Emphasis on use of the computer to perform statistical data analysis through use of integrated statistical packages. Instruction includes use of SAS and Splus.
Introduction to descriptive and inferential statistics. Topics may be selected from the following: descriptive statistics and graphs, probability, regression, correlation, tests of hypotheses, interval estimation, measurement, reliability, experimental design, analysis of variance, nonparametric methods, and multivariate methods.
Simple and complex analysis of variance and analysis of covariance designs. The general linear model approach, including full-rank and less than full-rank models, will be emphasized.
The course examines a variety of complex experimental designs that are available to researchers including split-plot factorial designs, confounded factorial designs, fractional factorial designs, incomplete block designs, and analysis of covariance. The designs are examined within the framework of the general linear model. Extensive use is made of computer software.
Introduction to mathematics of statistics. Fundamentals of probability theory, convergence concepts, sampling distributions, and matrix algebra.
Theory of random variables, distribution and density functions, statistical estimation, and hypothesis testing. Topics include probability, probability distributions, expectation, point and interval estimation, and sufficiency.
Topics include sampling distributions, likelihood and sufficiency principles, point and interval estimation, loss functions, Bayesian analysis, asymptotic convergence, and test of hypothesis.
Statistical methods of analyzing time series. Topics include autocorrelation function and spectrum, stationary and non-stationary time series, linear filtering, trend elimination, forecasting, general models and auto regressive integrated moving average models with applications in economics and engineering.
Basic concepts of lifetime distributions. Topics include types of censoring, inference procedures for exponential, Weibull, extreme value distributions, parametric and nonparametric estimation of survival function and accelerated life testing.
Traditional designs of experiments are presented within the framework of the general linear model. Also included are the latest designs and analyses for clinical trials and longitudinal studies.
This course presents the basic principles of epidemiology with particular emphasis on applications in healthcare management. Topics include specific tools of epidemiology used for purposes of planning, monitoring, and evaluating population health. These include identification and of disease, measures of incidence and prevalence, study designs, confidence intervals, p-values, statistical interaction, causal inference, and survival analysis. Methods for managing the health of populations using an understanding of the factors that influence population health are discussed. Strategies that health care organizations and systems can use to control these factors are also considered.
Exploratory spatial data analysis using both graphical and quantitative descriptions of spatial data including the empirical variogram. Topics include several theoretical isotropic and anisotropic variogram models and various methods for fitting variogram models such as maximum likelihood, restricted maximum likelihood, and weighted least squares. Techniques for prediction of spatial processes will include simple, ordinary, universal, and Bayesian kriging. Spatial sampling procedures, lattice data, and spatial point processes will also be considered. Existing software and case studies involving data from the environment, geological, and social sciences will be discussed.
Introduction to the more common statistical concepts and methods. Interval estimation, tests of hypotheses, non-parametric methods, linear regression and correlation, categorical data analysis, design of experiments and analysis of variance, and the use of computer packages.
Statistical methods and linear algebra. Theory and applications of simple and multiple regression models. Topics include review of statistical theory inference in regression, model selection, residual analysis, general linear regression model, multicollinearity, partial correlation coefficients, logistic regression, and other appropriate topics.
Statistical models and procedures for describing and analyzing random vector response data. Supporting theoretical topics include matrix algebra, vector geometry, the multivariate normal distribution and inference on multivariate parameters. Various procedures are used to analyze multivariate data sets.
Discriminant analysis, canonical correlation analysis, and multivariate analysis of variance.
The study of probability theory as motivated by applications from a variety of subject matters. Topics include: Markov chains, branching processes, Poisson processes, continuous time Markov chains with applications to queuing systems, and renewal theory.
Selected topics in Statistics. May be repeated once with change of topic.
Consulting, research, and teaching in statistics.
Selected topics in statistics. May involve texts, current literature, or an applied data model analysis. This course may be repeated with change of topic.
Supervised research for the master’s thesis. A maximum of three semester hours to count for the degree.
Large sample theory, including convergence concepts, laws of large numbers, central limit theorems, and asymptotic concepts in inference.
Bayesian statistical inference, including foundations, decision theory, prior construction, Bayesian point and interval estimation, and other inference topics. Comparisons between Bayesian and non-Bayesian methods are emphasized throughout.
Semiparametric inference, with an emphasis on regression models applicable to a wider class of problems than can be addressed with parametric regression models. Topics include scatterplot smoothing, mixed models, additive models, interaction models, and generalized regression. Models are implemented using various statistical computing packages.
Bayesian methods for data analysis. Includes an overview of the Bayesian approach to statistical inference, performance of Bayesian procedures, Bayesian computational issues, model criticism, and model selection. Case studies from a variety of fields are incorporated into the study. Implementation of models using Markov chain Monte Carlo methods is emphasized.
Critical evaluation of current statistical methodology used for the analysis of genomic and proteomic data.
Topics in statistical simulation and computation including pseudo-random variate generation, optimization, Monte Carlo simulation, Bootstrap and Jackknife methods.
Theory of general linear models including regression models, experimental design models, and variance component models. Least squares estimation. Gauss-Markov theorem and less than full rank hypotheses.
Multivariate normal and related distributions. Topics include generalizations of classical test statistics including Wilk's Lambda and Hotelling's T2, discriminant analysis, canonical variate analysis, and principal component analysis.
Theory of generalized linear models including logistic, probit, and log linear models with special application to categorical and ordinal categorical data analysis.
Supervised research for the doctoral dissertation. Maximum of nine semester hours will count for the degree. A student may register for one to six semester hours in one semester.