Statistics
Apply NowAdmission Requirements
The well-prepared applicant to the department's Master's programs has good grades in a three-semester calculus sequence, a two-semester advanced calculus sequence, a semester of linear algebra, and a two-semester sequence in probability and statistics. Some of these courses may be taken as part of the program, but this may result in lengthening the stay. Students may apply to either the Master’s or PhD program directly from a Bachelor’s degree. GRE General Test scores are required for the in-person program, but Subject Test scores are not. Due to the differences in student backgrounds, there is a separate admissions process for the online and in-person programs.
The written statement should not exceed two pages and should describe the applicant's academic and career goals as well as special interests in the area of statistics. Applicants may also submit a resume. Individuals applying for fall enrollment and who wish to be considered for financial aid should have their completed applications in by no later than December 15 of the preceding year. Applications arriving after that will be considered but may be assigned lower priority. Starting Summer of 2013, we will begin to offer courses to allow a student to complete the Master of Statistics degree in one calendar year. The one year masters program has the same requirements as the current Master of Statistics program. Since courses start in the summer, the deadline to submit completed applications is January 15 of the same year, and student should apply for 'Summer 1' admission. Students are not normally admitted for spring.
Master's Degree Requirements
All Master's programs in statistics require a minimum of 34 credit hours, of which 12 are first-year core (ST 512, ST 521, ST 522, ST 552 and their labs), one is supervised consulting (ST 641). The remainders are statistics and/or supporting electives.
Doctoral Degree Requirements
The Ph.D. program in statistics requires 22 course credit hours beyond the Master's, of which 9 are Ph.D. core courses (ST 779, ST 793, and ST 758), one is supervised consulting (ST 841), and 12 are Ph.D.-level statistics electives.
Student Financial Support
Departmental assistantships and fellowships are awarded to students in the Ph.D. program each year on a competitive basis.
Other Relevant Information
With a large graduate faculty representing virtually all major statistical specializations, the department is recognized as a world leader in graduate education and research in statistics. The Department provides a dynamic environment for teaching, core research and collaborative research across disciplines, with formal program concentrations in biostatistics, bioinformatics, environmental, financial and mathematical statistics.
Degrees
- Statistics (MR)
- Statistics (MR): Biostatistics Concentration
- Statistics (MR): Distance Track
- Statistics (MR): Environmental Statistics Concentration
- Statistics (MR): Financial Concentration
- Statistics (MR): Statistical Genetics Concentration
- Statistics (PhD)
- Statistics (Minor)
- Applied Statistics and Data Management (Certificate)
- Statistics Education (Certificate)
Faculty
Full Professors
- Dennis D. Boos
- Marie Davidian
- Sujit K. Ghosh
- Subhashis Ghoshal
- Kevin Gross
- Marcia Lynn Gumpertz
- Jacqueline M. Hughes-Oliver
- Eric Benjamin Laber
- Wenbin Lu
- Ryan G. Martin
- Spencer V. Muse
- Jason A. Osborne
- Brian J. Reich
- Rui Song
- Ana-Maria Staicu
- Leonard A. Stefanski
- Jeffrey L. Thorne
- Jung-Ying Tzeng
- Alyson Gabbard Wilson
- Fred Andrew Wright
- Daowen Zhang
Associate Professors
- Xinge Jessie Jeng
- Arnab Maity
- Donald Eugene Kemp Martin
- Thomas W. Reiland
- Charles Eugene Smith
Assistant Professors
- Eric C. Chi
- Emily Hector
- Srijan Sengupta
- Jonathan W. Stallrich
- Minh Tang
- Jonathan Paul Williams
- Luo Xiao
- Shu Yang
Practice/Research/Teaching Professors
- Jonathan W. Duggins
- Emily H. Griffith
- Herle M. McGowan
- Logan J. Opperman
- Justin B. Post
- Paul R. Savariappan
- Shuting Wang
Emeritus Faculty
- William Reid Atchley
- Peter Bloomfield
- Cavell Brownie
- David Alan Dickey
- Thomas Michael Gerig
- Harvey J. Gold
- Thomas Johnson
- John F. Monahan
- Kenneth Hugh Pollock
- Charles P. Quesenberry
- John Oren Rawlings
- Don L. Ridgeway
- Moon Won Suh
- William H. Swallow
- Anastasios A. Tsiatis
- John L. Wasik
Adjunct Faculty
- Howard D. Bondell
- Soumendra Nath Lahiri
- Alison Anne Motsinger-Reif
- Eric A. Stone
- Yichao Wu
Courses
First of a two-semester sequence in probability and statistics taught at a calculus-based level. Probability: discrete and continuous distributions, expected values, transformations of random variables, sampling distributions. Credit not given for both ST 701 and ST 501. Note: this course will be offered in person (Fall) and online (Summer).
