Statistics

http://www.uvm.edu/~cems/mathstat/

Overview

The Statistics Program offers biostatistics, statistics, and probability courses for the entire university community along with traditional degree programs and individually designed degree programs emphasizing statistics applied to other fields. The degree programs are designed primarily for students who plan careers in business, actuarial science, industry, and government or advanced training in disciplines that make extensive use of statistical principles and methods. The program faculty is deeply involved in consulting and collaborative research in a wide variety of fields, including industry, agriculture, and in the basic and clinical medical sciences. These research activities along with the research of other quantitative UVM faculty offer students unique opportunities to apply their classroom training to "real world" problems. Qualified students with the goal of learning statistics to use in a specialized area of application are especially encouraged to take advantage of these cooperative arrangements.

Program faculty have active statistics research efforts in areas such as bioinformatics, sequential analysis, three stage sampling, time series analysis, survival data analysis, discriminant analysis, bootstrap methods, categorical data analysis, measurement error models, and experimental design. Students seeking the traditional graduate degree in statistics (along with course work in mathematics and computer science, if desired) have excellent opportunities to participate in the faculty's research.

Degrees

Ashikaga, Takamaru; Professor, Department of Mathematics and Statistics; PHD, University of California Los Angeles
Bentil, Daniel E.; Associate Professor, Department of Mathematics and Statistics; DPHIL, University of Oxford
Bunn, Janice Yanushka; Research Associate Professor, Department of Mathematics and Statistics; PHD, Ohio State University
Buzas, Jeff Sandor; Professor, Department of Mathematics and Statistics; PHD, North Carolina State University Raleigh
Callas, Peter W.; Research Associate Professor, Department of Mathematics and Statistics; PHD, University of Massachusetts Amherst
Danforth, Christopher M.; Associate Professor, Department of Mathematics and Statistics; PHD, University of Maryland College Park
Dinitz, Jeffrey Howard; Professor, Department of Mathematics and Statistics; PHD, Ohio State University
Dodds, Peter S.; Professor, Department of Mathematics and Statistics; PHD, Massachusetts Institute of Technology
Ellis-Monaghan, Joanna; Adjunct Professor, Department of Mathematics & Statistics, PHD, University of North Carolina, Chapel Hill
Foote, Richard Martin; Professor, Department of Mathematics and Statistics; PHD, University of Cambridge
Golden, Kenneth Ivan; Professor, Department of Mathematics and Statistics; PHD, University De Paris
Jefferys, William; Lecturer I, Department of Mathematics and Statistics; PHD, Yale University
Lakoba, Taras Igorevich; Associate Professor, Department of Mathematics and Statistics; PHD, Clarkson University
Mickey, Ruth Mary; Professor, Department of Mathematics and Statistics; PHD, University of California Los Angeles
Sands, Jonathan Winslow; Professor, Department of Mathematics and Statistics; PHD, University of California San Diego
Scarpino, Samuel V.; Assistant Professor, Department of Mathematics and Statistics; PHD, University of Texas at Austin
Single, Richard M.; Associate Professor, Department of Mathematics and Statistics; PHD, SUNY Stony Brook
Son, Mun Shig; Professor, Department of Mathematics and Statistics; PHD, Oklahoma State University
Warrington, Gregory S.; Assistant Professor, Department of Mathematics and Statistics; PHD, Harvard University
Wilson, James Michael; Professor, Department of Mathematics and Statistics; PHD, University of California Los Angeles
Yang, Jianke; Professor, Department of Mathematics and Statistics; PHD, Massachusetts Institute of Technology
Yu, Jun; Professor, Department of Mathematics and Statistics; PHD, University of Washington Seattle

Courses

STAT 200. Med Biostatistics&Epidemiology. 3 Credits.

Introductory design and analysis of medical studies. Epidemiological concepts, case-control and cohort studies. Clinical trials. Students evaluate statistical aspects of published health science studies. Prerequisite: STAT 111, STAT 141, STAT 143, or STAT 211. Cross-listed with: BIOS 200.

STAT 201. Stat Computing & Data Analysis. 3 Credits.

Fundamental data processing, code development, graphing and analysis using statistical software packages, including SAS and R. Analysis of data and interpretation of results. Prerequisite: STAT 111 with Instructor permission, or STAT 141 or STAT 211.

STAT 211. Statistical Methods I. 3 Credits.

Fundamental concepts for data analysis and experimental design. Descriptive and inferential statistics, including classical and nonparametric methods, regression, correlation, and analysis of variance. Statistical software. Prerequisite: Junior standing. Cross-listed with: BIOS 211.

STAT 221. Statistical Methods II. 3 Credits.

Cross-listed with: BIOS 221. Multiple regression and correlation. Basic experimental design. Analysis of variance (fixed, random, and mixed models). Analysis of covariance. Computer software usage. Prerequisite: STAT 141, STAT 143, or STAT 211.

STAT 223. Applied Multivariate Analysis. 3 Credits.

