UF-Statistics UFL

Information Concerning the STA 6934 Offerings

Applied Mixed Models

Mixed models are a powerful tool for analyzing data arising from agricultural, biological, and environmental experiments. This is especially the case when data is collected over time or space. Recent advances in statistical software packages have helped make mixed models accessible. In this course, a general approach to using mixed models will be developed. The focus will be on applications, the statistical foundations, and open questions. The mixed models will be implemented in SAS. A partial list of possible course topics include: Graphical methods in SAS; Linear Regression and ANOVA (review); Linear Mixed Models (normally distributed data); Random effects estimation and testing; Heteroscedasticity; Repeated measures/ longitudinal data; General methods for correlated data; Logistic and Poisson Regression (binary and count data); Generalized Linear Mixed Models (non-normal data).

Prerequisites: Basic SAS skill is assumed as well as knowledge of basic statistical thinking such as that in STA 6167 or STA 6207.

Advanced Topics in Linear Models

The course is a continuation of STA 6246 (Linear Models). It mainly deals with the analysis of unbalanced mixed models. In particular, it covers the following topics: Estimation of variance components for unbalanced models, measures of data imbalance, exact tests concerning unbalanced random and mixed two-way models, exact tests concerning unbalanced random models with unequal cell frequencies in the last stage, comparison of designs for random models, and an introduction to generalized linear mixed models.

Prerequisites: STA 6246

Bayesian Methods

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Bayesian Theory

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Inference and Modeling for Research

This course is designed for students who have completed one or more introductory-level courses in statistics and require additional training in model-based inference and methods of data analysis. This training will include (1) an overview of theoretical results needed for computing likelihood-based inferences from either a frequentist (classical) or Bayesian perspective, and (2) development of computational skills needed to use these results in the analysis of data. An integral part of the course is the formulation of statistical models to meet scientific objectives.

Prerequisites: Students must have completed at least one introductory-level course in statistics (equivalent to STA 6166) and one course in calculus (equivalent to MAC 2233). Previous knowledge of a computer programming language is not required; however, the S programming language (on which R is based) will be used extensively.

Longitudinal Data

Likelihood-based and semiparametric methods for longitudinal data. Also, discussion of how to deal with missing data and its impact both theoretically and practically on inference.

Prerequisites: STA 6326-6327 and STA 6207-6208 and Stat 6246.

Markov chain Monte Carlo

Monte Carlo methods are increasingly used in many scientific areas, including statistical physics (where they originated), Bayesian and frequentist statistical inference, and image reconstruction. The basic idea is to carry out a simulation to estimate quantities of interest that cannot be computed analytically. This course will begin with a brief discussion of standard Monte Carlo schemes, and then focus on Monte Carlo methods based on Markov chains.

Prerequisites: STA 6466-7 (Probability Theory I and II) and STA 7346 (Statistical Inference I)

This is a course intended for Ph.D. students in the Statistics Department. Students who are not in the Statistics Department and who do not have the prerequisites should not take this course.

Modern Nonparametric Statistics

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Monte Carlo Statistical Methods

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Sampling Design for Spatial Analyses

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Spatial Statistics

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Statistical Ecology

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Statistical Analysis of Gene Expression Microarray Data

This course is designed to give an introduction to gene microarray technology and discuss various statistical methods that can be used for analyzing such high-throughput data. Topics covered include both low level and high level analysis. Conceptual and methodological underpinning of data analysis tools will be described. Implementation of analysis approaches using R package will be discussed in several lab sessions. The goal is to provide guidance in deciding which statistical approaches and packages may be used for particular projects and correctly interpreting the results. Potential research topic will also be discussed in the course. Performance in the course will be evaluated based on computing assignments, in-class presentation and a final data project.

Prerequisites: STA 4321-2; knowledge of STA 5701 and programming experience in R/Splus or matlab will be very helpful.

Topics in Basic Analysis

An introduction to real analysis, including set theory, the real numbers with heavy emphasis on the completeness property, sequences of real numbers and convergence concepts, limit superior and limit inferior of sequences, metric space topology, compactness, the Bolzano-Weierstrass theorem and the Heine-Borel Theorem, continuity of functions, sequences of functions, infinite series, Riemann integration. Emphasis is placed on rigorous development of mathematical concepts and the development of critical thinking skills. The course is designed to prepare students for the study of measure-theoretic probability (STA 6466-7).

Prerequisites: As a minimum the student should have complete three semesters of honest calculus. Additional work in mathematics would be helpful but strictly speaking not necessary.

Note: It is not appropriate to think of this course as "Calculus Four" or "Advanced Calculus". Indeed, it would be better to think of it as "Calculus Zero" or "Calculus Infinity". We will be concerned with foundational matters. For example, instead of developing (say) a dozen or so tests for convergence of series, we will present just a few and emphasize what it really means for a series to converge.

Topics in Stochastic Processes

Basic theory of Markov chains.

Prerequisites: STA 6466-7