Prerequisite: MA 242 or equivalent
Typically offered in Fall and Summer
Second of a two-semester sequence in probability and statistics taught at a calculus-based level. Statistical inference: methods of construction and evaluation of estimators, hypothesis tests, and interval estimators, including maximum likelihood. Credit not given for both ST 702 and ST 502. Note: this course will be offered in person (Spring) and online (Fall).
Prerequisite: ST 501
Typically offered in Fall and Spring
Estimation and testing in full and non-full rank linear models. Normal theory distributional properties. Least squares principle and the Gauss-Markov theorem. Estimability, analysis of variance and co variance in a unified manner. Practical model-building in linear regression including residual analysis, regression diagnostics, and variable selection. Emphasis on use of the computer to apply methods with data sets. Credit not given for both ST 705 and ST 503. Note: this course will be offered in person (Spring) and online (Summer).
Typically offered in Spring and Summer
Statistical methods requiring relatively mild assumptions about the form of the population distribution. Classical nonparametric hypothesis testing methods, Spearman and Kendall correlation coefficients, permutation tests, bootstrap methods, and nonparametric regressions will be covered.
Typically offered in Fall only
Statistical methods applicable to sampling of wildlife populations, including capture-recapture, removal, change in ratio, quadrant and line transect sampling. Emphasis on model assumptions and study design.
Prerequisite: ST 512
Typically offered in Fall only
A general introduction to the use of descriptive and inferential statistics in behavioral science research. Methods for describing and summarizing data presented, followed by procedures for estimating population parameters and testing hypotheses concerning summarized data.
Prerequisite: Graduate standing
Typically offered in Fall and Spring
Introduction to use of statistical design principles in behavioral science research. Presentation of use of a statistical model to represent structure of data collected from a designed experiment or survey study. Opportunities provided for use of a computer to perform analyses of data, to evaluate proposed statistical model and to assist in post-hoc analysis procedures. Least squares principles used to integrate topics of multiple linear regression analysis, the analysis of variance and analysis of covariance.
Prerequisite: ST 507
Typically offered in Spring only
Basic concepts of statistical models and use of samples; variation, statistical measures, distributions, tests of significance, analysis of variance and elementary experimental design, regression and correlation, chi-square.
Prerequisite: Graduate Standing
Typically offered in Fall, Spring, and Summer
Covariance, multiple regression, curvilinear regression, concepts of experimental design, factorial experiments, confounded factorials, individual degrees of freedom and split-plot experiments. Computing laboratory addressing computational issues and use of statistical software.
Typically offered in Fall, Spring, and Summer
Analysis of data to represent facts, guide decisions and test opinions in managing systems and processes. Graphical and numerical data analysis for descriptive and predictive decisions. Scatter plot smoothing and regression analysis. Basic statistical inference. Integrated use of computer.
Prerequisite: Graduate standing
Typically offered in Fall and Spring
Linear regression, multiple regression and concepts of designed experiments in an integrated approach, principles of the design and analysis of sample surveys, use of computer for analysis of data.
Prerequisite: ST 513
Typically offered in Spring and Summer
General statistical concepts and techniques useful to research workers in engineering, textiles, wood technology, etc. Probability distributions, measurement of precision, simple and multiple regression, tests of significance, analysis of variance,enumeration data and experimental design.
