STATISTICS
Professors J.L. Gastwirth, N.D. Singpurwalla, J.M. Lachin III, H.M. Mahmoud, T.K. Nayak, Z. Li, J. Chandra (Research), R. Modarres (Chair)
Associate Professors S. Bose, E. Bura, S. Kundu, M. Larsen, Y. Lai, J.R. Stroud
Assistant Professors S. Balaji, Q. Pan, J. Landon
Professorial Lecturers F. Ponti, P. Chandhok, R.F. Teitel, C.M. Fleming
Master of Science in the field of statistics-General prerequisite: course work in multivariate calculus, matrix theory, and at least two undergraduate statistics courses.
Required: The general requirements stated under Columbian College of Arts and Sciences. The program of study consists of 30 credit hours of graduate course work without a thesis. The department may also approve a program of study consisting of 24 credit hours of course work plus a thesis (Stat 6998- 99). All candidates must take Stat 6201- 2. Courses may be chosen in related fields (economics, mathematics, finance, management, computer science, engineering, public health) with approval of the advisor.
Doctor of Philosophy in the field of statistics-Prerequisite: A master's degree in statistics or a related discipline. The main requirement is a strong background in mathematics, including courses in advanced calculus, linear algebra, and mathematical statistics. Some deficiencies may be made up concurrently during the student's first year. In some instances, a student may enter the Ph.D. program with a bachelor's degree.
Required: The general requirements stated under Columbian College of Arts and Sciences, including satisfactory completion of (1) Stat 6201- 2, 6217- 18, 6223 or 8271, 8257, 8258, 8263, 8264, and at least two courses chosen from among Stat 8262, 8265- 66, and 8273- 74; (2) a minimum of 15 additional credit hours as determined by consultation with the departmental doctoral committee; (3) the General Examination, consisting of two parts: (a) a written qualifying examination that must be taken within 24 months from the date of enrollment in the program and is based on Stat 6201- 2, 8257, and 8263 and (b) an examination to determine the student's readiness to carry out the proposed dissertation research; and (4) a dissertation demonstrating the candidate's ability to do original research in one of the following fields: Bayesian inference, biostatistics, design of experiments, multivariate analysis, nonparametric statistics, probability (theoretical or applied), reliability theory, robust methods, sampling, statistical computing, statistical inference, stochastic processes, and time series.
Master of Science and Doctor of Philosophy in the fields of biostatistics and epidemiology-See Biostatistics and Epidemiology.
In addition to its degree programs, the Statistics Department offers graduate certificates in applied quantitative risk analysis and in survey design and data analysis.
With permission, a limited number of upper-level undergraduate courses in the department may be taken for graduate credit; additional course work is required. See the Undergraduate Programs Bulletin for course listings.
| 6104 |
Statistics in Management, Administration, and Policy Studies(3) |
Staff |
| |
Introductory study of statistical techniques for research problems. For graduate students in fields other than statistics who have no previous statistics training. May not be taken by graduate students in statistics. |
| 6201-02 |
Mathematical Statistics(3-3) |
Balaji, Mahmoud |
| |
Probability, distribution theory, sampling theory, estimation, sufficient statistics, hypothesis testing, analysis of variance, multivariate normal distribution. Prerequisite: Math 2233, 2184. (Academic year) |
| 6207 |
Methods of Statistical Computing I(3) |
Modarres |
| |
Error analysis, computational aspects of linear models, sweep operator, random number generation, simulation, resampling. Optimization, numerical integration (Gaussian quadrature, Simpson's rule); E-M algorithm. Prerequisite: Stat 2118, 4157- 58; Math 2184; knowledge of a programming language. |
| 6208 |
Methods of Statistical Computing II(3) |
Modarres |
| |
Numerical linear algebra, matrix decomposition and eigenvalue problems. Smoothing and density estimation. Graphics, interactive and dynamic techniques for data display. Object-oriented programming. Prerequisite: Stat 2118, 4157- 58; Math 2184; and knowledge of a programming language. |
| 6210 |
Data Analysis(3) |
Lai |
| |
Review of statistical principles of data analysis, using computerized statistical procedures. Multiple regression and the general linear model, analysis of contingency tables and categorical data, logistic regression for qualitative responses. Prerequisite: Stat 2118, 4157 or 6201, and 2183 or equivalent. (Spring) |
| 6213 |
Intermediate Probability and Stochastic Processes(3) |
Li |
| |
Discrete and continuous random variables and their distributions, conditional distributions and conditional expectation, generating functions and their applications, convergence of random variables; introduction to Brownian motion, homogeneous and nonhomogeneous Poisson processes and martingales. Prerequisite: Stat 6201- 2 or equivalent.(Spring, alternate years) |