Multivariate normal distribution. Inference for mean vectors and covariance matrices. Multivariate analysis of variance (MANOVA), discrimination and classification, principal components, factor and cluster analysis. Prerequisite: Any 200-level Statistics course, STAT 221 or STAT 225 recommended, matrix algebra recommended. Cross-listed with: BIOS 223.

STAT 224. Stats for Quality&Productivity. 3 Credits.

Statistical process control; Shewhart, cusum and other control charts; process capability studies. Total Quality Management. Acceptance, continuous, sequential sampling. Process design and improvement. Case studies. Prerequisite: STAT 141, STAT 143, or STAT 211.

STAT 225. Applied Regression Analysis. 3 Credits.

Simple linear and multiple regression models; least squares estimates, correlation, prediction, forecasting. Problems of multicollinearity and influential data (outliers).

STAT 229. Survival/Logistic Regression. 3 Credits.

Models and inference for time-to-event and binary data. Censored data, life tables, Kaplan-Meier estimation, logrank tests, proportional hazards models. Logistic regression-interpretation, assessment, model building, special topics. Prerequisite: STAT 221 or above. Cross-listed with: BIOS 229.

STAT 231. Experimental Design. 3 Credits.

Randomization, complete and incomplete blocks, cross-overs, Latin squares, covariance analysis, factorial experiments, confounding, fractional factorials, nesting, split plots, repeated measures, mixed models, response surface optimization. Prerequisite: STAT 211; STAT 221 recommended.

STAT 233. Survey Sampling. 3 Credits.

Design and data analysis for sample surveys. Simple random, stratified, systematic, cluster, multistage sampling. Practical issues in planning and conducting surveys. Prerequisite: STAT 211; or STAT 141 or STAT 143 with Instructor permission.

STAT 235. Categorical Data Analysis. 3 Credits.

Measures of association and inference for categorical and ordinal data in multiway contingency tables. Log linear and logistic regression models. Prerequisite: STAT 211. Cross-listed with: BIOS 235.

STAT 237. Nonparametric Statistical Mthd. 3 Credits.

Nonparametric and distribution free methods; categorical, ordinal, and quantitative data; confidence intervals; rank and chi-square hypothesis tests; computer-intensive procedures (bootstrap, exact tests). Prerequisite: STAT 211; or STAT 141 or STAT 143 with Instructor permission.

STAT 241. Statistical Inference. 3 Credits.

Introduction to statistical theory: related probability fundamentals, derivation of statistical principles, and methodology for parameter estimation and hypothesis testing. Prerequisites: STAT 151, STAT 153, or STAT 251, and STAT 141 or equivalent, and MATH 121. Cross-listed with: BIOS 241.

STAT 251. Probability Theory. 3 Credits.

Distributions of random variables and functions of random variables. Expectations, stochastic independence, sampling and limiting distributions (central limit theorems). Concepts of random number generation. Prerequisite: MATH 121; STAT 151 or STAT 153 recommended. Cross-listed with: MATH 207, BIOS 251.

STAT 252. Appl Discr Stochas Proc Models. 1 Credit.

Markov chain models for biological, social, and behavioral systems models. Random walks, transition and steady-state probabilities, passage and recurrence times. Prerequisite: STAT 151, STAT 153, or STAT 251.

STAT 253. Appl Time Series & Forecasting. 3 Credits.

Autoregressive moving average (Box-Jenkins) models, autocorrelation, partial correlation, differencing for nonstationarity, computer modeling. Forecasting, seasonal or cyclic variation, transfer function and intervention analysis, spectral analysis. Prerequisite: STAT 211 or STAT 225; or STAT 141 or STAT 143 with Instructor permission. Cross-listed with: CSYS 253.

STAT 256. Neural Computation. 3 Credits.

Introduction to artificial neural networks, their computational capabilities and limitations, and the algorithms used to train them. Statistical capacity, convergence theorems, backpropagation, reinforcement learning, generalization. Prerequisites: MATH 122 or MATH 124 or MATH 271; STAT 143 or STAT 153 or equivalent; CS 110. Cross-listed with: CS 256, CSYS 256.

STAT 261. Statistical Theory. 3 Credits.

Point and interval estimation, hypothesis testing, and decision theory. Application of general statistical principles to areas such as nonparametric tests, sequential analysis, and linear models. Prerequisite: STAT 251; or STAT 151 or STAT 153 with Instructor permission. Cross-listed with: BIOS 261.

STAT 265. Integrated Product Development. 3 Credits.

Project-based course focusing on the entire product life cycle. Team dynamics, process and product design, quality, materials, management, and environmentally-conscious manufacturing. Prerequisite: Senior standing. Cross-listed with: BSAD 293.

STAT 281. Statistics Practicum. 1-3 Credits.

Intensive experience in carrying out a complete statistical analysis for a research project in substantive area with close consultation with a project investigator. Prerequisite: STAT 200 or STAT 201 or STAT 221 through STAT 237 or STAT 253; some statistical software experience; Instructor permission.

STAT 287. Data Science I. 3 Credits.