Prerequisite: Graduate standing
Typically offered in Fall and Spring
General statistical concepts and techniques useful to research workers in engineering, textiles, wood technology, etc. Probability distributions, measurement of precision, simple and multiple regression, tests of significance, analysis of variance, enumeration data and experimental designs.
Prerequisite: ST 515
Typically offered in Fall and Spring
Course covers basic methods for summarizing and describing data, accounting for variability in data, and techniques for inference. Topics include basic exploratory data analysis, probability distributions, confidence intervals, hypothesis testing, and regression analysis. This is a calculus-based course. Statistical software is used; however, there is no lab associated with the course. Credit not given for this course and ST 511 or ST 513 or ST 515. This course does NOT count as an elective towards a degree or a minor in Statistics. Note: the course will be offered in person (Fall) and online (Fall and Summer).
Typically offered in Fall and Summer
This second course in statistics for graduate students is intended to further expand students' background in the statistical methods that will assist them in the analysis of data. Course covers many fundamental analysis methods currently used to analyze a wide array of data, mostly arising from designed experiments. Topics include multiple regression models, factorial effects models, general linear models, mixed effect models, logistic regression analysis, and basic repeated measures analysis. This is a calculus-based course. Statistical software is used, however, there is no lab associated with the course. Credit not given for this course and ST 512 or ST 514 or ST 516. Note: this course will be offered in person (Spring) and online (Fall and Spring).
Prerequisite: ST 517
Typically offered in Fall and Spring
This course is designed to bridge theory and practice on how students develop understandings of key concepts in data analysis, statistics, and probability. Discussion of students' understandings, teaching strategies and the use of manipulatives and technology tools. Topics include distribution, measures of center and spread, sampling, sampling distribution, randomness, and law of large numbers. Must complete a first level graduate statistics course ( ST 507, ST 511, or equivalent) before enrolling.
Typically offered in Spring only
Statistical methods for design and analysis of clinical trials and epidemiological studies. Phase I, II, and III clinical trials. Principle of Intention-to-Treat, effects of non-compliance, drop-outs. Interim monitoring of clinical trials and data safety monitoring boards. Introduction to meta-analysis. There is also discussion of Epidemiological methods time permitting.
Typically offered in Fall only
Principles and techniques of planning, establishing and executing field and greenhouse experiments. Size, shape and orientation of plots; border effects; estimation of size of experiments for specified accuracy; subsampling plots and yields for laboratory analysis; combining data from a series of years and/or locations; rotation experiments; repeated measures data; multiple comparisons in variety trial results; selection of predictors in multiple regression; introduction to interspecies and intraspecies plant competition experiments and models.
Prerequisite: ST 512
Typically offered in Fall only
Overview and comparison of observational studies and designed experiments followed by a thorough discussion of design principles. Review of estimation and inference for regression and ANOVA models from an experimental design perspective. Review of design and analysis for completely randomized, randomized complete block, and Latin square designs. Designs and analysis methods for factorial experiments, general blocking structures, incomplete block designs, confounded factorials, split-plot experiments, and fractional factorial designs. Examples used to illustrate application and analysis of these designs.
Typically offered in Fall only
Introduction to statistical models and methods for analyzing various types of spatially referenced data. The focus is on applications with real data and their analysis with statistical programs such as R and SAS. Students are required to write, modify, and run computer code in order to complete homework assignments and final projects.
Typically offered in Spring only
Statistical models and methods for the analysis of time series data using both time domain and frequency domain approaches. A brief review of necessary statistical concepts and R will be given at the beginning. Analyses of real data sets using the stati
Typically offered in Fall only
Use of statistics for quality control and productivity improvement. Control chart calculations and graphing, process control and specification; sampling plans; and reliability. Computer use will be stressed for performing calculations and graphing.
Typically offered in Fall only
An introduction to use of statistical methods for analyzing multivariate and longitudinal data collected in experiments and surveys. Topics covered include multivariate analysis of variance, discriminant analysis, principal components analysis, factor analysis, covariance modeling, and mixed effects models such as growth curves and random coefficient models. Emphasis is on use of a computer to perform statistical analysis of multivariate and longitudinal data.