| 6214 |
Applied Linear Models(3) |
Bura |
| |
Introduction to regression techniques for discrete and continuous response variables. The course includes a computing component using SAS and S+. Prerequisite: Math 2233 and 2184. (Fall, alternate years) |
| 6215-16 |
Applied Multivariate Analysis(3-3) |
Modarres |
| |
Application of multivariate statistical techniques to multidimensional research data from the behavioral, social, biological, medical, and physical sciences. Prerequisite: Stat 3119, 4157- 58; Math 2184.(Alternate academic years) |
| 6217 |
Design of Experiments(3) |
Bura, Li |
| |
Design and analysis of single- and multiple-factor experiments. Includes block designs, repeated measures, factorial and fractional factorial experiments, response surface experimentation. Prerequisite: Stat 4157- 58; Math 2184. (Fall, alternate years) |
| 6218 |
Linear Models(3) |
Kundu |
| |
Theory of the general linear parametric model. Includes least squares estimation, multiple comparisons procedures, variance components estimation. Prerequisite: Stat 6201- 2; Math 2184. (Spring, alternate years) |
| 6221 |
Design of Experiments for Behavioral Sciences(3) |
Staff |
| |
Applications of advanced experimental design to research problems in behavioral sciences and education. Prerequisite: Stat 2105 or 2118 or equivalent and permission of instructor. Not open to graduate students in statistics. (Spring) |
| 6223 |
Bayesian Statistics: Theory and Applications(3) |
Singpurwalla, Bose |
| |
An overview of Bayesian statistics, including its foundational issues, decision under uncertainty, linear models, expert opinion, and computational issues. Prerequisite: Stat 6201- 2. (Spring, alternate years) |
| 6227 |
Survival Analysis(3) |
Li, Pan |
| |
Parametric and nonparametric methods for the analysis of events observed in time (survival data), including Kaplan-Meier estimate of survival functions, logrank and generalized Wilcoxon tests, the Cox proportional hazards model and an introduction to counting processes. Prerequisite: Stat 6201- 2 or permission of instructor. (Fall) |
| 6231 |
Categorical Data Analysis(3) |
Kundu |
| |
A study of the theoretical bases underlying the analysis of categorical data. Measures and tests of association; Mantel-Haenszel procedure; weighted least squares and maximum likelihood estimators in linear models; estimating equations; logistic regression; loglinear models. Prerequisite: Stat 6201- 2. (Fall, alternate years) |
| 6233 |
Questionnaire Design(3) |
Staff |
| |
Questionnaire development from the perspective of cognitive techniques. Questionnaire issues range from choosing the mode of data collection (mail, telephone, or in-person) to selecting the respondent to the differences between asking attitude and factual questions. Pretesting the instrument chosen. |
| 6234 |
Intermediate Statistical Laboratory: Statistical Computing Packages(3) |
Staff |
| |
Application of program packages (e.g., SAS, SPSS) to the solution of one-, two- and k-sample parametric and nonparametric statistical problems. Basic concepts in data preparation, modification, analysis and interpretation of results. Prerequisite: an introductory statistics course. (Fall and spring) |
| 6236 |
Introduction to Sampling(3) |
Staff |
| |
Problems of sampling and sample design. Simple random, stratified, systematic, cluster, and multistate designs; control of sampling and non-sampling errors. Prerequisite: Stat 1051 or equivalent. (Fall) |
| 6238 |
Survey Management(3) |
Staff |
| |
Tools used in the management of a survey operation from the initial customer contacts through training, fieldwork, data processing, data analysis, report writing, and presentation of results. Issues in budgeting, staffing, and scheduling, with emphasis on quality management. (Fall) |
| 6242 |
Regression Graphics/Nonparametric Regression(3) |
Bura |
| |
Linear regression, nonparametric regression, smoothing techniques, additive models, regression trees, neural networks, and dimension reduction methods. Prerequisite: Stat 2118; Math 2233, 2184, or equivalent. (Spring, alternate years) |
| 6282 |
Foundational Issues in Risk Analysis(3) |
Landon |
| |
Descriptive statistics, classical probability, Venn diagrams, conditional probability, Bayes' law and law of total probability. Independence and interdependence, discrete and continuous random variables. Probability models, correlation, interpretation of probability (physical, logical, personal, and subjective). The likelihood function and personal probability. Statistical inference (frequentist and Bayesian). |
| 6283 |
Essentials of Risk Analysis(3) |
Singpurwalla and Staff |
| |
Utility and risk. The psychology of risk. Decision trees and decision making under uncertainty. Fault and event trees. Decision trees in risk, safety analysis, infrastructure protection. Simulating rare events. The failure rate functions. The cumulative hazard and survival function. Univariate and multivariate failure models. Causal, cascading, and interdependent failure events. Graphical analysis. Network survivability assessments. |
