Course Guide for Spring 2005

Graduate level courses in statistics and quantitative methods are listed by department (alphabetically). Some advanced undergraduate level courses are also listed. Links are provided to course descriptions. Please report problems or suggestions concerning this web page to sguo@email.unc.edu

BIOS 151: Elements of Probability and Statistical Inference II.

This course discusses the basic theory and common application of the general linear model, an introduction to non-linear modeling methods (e.g., logistic regression and proportional hazards regression), and an introduction to random effects ANOVA.

BIOS 161: Probability and Statistical Inference II.

Distribution of functions of random variables; Helmert transformation theory; central limit theorem and other asymptotic theory; estimation theory; maximum likelihood methods; hypothesis testing; power; Neyman-Pearson Theorem, likelihood ratio, score, and Wald tests; noncentral distributions.

BIOS 163: Intermediate Linear Models.

Matrix-based treatment of regression, ANOVA, and ANCOVA, emphasizing the general linear model and hypothesis as well as diagnostics and model building. The course concludes with some treatment of random effects models and logistic regression models.

BIOS 164: Introduction to Sample Survey Methods.

Fundamental principles and methods of sampling populations, with primary attention given to simple random sampling, stratified sampling, and cluster sampling. Also, the calculation of sample weights, dealing with sources of nonsampling error, and analysis of data from complex sample designs are covered. Practical experience in sampling is provided by student participation in the design, execution, and analysis of a sampling project.

BIOS 167: Applied Stochastic Processes.

Poisson processes and extensions, epidemic models, branching processes and other stochastic models of empirical processes. Disease, population, and other biostatistical applications.

BIOS 168: Design of Public Health Studies.

Statistical concepts in basic public health study designs: cross-sectional, case-control, prospective, and experimental (including clinical trials). Validity, measurement of response, sample size determination, matching and random allocation methods.

BIOS 180: Introductory Survival Analysis.

Introduction to concepts and techniques used in the analysis of time to event data, including censoring, hazard rates, estimation of survival curves, regression techniques, applications to clinical trails.

BIOS 240: Statistical Considerations for Confirmatory Regulatory Clinical Trails.

The objective of this course is to illuminate the process of statistical evaluation of study designs and licensing applications at the Food and Drug Administrations (FDA). After some discussion of the history of the FDA and role of regulations, we will cover a number of methodological as well as practical topics. NOTE: A more detailed posting is located on bulletin boards.

BIOS 261: Advanced Probability and Statistical Inference II.

Unbiasedness, consistency, sufficiency, and efficiency properties. Invariance, completeness, admissibility, ancillarity, minimal sufficiency, and optimality properties. Unbiased and locally most powerful tests (including the multiparameter case). Envelope power function; best average power test. Bayes and empirical Bayes procedures. Likelihood, quasi-likelihood, and profile likelihood. Order statistics and empirical distributions; general central limit theorems; variance stabilizing transformations; U-statistics; least squares, weighted least squares, and generalized least squares estimation. Generalized estimating equations; asymptotic theory for BAN estimators; asymptotic theory for likelihood ratio, Wald, and score tests; log-linear models; asymptotics for linear inference; robust statistical inference.

BIOS 263: Generalized Linear Model Theory & Applications.

Topics include logistic regression, over-dispersion, Poisson regression, log-linear models, conditional likelihoods, multivariate regression models, generalized mixed models, and regression diagnostics.

BIOS 265: Linear Models in Categorical Data Analysis.

Prerequisites: BIOS 161, 163, 165, and 166 or equivalent. Theory of statistical methods for analyzing categorical data by means of linear models, multifactor, and multiresponse situations; interpretation of interactions.

BIOS 267: Advanced Linear Models II.

Theory and methods of linear statistical models for continuous response data, including definitions of parameters, hypotheses, orthogonal ploynomials, incomplete/informatively censored data; general linear univariate, multivariate, and longitudinal studies; models and parameterizations for various classes of designed experiments and longitudinal studies; modling covariance structures.