Typically offered in Spring only
Introduction to Bayesian concepts of statistical inference; Bayesian learning; Markov chain Monte Carlo methods using existing software (SAS and OpenBUGS); linear and hierarchical models; model selection and diagnostics.
Typically offered in Spring only
This course will provide a discussion-based introduction to statistical practice geared towards students in the final semester of their Master of Statistics degree. Note: the course will be offered in person (Fall) and online (Spring and Summer).
Typically offered in Fall, Spring, and Summer
This course focuses on the concepts, methods, and models used to analyze categorical data, particularly contingency tables, count data and binary/binomial type of data. The topics covered include Pearson Chi-squared independence test for contingency tables, measures of marginal and conditional associations, small-sample inference, logistic regression models for independent binary/binomial data and many extended models for correlated binary/binomial data including matched data and longitudinal data. The course emphasizes the implementation of methods/models using SAS and the interpretation of the results from the output.
Typically offered in Fall only
Modern introduction to Probability Theory and Stochastic Processes. The choice of material is motivated by applications to problems such as queueing networks, filtering and financial mathematics. Topics include: review of discrete probability and continuous random variables, random walks, markov chains, martingales, stopping times, erodicity, conditional expectations, continuous-time Markov chains, laws of large numbers, central limit theorem and large deviations.
Typically offered in Fall only
An introduction to programming and data management using SAS, the industry standard for statistical practice. Detailed discussion of the program data vector and data handling techniques that are required to apply statistical methods. Topics are based on the current content of the Base SAS Certification Exam and typically include: importing, validating, and exporting of data files; manipulating, subsetting, and grouping data; merging and appending data sets; basic detail and summary reporting; and code debugging. Additional topics with practical applications are also introduced, such as graphics and advanced reporting. Statistical methods for analyzing data are not covered in this course. Regular access to a computer for homework and class exercises is required. Previous exposure to SAS is not expected.
Prerequisite: Graduate standing
Typically offered in Fall, Spring, and Summer
Statistical procedures for importing/managing complex data structures using SQL, automated analysis using macro programming, basic simulation methods and text parsing/analysis procedures. Students learn SAS, the industry standard for statistical practice. Regular access to a computer for homework and class exercises is required.
P: ST 555 or Base SAS Certification
Typically offered in Spring and Summer
This course will provide statistics educators with an in-depth introduction to applying technology for teaching college statistics. In this course, students will explore a variety of available statistical packages, demonstration applets, and other technologies for teaching statistics. Students will learn pedagogy t help them structure learning activities around these technologies. Students will also learn to identify key elements in technologies that support pedagogical goals.
Typically offered in Fall only
Methods for reading, manipulating, and combining data sources including databases. Custom functions, visualizations, and summaries. Common analyses done by data scientists. Methods for communicating results including dashboards. Regular access to a computer for homework and class exercises is required.
Typically offered in Fall and Summer
Introduction and application of econometrics methods for analyzing cross-sectional data in economics, and other social science disciplines, such as OLS, IV regressions, and simultaneous equations models. Students should have had a statistical methods course at the 300 level or above as well as Calculus I and II.
Typically offered in Fall only
This is a hands-on course using modeling techniques designed mostly for large observational studies. Estimation topics include recursive splitting, ordinary and logistic regression, neural networks, and discriminant analysis. Clustering and association analysis are covered under the topic "unsupervised learning," and the use of training and validation data sets is emphasized. Model evaluation alternatives to statistical significance include lift charts and receiver operating characteristic curves. SAS Enterprise Miner is used in the demonstrations, and some knowledge of basic SAS programming is helpful.
Typically offered in Spring only
This course will introduce common statistical learning methods for supervised and unsupervised predictive learning in both the regression and classification settings. Topics covered will include linear and polynomial regression, logistic regression and discriminant analysis, cross-validation and the bootstrap, model selection and regularization methods, splines and generalized additive models, principal components, hierarchical clustering, nearest neighbor, kernel, and tree-based methods, ensemble methods, boosting, and support-vector machines.
Typically offered in Summer only
Typically offered in Fall, Spring, and Summer
Typically offered in Fall, Spring, and Summer
Special topics in Statistics.
