### Statistics

**Head:** R. Fricker

**Professors:** S. Keller, R. Gramacy, D. Higdon, I. Hoeschelle, S. Morton, J. Morgan, E. Smith, G. Vining, and W. Woodall

**Associate Professors:** X. Deng, P. Du, M. Ferreira, F. Guo, Y. Hong, L. House, I. Kim, S. Leman, and G. Terrell

**Associate Professor of Practice:** F. Faltin and J. Van Mullekom

**Assistant Professors:** C. Franck, L. Johnson, S. Ranganathan, S. Sengupta, X. Wu, and H. Zhu

**Collegiate Assistant Professors:** A. Driscoll, C. Lucero, H. Mahmoud, and J. Robertson Evia

**Research Assistant Professor:** A. Tegge

**Instructors:** H. Tavera and Z. Zhang

Web: www.stat.vt.edu

### Overview

Statistics courses are offered at both the undergraduate and the graduate levels for students preparing for professions in statistics, for students who need statistical tools to engage in scientific research, and for students who want to acquire knowledge of the important concepts of probability and statistical inference.

Statistics courses for graduate students and programs leading to the M.S. and Ph.D. degrees in statistics are described in the Graduate Catalog and in a special bulletin available from the department.

### Bachelor of Science in Statistics

All statistics majors are required to own specified personal computers and software. Consult the department for details.

A special brochure describing the department and the B.S. program, intended for prospective entering freshmen, is available from the department upon request.

Cooperative Education and Internship positions are available in industry and government, offering valuable practical experience. Students participating in such an experience can receive academic credit which will count towards graduation requirements.

#### Degree Requirements

The graduation requirements in effect at the time of graduation apply. When choosing the degree requirements information, always choose the year of your expected date of graduation. Requirements for graduation are referred to via university publications as "Checksheets". The number of credit hours required for degree completion varies among curricula. Students must satisfactorily complete all requirements and university obligations for degree completion.

The university reserves the right to modify requirements in a degree program. However, the university will not alter degree requirements less than two years from the expected graduation year unless there is a transition plan for students already in the degree program.

Please visit the University Registrar website at http://registrar.vt.edu/graduation-multi-brief/index1.html for degree requirements.

### Minor in Statistics

Please visit the University Registrar website at http://registrar.vt.edu/graduation-multi-brief/index1.html to view requirements for the minor.

The department reserves the right to withhold credit if a student takes a course, the content of which is partially duplicated in a course already taken (see "Course Duplications" below).

### The Statistical Applications and Innovations Group

Associated with the Department, the Statistical Applications and Innovations Group (SAIG) provides assistance for research projects to participating members of the University community and outside organizations. Statistics Department faculty members and students collaborate to design studies, analyze data, and interpret results for Virginia Tech affiliated clients and external clients in business, industry, government, and non-profit organizations. SAIG provides both experiential learning for statistics students and service to the University and beyond. To learn more, visit https://saig.stat.vt.edu/.

### Satisfactory Progress

University policy requires that students who are making satisfactory progress toward a degree meet minimum criteria toward the General Education (Curriculum for Liberal Education) (see "Academics") and toward the degree.

Satisfactory progress requirements toward the B.S. in Statistics can be found on the major checksheet by visiting the University Registrar website at http://registrar.vt.edu/graduation-multi-brief/index1.html.

### Course Duplications

- No credit will be given for 2004 if taken with or after any other statistics course, except STAT 2984.
- For non-majors, all of the following are partial duplications: 3005, 3604, 3615, 4604, and 4705.
- For majors, 4604 and 4705 may replace 3005 if taken before becoming a major.
- All the following are partial duplications: 3006, 3616, and 4706.
- No credit will be given for 3704 if taken after any of the following: 3005, 3615, 4604, and 4705.
- BIT 2405 may not be used as a substitute for credit as a statistics course unless the student was officially registered as a Business major at the time BIT 2405 was taken.

### Computer Literacy

Many statistics courses involve the use of statistics software, primarily MINITAB, SAS, JMP or R. Experience with the software is not expected, but students should have familiarity with either the Windows or Macintosh operating system and have access to a computer.

### Course Projects

Many of the upper-division courses include a project, generally to be completed in small groups. These projects are designed to give students the kind of insight and experience in realistic statistical practice that cannot be obtained in classroom lectures or short-term homework assignments.