Data harvesting, cleaning, and summarizing. Working with non-traditional, non-numeric data (social network, natural language textual data, etc.). Scientific visualization using static and interactive "infographics". A practical focus on real datasets, and developing good habits for rigorous and reproducible computational science. Prerequisites: CS 020 or CS 021; STAT 141 or STAT 143 or STAT 211; CS 110 and MATH 124 recommended.

STAT 295. Advanced Special Topics. 1-18 Credits.

For advanced students. Lectures, reports, and directed readings on advanced topics. Prerequisite: As listed in schedule of courses.

STAT 308. Applied Biostatistics. 3 Credits.

The rationale and application of biostatistical methods in the biological, health and life sciences with emphasis on interpreting and reporting results. sciences. Prerequisite: STAT 141 or equivalent. Cross-listed with: MPBP 308, BIOS 308.

STAT 321. Seminar in Advanced Statistics. 1 Credit.

Seminar presentations and discussions of statistical literature pertaining to the theoretical aspects of methods studied in STAT 221, STAT 223, STAT 224, STAT 225, and STAT 229, respectively. Corequisites: STAT 221; STAT 241 or STAT 261 recommended.

STAT 323. Seminar in Advanced Statistics. 1 Credit.

Seminar presentations and discussions of statistical literature pertaining to the theoretical aspects of methods studied in STAT 221, STAT 223, STAT 224, STAT 225, and STAT 229, respectively. Co-requisites: STAT 223; STAT 241 or STAT 261 recommended.

STAT 324. Seminar in Advanced Statistics. 1 Credit.

Seminar presentations and discussions of statistical literature pertaining to the theoretical aspects of methods studied in STAT 221, STAT 223, STAT 224, STAT 225, and STAT 229, respectively Co-requisites: STAT 224; STAT 241 or STAT 261 recommended.

STAT 325. Seminar in Advanced Statistics. 1 Credit.

Seminar presentations and discussions of statistical literature pertaining to the theoretical aspects of methods studied in STAT 221, STAT 223, STAT 224, STAT 225, and STAT 229, respectively. Co-requisites: STAT 225 or STAT 221; STAT 241 or STAT 261 recommended.

STAT 329. Seminar in Advanced Statistics. 1 Credit.

Seminar presentations and discussions of statistical literature pertaining to the theoretical aspects of methods studied in STAT 221, STAT 223, STAT 224, STAT 225, and STAT 229, respectively. Co-requisite: STAT 229; STAT 241 or STAT 261 recommended.

STAT 330. Bayesian Statistics. 3 Credits.

Introduction to Bayesian inference. Posterior inference, predictive distributions, prior distribution selection. MCMC algorithms. Hierarchical models. Model checking and selection. Use of computer software. Pre/co-requisite: STAT 241 or STAT 251 or Instructor permission.

STAT 355. Statisticl Pattern Recognition. 3 Credits.

Analysis of algorithms used for feature selection, density estimation, and pattern classification, including Bayes classifiers, maximum likelihood, nearest neighbors, kernels, discriminants, neural networks and clustering. Prerequsite: STAT 241 or STAT 251, or Instructor permission. Cross-listed with: CS 355, CSYS 355.

STAT 360. Linear Models. 3 Credits.

Theory of linear models, least squares and maximum likelihood estimation, fixed, random and mixed models, variance component estimation, introduction to generalized linear models, bootstrapping. Prerequisites: STAT 261 and knowledge of matrix algebra or Instructor permission.

STAT 369. Applied Geostatistics. 3 Credits.

Introduction to the theory of regionalized variables, geostatistics (kriging techniques): special topics in multivariate analysis; Applications to real data subject to spatial variation are emphasized. Pre/co-requisites: STAT 223 or STAT 225, and CS 016 or CE 011 or permission. Cross-listed with: CSYS 369.

STAT 380. Sem:Statistics & Biostatistics. 0.5-1 Credits.

Presentation and discussion of current topics, methodological research and applications in Statistics and Biostatistics by graduate students, faculty and guest speakers. Prerequisite: Instructor Permission.

STAT 381. Statistical Research. 1-3 Credits.

Methodologic or data analytic research culminating in oral and written reports to the faculty. Prerequisite: Instructor permission. Cross-listed with: BIOS 381.

STAT 385. Consulting Practicum. 1-3 Credits.

Supervised field work in statistical consulting. Experiences may include advising UVM faculty and students or clients in applied settings such as industry and government agencies. Prerequisites: Second year Graduate standing in Statistics or Biostatistics and permission of Statistics Program Director.

STAT 387. Data Science II. 3 Credits.

Advanced data analysis, collection, and filtering. Statistical modeling, monte carlo statistical methods, and in particular Bayesian data analysis, including necessary probabilistic background material. A practical focus on real datasets and developing good habits for rigorous and reproducible computational science. Prerequisite: STAT 287 or Instructor permission.

STAT 391. Master's Thesis Research. 1-6 Credits.

STAT 395. Advanced Special Topics. 1-18 Credits.

Lectures or directed readings on advanced and contemporary topics not presently included in other statistics courses. Prerequisites: As listed in schedule of courses.