Typically offered in Fall, Spring, and Summer
Typically offered in Spring only
Participation in regularly scheduled supervised statistical consulting sessions with faculty member and client. Consultant's report written for each session. Regularly scheduled meetings with course instructor and other student consultants to present an
Typically offered in Fall, Spring, and Summer
Teaching experience under the mentorship of faculty who assist the student in planning for the teaching assignment, observe and provide feedback to the student during the teaching assignment, and evaluate the student upon completion of the assignment.
Prerequisite: Master's student
Typically offered in Fall, Spring, and Summer
For students in non thesis master's programs who have completed all other requirements of the degree except preparing for and taking the final master's exam.
Prerequisite: Master's student
Typically offered in Fall, Spring, and Summer
Instruction in research and research under the mentorship of a member of the Graduate Faculty.
Prerequisite: Master's student
Typically offered in Fall, Spring, and Summer
Thesis Research
Prerequisite: Master's student
Typically offered in Fall, Spring, and Summer
For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.
Prerequisite: Master's student
Typically offered in Summer only
For students who have completed all credit hour requirements and full-time enrollment for the master's degree and are writing and defending their thesis. Credits Arranged
Prerequisite: Master's student
Typically offered in Fall, Spring, and Summer
Probability tools for statistics: description of discrete and absolutely continuous distributions, expected values, moments, moment generating functions, transformation of random variables, marginal and conditional distributions, independence, orderstatistics, multivariate distributions, concept of random sample, derivation of many sampling distributions.
Typically offered in Fall only
General framework for statistical inference. Point estimators: biased and unbiased, minimum variance unbiased, least mean square error, maximum likelihood and least squares, asymptotic properties. Interval estimators and tests of hypotheses: confidence intervals, power functions, Neyman-Pearson lemma, likelihood ratio tests, unbiasedness, efficiency and sufficiency.
Prerequisite: ST 701
Typically offered in Spring only
Introduction of statistical methods. Examples include multiple linear regression, concepts of experimental design, factorial experiments, and random-effects modeling. A computing laboratory addresses computational issues and use of statistical software. This course is a prerequisite for most advanced courses in statistics. This section is restricted to statistics and closely related majors.
R: 17STPHD Students Only
Typically offered in Fall only
This course will introduce many methods that are commonly used in applications. Examples include: model generation, selection, assessment, and diagnostics in the context of multiple linear regression (including penalized regression); linear mixed models; generalized linear models; generalized linear mixed models; nonparametric regression and smoothing; and finite-population sampling basics. Coverage will include some theory, plus implementation using SAS and/or R.
Typically offered in Spring only
Theory of estimation and testing in full and non-full rank linear models. Normal theory distributional properties. Least squares principle and the Gauss-Markoff theorem. Estimability and properties of best linear unbiased estimators. General linear hypo
Corequisite: ST 702
Typically offered in Spring only
An advanced mathematical treatment of analytical and algorithmic aspects of finite dimensional nonlinear programming. Including an examination of structure and effectiveness of computational methods for unconstrained and constrained minimization. Specia
Prerequisite: OR(IE,MA) 505 and MA 425
Typically offered in Spring only
Least squares estimation and hypothesis testing procedures for linear models. Consideration of regression, analysis of variance and covariance in a unified manner. Emphasis on use of the computer to apply these techniques to experimental (including unequal cell sizes) and survey situations.
Prerequisite: ST 512
Typically offered in Fall only
Review of completely randomized, randomized complete block and Latin square designs and basic concepts in the techniques of experimental design. Designs and analysis methods in factorial experiments, confounded factorials, response surface methodology, change-over design, split-plot experiments and incomplete block designs. Examples used to illustrate application and analysis of these designs.
Typically offered in Fall only
Principles for interpretation and design of sample surveys. Estimator biases, variances and comparative costs. Simple random sample, cluster sample, ratio estimation, stratification, varying probabilities of selection. Multi-stage, systematic and double sampling. Response errors.