BIOS 271: Demographic Techniques II

Prerequisites: BIOS 170 and integral calculus. Life table techniques; methods of analysis when data are deficient; population projection methods; interrelations among demographic variables; migration analysis; uses of population models.

BIOS 283: Statistical Methods in Quantitative Genetics.

An introduction to the statistical basis of variation in quantitative traits, with focus on decomposition of trait variation; linkage map construction; statistical methodologies and computer software for mapping quantitative trait loci. Issues involving whole-genome analysis will be highlighted.

BIOS 341: Principles of Statistical Consulting.

An introduction to the statistical consulting process, emphasizing its nontechnical aspects.

ECON 225: Game Theory II.

Prerequisite, Economics 200, 201, or permission of the instructor. Topics covered will be chosen from those listed, but not covered in Economics 221.

ECON 272: Econometrics.

Prerequisite, Economics 271 or equivalent. One semester coverage of basic econometrics. Topics include: regression under ideal and nonideal conditions; special models, including simultaneous equations models; and applications and econometric computer programs.

ECON 274: Time Series Econometrics.

Prerequisite, Economics 273. Covers stationary univariate and multivariate time series models, spectral analysis methods, nonstationary models with time trends, unit roots and cointegration, and special topics such as conditional volatility, the Kalman filter and changes of regime.

ECON 276: Cross Sectional Econometrics.

Prerequisite, Economics 273. Maximum likelihood methods for limited dependent variables. Longitudinal data models and methods. Hazard models. Multivariate models with limited dependent variables.

ECON 386: Introduction to Empirical Finance.

Corequisite or Prerequisite, Economics 272. This course provides an introduction to the econometric techniques commonly applied to empirical issues in finance.

EDUC 284: Statistical Analysis of Educational Data II (Linear Models).

Prerequisites: EDUC 184, EDFO 285 or equivalent, or permission of the instructor. A linear model approach to the analysis of data collected in educational settings. Topics include multiple regression, analysis of variance, and analysis of covariance, using computer packages.

EDUC 388: Introduction to SEM.

Introduces structural equation modeling with both observed and latent variables. Applications include confirmatory factor analysis, multiple group analyses, longitudinal analyses, and multitrait-multimethod models.

 
Epidemiology

EPID 268: Theory and Quantitative Methods in Epidemiology.

Prerequisites: EPID 168 and BIOS 145. Permission of instructor required for non-majors. An in-depth treatment of key methodological topics in epidemiology, including concepts of cause confounding and its control subject selection, data quality, sampling variability, and effect modification. Three lecture and two laboratory hours per week.

EPID 271: Time To Event Data.

N/A

Mathematics

MATH 181: Introductory Topology.

The prerequisites for this course are Math 180 and the material on metric spaces covered in Math 193. Important illustrative examples will be presented at every opportunity, and pathologies will be used sparingly, only to indicate subleties.

MATH 192: Scientific Computation II.

This course is the second half of a two semester introduction to graduate level numerical analysis and scientific computing. The majority of the class concerns a mathematical approach to the theory and practice of numerically solving applied linear algebra problems which frequently arise in the physical sciences, particularly from the discretization of partial differential equations.

MATH 199: Methods of Applied Mathematics II.

Possible Topics: Perturbation Methods, Elementary Nonlinear Evolution Equations, Modulation Theory for Linear and Nonlinear Wave Equations, Green's Functions, and Elementary Dynamical Systems Tools.

MATH 229: Mathematical Modeling II.

Current models in science and technology: topics ranging from material science applications (e.g. flow of polymers and LCPs); geophysical applications (e.g., ocean circulation, quasi-geostrophic models, atmospheric vortices).

MATH 272: Differential Geometry.