### Undergraduate Course Descriptions (STAT)

1004: THE FIRST YEAR EXPERIENCE IN LEARNING FROM DATA

Introduction to the field of statistics and aspects of college life for first year students. Topics included: history of the statistics; key roles of statisticians in field, such as actuarial sciences, pharmaceutical, medical, and bioinformatics industries, governmental agencies, academia; fundamental principles of statistical fields of study and applications; exploring data sets; and aspects of college life for first-year students. (2H,2C)

1014: DATA IN OUR LIVES

Develop and practice the process of thinking critically with data in the context of real world problems. Import, manage, summarize, and visualize data using programmable, statistical software. Make data discoveries, make decisions, generate hypotheses, and/or communicate findings in data. Consider laws of probability and personal biases to weigh decisions. Recognize ethical issues and vulnerabilities in analyses when learning from data and extrapolating to large populations. (3H,3C)

1984: SPECIAL STUDY

Variable credit course.

2004: INTRODUCTORY STATISTICS

Fundamental concepts and methods of statistics with emphasis on interpretation of statistical arguments and statistical reasoning. Using modern, accessible statistical software and technology, an introduction to design of experiments (including data collection), data analysis, data visualization, correlation and regression, concepts of probability theory, sampling errors, confidence intervals, and hypothesis tests. Include real-world applications to develop problem-solving skills and consider ethical implications within the context of learning from data. Pre: MATH 1014 or MATH 1025 or MATH 1225 or MATH 1524 or MATH 1525. (3H,3C)

2524: DATA SCIENCE

Organize, summarize, and visualize large-scale datasets from web studies. Interpret visualizations and communicate information discovered by data explorations. Program in R or comparable statistics programming language. Not intended for statistics majors. Pre: (3005 or 3615), (MATH 1114, MATH 1206 or MATH 2015), (CS 1054 or CS 1064). (3H,3C)

2964: FIELD STUDY

Pass/Fail only. Variable credit course.

2974H: INDEPENDENT STUDY

Honors section. Variable credit course.

2984: SPECIAL STUDY

Variable credit course.

3005-3006: STATISTICAL METHODS

3005: Basic statistical methodology: exploratory data techniques, estimation, inference, comparative analysis by parametric, nonparametric, and robust procedures. Analysis of variance (one-way), multiple comparisons, and categorical data. Includes real-world examples. Develops problem-solving skills and ethical reasoning within the context of learning from data. 3006: Analysis of variance, simple and multiple, linear and nonlinear regression, analysis of covariance. Use of MINITAB. STAT 3005 duplicates STAT 3615 and STAT 4604, only one may be taken for credit. STAT 3006 duplicates STAT 3616, STAT 4604 and STAT 4706, only one may be taken for credit. Co: MATH 1206 or MATH 1226 for 3005. Pre: MATH 1205 or MATH 1225 for 3005; 3005 for 3006. (3H,3C)

3094: SAS PROGRAMMING

Introduction to basic programming techniques: creating DATA and PROC statements, libraries, functions, programming syntax and formats. Other topics include loops, SAS Macros and PROC IML. Emphasis is placed on using these tools for statistical analyses. The pre-requisite may be substituted for an equivalent course. Pre: 3005 or CMDA 2006. (3H,3C)

3104: PROBABILITY AND DISTRIBUTIONS

Probability theory, including set theoretic and combinatorial concepts; in-depth treatment of discrete random variables and distributions, with some introduction to continuous random variables; introduction to estimation and hypothesis testing. Pre: (MATH 1206 or MATH 1226 or MATH 2015 or MATH 1026 or MATH 1526), (STAT 3005 or S TAT 3615 or CMDA 2006). (3H,3C)

3424: INTRODUCTION TO STATISTICAL NEUROSCIENCE AND IMAGE ANALYSIS

Analysis of data arising in studies in neuroscience and from fMRI neuroimaging. Topics include background on neuroscience and the brain, overview of structural and functional MRI data, introduction to MATLAB, overview of linear models, contrasts, and statistical parametric mapping, experimental design, and Bayesian analysis. Pre: 3006 or 3616. (3H,3C)

3504: NONPARAMETRIC STATISTICS

Statistical methodology based on ranks, empirical distributions, and runs. One and two sample tests, ANOVA, correlation, goodness of fit, and rank regression, R-estimates and confidence intervals. Comparisons with classical parametric methods. Emphasis on assumptions and interpretation. Pre: 3006 or 3616 or 4106 or 4604 or 4706 or CMDA 2006. (3H,3C)

3604: STATISTICS FOR SOCIAL SCIENCE

Statistical methods for nominal, ordinal, and interval levels of measurement. Topics include descriptive statistics, elements of probability, discrete and continuous distributions, one and two sample tests, measures of association. Emphasis on comparison of methods and interpretations at different measurement levels. Includes real-world applications to develop problem-solving skills and ethical reasoning within the context of learning from data. Pre: MATH 1014 or MATH 1025 or MATH 1225 or MATH 1524 or MATH 1525. (3H,3C)