Typically offered in Fall only
Analysis of discrete data, illustrated with genetic data on morphological characters allozymes, restriction fragment length polymorphisms and DNA sequences. Maximum likelihood estimation, including iterative procedures. Numerical resampling. Development of statistical techniques for characterizing genetic disequilibrium and diversity. Measures of population structure and genetic distance. Construction of phylogenetic trees. Finding alignments and similarities between DNA sequences. Locating genes with markers.
Typically offered in Spring only
An introduction to use of statistical methods for analyzing and forecasting data observed over time. Trigonometric regression, periodogram/spectral analysis. Smoothing. Autoregressive moving average models. Regression with autocorrelated errors. Linear filters and bivariate spectral analysis. Stress on methods and applications; software implementations described and used in assignments.
Prerequisite: ST 512
Typically offered in Fall only
Introduction to modeling longitudinal data; Population-averaged vs. subject-specific modeling; Classical repeated measures analysis of variance methods and drawbacks; Review of estimating equations; Population-averaged linear models; Linear mixed effects models; Maximum likelihood, restricted maximum likelihood, and large sample theory; Review of nonlinear and generalized linear regression models; Population-averaged models and generalized estimating equations; Nonlinear and generalized linear mixed effects models; Implications of missing data; Advanced topics (including Bayesian framework, complex nonlinear models, multi-level hierarchical models, relaxing assumptions on random effects in mixed effects models, among others). Implementation in SAS and R.
Typically offered in Spring only
Introduction to the theory and methods of spatial data analysis including: visualization; Gaussian processes; spectral representation; variograms; kriging; computationally-efficient methods; nonstationary processes; spatiotemporal and multivariate models.
Prerequisite: ST 705
Typically offered in Spring only
Introduction to Bayesian inference; specifying prior distributions; conjugate priors, summarizing posterior information, predictive distributions, hierachical models, asymptotic consistency and asymptotic normality. Markov Chain Monte Carlo (MCMC) methods and the use of exising software(e.g., WinBUGS).
Prerequisite: ST 702
Typically offered in Fall only
Statistical models and methods for categorical responses including the analysis of contingency tables, logistic and Poisson regression, and generalized linear models. Survey of asymptotic and exact methods and their implementation using standard statistical software.
Typically offered in Spring only
Statistical methods for analysis of time-to-event data, with application to situations with data subject to right-censoring and staggered entry, including clinical trials. Survival distribution and hazard rate; Kaplan-Meier estimator for survival distribution and Greenwood's formula; log-rank and weighted long-rank tests; design issues in clinical trials. Regression models, including accelerated failure time and proportional hazards; partial likelihood; diagnostics.
Typically offered in Spring only
Markov chains and Markov processes, Poisson process, birth and death processes, queuing theory, renewal theory, stationary processes, Brownian motion.
Prerequisite: MA 405 and MA(ST) 546 or ST 521
Typically offered in Spring only
Fundamental mathematical results of probabilistic measure theory needed for advanced applications in stochastic processes. Probability measures, sigma-algebras, random variables, Lebesgue integration, expectation and conditional expectations w.r.t.sigma algebras, characteristic functions, notions of convergence of sequences of random variables, weak convergence of measures, Gaussian systems, Poisson processes, mixing properties, discrete-time martingales, continuous-time markov chains.
Prerequisite: MA(ST) 546
Typically offered in Spring only
Theory of stochastic differential equations driven by Brownian motions. Current techniques in filtering and financial mathematics. Construction and properties of Brownian motion, wiener measure, Ito's integrals, martingale representation theorem, stochastic differential equations and diffusion processes, Girsanov's theorem, relation to partial differential equations, the Feynman-Kac formula.
Prerequisite: MA(ST) 747
Typically offered in Fall only
Introduction to principles of estimation of linear regression models, such as ordinary least squares and generalized least squares. Extensions to time series and panel data. Consideration of endogeneity and instrumental variables estimation. Limited dependent variable and sample selection models. Attention to implementation of econometric methods using a statistical package and microeconomic and macroeconomic data sets.
Typically offered in Spring only
Introduction to important econometric methods of estimation such as Least Squares, instrumentatl Variables, Maximum Likelihood, and Generalized Method of Moments and their application to the estimation of linear models for cross-sectional ecomomic data. Discussion of important concepts in the asymptotic statistical analysis of vector process with application to the inference procedures based on the aforementioned estimation methods.