Possible Topics: Riemannian manifolds, Connections on vector bundles, Curvature, The second fundamental form (shape operator), Gauss' Theorema Egregium, the Codazzi equation, Mean curvature, the Gauss map, Fundamental theorem of surface theory, geometry of subbundles, Principal bundles and geometry, and Chern-Weil theory.

Political Science

POLI 282: Intermediate Statistics.

This course extends the coverage of Political Science 281. Topics to be covered include analysis of variance, multiple and partials correlation, and multiple regression.

POLI 284: Time Series Analysis of Political Data.

Prerequisites, Political Science 282 or permission of the instructor. Discusses the problems that arise when regression methodologies are applied to time series and pooled time series data.

Psychology

PSYC 231: Structural Equation Models with Latent Variables.

Prerequisite, Psychology 282 or permission of the instructor. Examination of a wide range of topics in covariance structure models, including their history, underlying theory, controversies, and practical use with major computer packages.

PSYC 282: Statistical Methods in Psychology II.

Prerequisite, Psychology 281. Statistical estimation and hypothesis testing for linear models (ANOVA, ANCOVA, regression analysis); statistical models in the design and analysis of experiments.

Sociology

SOCI 207: Measurement Data & Collection.

Provides an introduction to measurement theory and a review of various methods of data-gathering. Gaining experience with a variety of techniques of measurement and preparing a pretested research proposal are required for all students.

SOCI 209: Linear Regression Models.

The course presents regression analysis (simple and multiple) and related techniques. The major topics are: the assumptions of the regression model, matrix representation of the regression model, statistical inference including general linear tests, polynomial regression and interaction models, qualitative (dummy) independent variables, diagnostics and remedies for outliers and influential cases, collinearity, problems of model building and specification, heteroscedasticity, autocorrelation of errors in time series data, and problems of missing values and selection bias.

Statistics

STAT 126: Introduction To Probability.

Prerequisite, Mathematics 33. Introduction to mathematical theory of probability covering random variables, moments, binomial, Poisson, normal and related distributions, generating functions, sums and sequences of random variables, and statistical applications.

STAT 127: Mathematical Statistics.

Prerequisite, Statistics 126 or equivalent. Functions of random samples and their probability distributions; introductory theory of point and interval estimation and of hypothesis testing; elementary decision theory.

STAT 155: Probability.

Prerequisite, Statistics 154 or permission of instructor. Foundations of probability. Basic classical theorems. Modes of probabilistic convergence. Central limit problem. Generating functions, characteristic functions. Conditional probability and expectation.

STAT 165: Statistical Theory II.

Prerequisite, Statistics 164 or equivalent. Point estimation; Hypothesis testing and confidence sets; Contingency tables, nonparametric goodness-of-fit; Linear model optimality theory: BLUE, MVU, MLE; Multivariate tests; Introduction to decision theory and Bayesian inference.

STAT 175: Applied Statistics II.

Prerequisite Stat 174 or permission of the instructor. ANOVA (including nested and crossed models, multiple comparisons); GLM basics: exponential families, link functions, likelihood, quasi-likelihood, conditional likelihood; Numerical analysis; numerical linear algebra, optimization; GLM diagnostics; Simulation: transformation, rejection, Gibbs sampler.

STAT 185: Time Series And Multivariate Analysis.

Prerequisite, Statistics 126. Time Series: Exploratory and graphical analysis; Time domain analysis and ARMA models; Fourier analysis: FFT, periodogram, smoothing; State space analysis: Kalman filter, dynamic models. Multivariate: Principal components, canonical correlation; Classification, clustering; Dimension reduction: projection pursuit, alternating conditional sliced inverse regression.

STAT 190: Statistical Consulting.

Prerequisite, permission of instructor. Projects are assigned by the instructor. Typically these projects relate to requests for statistical consulting assistance from outside the Department. The class meets once per week over an academic year for a total of three credit hours.

STAT 321: Special Problems.

Prerequisite, permission of the instructor.

STAT 322: Special Problems.

Prerequisite, permission of the instructor.