| 6284 |
Case Studies: 9/11 Experience(3) |
Staff |
| |
Focus on 9/11-like risks to U.S. Critical Infrastructure Key Resources (CIKR). Critical overview of many approaches used in estimating risk in the CIKR arena. Real-time statistical and computer risk modeling. Topics include 18 CIKR sectors, basic risk models for CIKR assets, risk of complex targets and systems, and current state of practice. |
| 6285 |
Case Studies: Environmental, Health, and Financial Risk(3) |
Staff |
| |
Risks encountered in financial markets, sustainability and climate change, and drug safety and health delivery systems. Development of models and reliable tools for optimal decision-making. |
| 6287-8288 |
Modern Theory of Sample Surveys(3-3) |
Larsen |
| |
Application of statistical theory to the sampling of finite populations. Simple, stratified, cluster, double and subsampling. Special topics, including super-populations and randomized response. Prerequisite: Stat 4157- 58 or equivalent. (Alternate academic years) |
| 6289 |
Topics in Statistics(3) |
Staff |
| 6290 |
Principles of Demography(3) |
Staff |
| |
Same as Econ 6290. |
| 6291 |
Methods of Demographic Analysis(3) |
Staff |
| |
Same as Econ 6291. |
| 6295 |
Reading and Research(3) |
Staff |
| |
May be repeated once for credit. |
| 6998-99 |
Thesis Research(3-3) |
Staff |
| 8226 |
Advanced Biostatistical Methods(3) |
Li, Pan |
| |
Statistical methods for the analysis of longitudinal data: nonparametric, fixed effects, mixed effects, generalized estimating equations. Methods for the analysis of emerging data: group sequential analysis, Brownian motion, Bayesian methods, and stochastic curtailment. Other advanced topics of current research in biostatistics. Prerequisite: Stat 6201- 2 or permission of instructor. (Spring) |
| 8257 |
Probability(3) |
Balaji, Mahmoud |
| |
Probabilistic foundations of statistics, probability distributions, random variables, moments, characteristic functions, modes of convergence, limit theorems, probability bounds. Prerequisite: Stat 6201- 2, knowledge of calculus through functions of several variables and series. (Fall) |
| 8258 |
Distribution Theory(3) |
Gastwirth, Mahmoud |
| |
Special distributions of statistics, small and large sample theory, order statistics, and spacings. Prerequisite: Stat 8257. (Spring) |
| 8259 |
Advanced Probability(3) |
Mahmoud |
| |
Conditional expectation and martingales; weak convergence in general metric spaces and functional central limit theorems for i.i.d. random variables and martingales; applications to biostatistics. Prerequisite: Stat 8257 or an equivalent measure-theoretic introduction to probability. |
| 8262 |
Nonparametric Inference(3) |
Kundu |
| |
Inference when the form of the underlying distribution is unspecified. Prerequisite: Stat 6201- 2. |
| 8263 |
Advanced Statistical Theory I(3) |
Nayak, Bose |
| |
Decision theoretic estimation, classical point estimation, hypothesis testing. Prerequisite: Stat 6201- 2. (Fall) |
| 8264 |
Advanced Statistical Theory II(3) |
Nayak, Bose |
| |
Asymptotic theory, hypothesis testing, confidence regions. Prerequisite: Stat 8257, 8263. (Spring) |
| 8265 |
Multivariate Analysis(3) |
Nayak, Modarres |
| |
Multivariate normal distribution. Hotelling's T2 and generalized T20, Wishart distribution, discrimination and classification. Prerequisite: Stat 6201- 2. (Fall, alternate years) |
| 8271 |
Foundational and Philosophical Issues in Statistics(3) |
Singpurwalla |
| |
Axiomatic underpinnings of Bayesian statistics, including subjective probability, belief, utility, decision and games, likelihood principle, and stopping rules. Examples from legal, forensic, biological, and engineering sciences. Students are expected to have a background in computer science, economics, mathematics, or operations research. Prerequisite: Stat 6201- 2. |
| 8273-74 |
Stochastic Processes(3-3) |
Mahmoud, Singpurwalla |
| |
Fundamental notions of Markov chains and processes, generating functions, recurrence, limit theorems, random walks, Poisson processes, birth and death processes, applications. Prerequisite: Stat 6201- 2. (Alternate academic years) |
| 8375 |
Econometrics I(3) |
Staff |
| |
Same as Econ 8375. |
| 8376 |
Econometrics II(3) |
Staff |
| |
Same as Econ 8376. |
| 8281 |
Advanced Time Series Analysis(3) |
Stroud |
| |
Autoregressive integrated moving average (ARIMA) modeling and forecasting of univariate and multivariate time series. Statespace or Kalman filter models, spectral analysis of multiple time series. Theory and applications using the University computer. Prerequisite: Math 2233, Stat 6201- 2 or equivalent. (Spring) |
| 8289 |
Seminar(3) |
Staff |
| |
Admission by permission of instructor. |
| 8998 |
Advanced Reading and Research(arr.) |
Staff |
| |
Limited to students preparing for the Doctor of Philosophy general examination. May be repeated for credit. |
| 8999 |
Dissertation Research(arr.) |
Staff |
| |
Limited to Doctor of Philosophy candidates. May be repeated for credit. |
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