certain aspects of discretization. Difference equation models.
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3.00 Credits
Continuation of topics of BMA 771. Some more advanced mathematical techniques concerning nonlinear differential equations of types encountered in BMA 771: several concepts of stability, asymptotic directions, Liapunov functions; different time-scales. Comparison of deterministic and stochastic models for several biological problems including birth and death processes. Discussion of various other applications of mathematics to biology, some recent research.
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