Typically offered in Fall only
The characteristics of macroeconomic and financial time series data. Discussion of stationarity and non-stationarity as they relate to economic time series. Linear models for stationary economic time series: autoregressive moving average (ARMA) models;
Prerequisite: ECG(ST) 751
Typically offered in Spring only
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-parametricmeth
Prerequisite: ECG 751
Typically offered in Spring only
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.
Prerequisite: ST 512, ST 552
Typically offered in Spring only
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.
Typically offered in Fall only
The essence of quantitative genetics is to study multiple genes and their relationship to phenotypes. How to study and interpret the relationship between phenotypes and whole genome genotypes in a cohesive framework is the focus of this course. We discuss how to use genomic tools to map quantitative trait loci, how to study epistasis, how to study genetic correlations and genotype-by-environment interactions. We put special emphasis in using genomic data to study and interpret general biological problems, such as adaptation and heterosis. The course is targeted for advanced graduate students interested in using genomic information to study a variety of problems in quantitative genetics.
Prerequisite: ST 511
Typically offered in Fall only
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.
Typically offered in Fall only
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.
Prerequisite: Advanced calculus, reasonable background in biology
Typically offered in Fall only
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.
Prerequisite: BMA 771, elementary probability theory
Typically offered in Spring only
Survey of modeling approaches and analysis methods for data from continuous state random processes. Emphasis on differential and difference equations with noisy input. Doob-Meyer decomposition of process into its signal and noise components. Examples from biological and physical sciences, and engineering. Student project.
Prerequisite: BMA 772 or ST (MA) 746
Typically offered in Spring only
Sets and classes, sigma-fields and related structures, probability measures and extensions, random variables, expectation and integration, uniform integrability, inequalities, L_p-spaces, product spaces, independence, zero-one laws, convergence notions, characteristic functions, simplest limit theorems, absolute continuity, conditional expectation and conditional probabilities, martingales.
Prerequisite: ST 702
Typically offered in Fall only
Survey of multivariate statistical theory. Multivariate distributions including the multinormal, Wishart, Hotelling's T, Fisher-Roy-Hsu, Wilks' and multivariate Beta distributions. Applications of maximum likelihood estimation, likelihood ratio testing and the union-intersection principle. Development of the theory of Hotelling's T tests and confidence sets, discriminant analysis, canonical correlation, multivariate analysis of variance and principal components.
Prerequisite: ST 522
Typically offered in Spring only
Typically offered in Fall, Spring, and Summer
Statistical inference with emphasis on the use of statistical models, construction and use of likelihoods, general estimating equations, and large sample methods. Includes introduction to Bayesian statistics and the jackknife and bootstrap.
Prerequisite: ST 702
Typically offered in Spring only
Typically offered in Fall and Spring
Typically offered in Fall and Spring
Typically offered in Fall and Spring
Typically offered in Spring only
Participation in regularly scheduled supervised statistical consulting sessions with faculty member and client. Consultant's report written for each session. Regularly scheduled meetings with course instructor and other student consultants to present an
Typically offered in Fall only
Teaching experience under the mentorship of faculty who assist the student in planing for the teaching assignment, observe and provide feedback to the student during the teaching assignment, and evaluate the student upon completion of the assignment.
Prerequisite: Doctoral student
Typically offered in Fall, Spring, and Summer
For students who are preparing for and taking written and/or oral preliminary exams.
Prerequisite: Doctoral student
Typically offered in Fall, Spring, and Summer
Instruction in research and research under the mentorship of a member of the Graduate Faculty.
Prerequisite: Doctoral student
Typically offered in Fall, Spring, and Summer
Dissertation Research
Prerequisite: Doctoral student
Typically offered in Fall, Spring, and Summer
For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.
Prerequisite: Doctoral student
Typically offered in Summer only
For students who have completed all credit hour requirements, full-time enrollment, preliminary examination, and residency requirements for the doctoral degree, and are writing and defending their dissertations.
Prerequisite: Doctoral student
Typically offered in Fall, Spring, and Summer