3615-3616: BIOLOGICAL STATISTICS

Descriptive and inferential statistics in a biological context with real-world examples. In analytical contexts, develops problem-solving skills and ethical reasoning. 3615: Fundamental principles, one- and two-sample parametric inference, simple linear regression, frequency data. 3616: One- and two-way ANOVA, multiple regression, correlation, nonparametrics, using a computer package. STAT 3615 partially duplicates STAT 3005 and STAT 4604, only one may be taken for credit. STAT 3616 partially duplicates STAT 3006, 4604 and 4706, only one may be taken for credit. Pre: MATH 1205 or MATH 1525 or MATH 1225 or MATH 1025 or MATH 1524 or ISC 1105 for 36 15; 3615 for 3616. (3H,3C)

3654 (CMDA 3654) (CS 3654): INTRODUCTORY DATA ANALYTICS & VISUALIZATION

Basic principles and techniques in data analytics; methods for the collection of, storing, accessing, and manipulating standard-size and large datasets; data visualization; and identifying sources of bias. Pre: (CS 1114 or CS 1044 or CS 1054 or CS 1064), (MATH 2224 or MATH 2224H or MATH 220 4 or MATH 2204H or MATH 2406H or CMDA 2005), (STAT 3006 or STAT 4705 or STAT 4714 or CMDA 2006). (3H,3C)

3704: STATISTICS FOR ENGINEERING APPLICATIONS

Introduction to statistical methodology with emphasis on engineering experimentation: probability distributions, estimation, hypothesis testing, regression, and analysis of variance. Only one of the courses 3704, 4604, 4705, and 4714 may be taken for credit. Pre: MATH 2224 or MATH 2224H or MATH 2204 or MATH 2204H or MATH 2406H. (2H,2C)

4004: METHODS OF STATISTICAL COMPUTING

Computationally intensive computer methods used in statistical analyses. Statistical univariate and multivariate graphics; resampling methods including bootstrap estimation and hypothesis testing and simulations; classification and regression trees; scatterplot smoothing and splines. Pre: (4105, 4214). (4H,3C)

4024: COMMUNICATION IN STATISTICAL COLLABORATIONS

Theory and examples of effective communication in the context of statistical collaborations. Practice developing the communication skills necessary to be effective statisticians using peer feedback and self-reflection. Topics include helping scientists answer their research questions, writing about and presenting statistical concepts to a non-statistical audience, and managing an effective statistical collaboration meeting. Senior standing in the Department of Statistics. Pre: 4214, 4204. (3H,3C)

4094: INTRODUCTION TO PROGRAMMING IN R

Introduction to R programming techniques with an emphasis on statistical analyses. Topics include: data objects, loops, importing/exporting datasets, graphics, functions, t-tests, ANOVA, linear regression, nonparametric tests, and logistic regression. Pre: 3615 or 3005. (1H,1C)

4105-4106: THEORETICAL STATISTICS

4105: Probability theory, counting techniques, conditional probability; random variables, moments; moment generating functions; multivariate distributions; transformations of random variables; order statistics. 4106: Convergence of sequences of random variables; central limit theorem; methods of estimation; hypothesis testing; linear models; analysis of variance. STAT 4105 partially duplicates STAT 4705, STAT 4714, and STAT 4724, only one may be taken for credit. Pre: MATH 2224 or MATH 2224H or MATH 2204 or MATH 2204H or MATH 2406H or CMDA 2005 for 4105; 4105 for 4106. (3H,3C)

4204: EXPERIMENTAL DESIGNS

Fundamental principles of designing and analyzing experiments with application to problems in various subject matter areas. Discussion of completely randomized, randomized complete block, and Latin square designs, analysis of covariance, split--plot designs, factorial and fractional designs, incomplete block designs. Pre: 3006 or 3616 or 4106 or 4706 or 5605 or 5615 or CMDA 2006. (3H,3C)

4214: METHODS OF REGRESSION ANALYSIS

Multiple regression including variable selection procedures; detection and effects of multicollinearity; identification and effects of influential observations; residual analysis; use of transformations. Non-linear regression, the use of indicator variables, and logistic regression. Use of SAS. Pre: 3006 or 3616 or 4106 or 4706 or 5606 or 5616 or CMDA 2006. (3H,3C)

4364: INTRODUCTION TO STATISTICAL GENOMICS

Statistical methods for bioinformatics and genetic studies, with an emphasis on statistical analysis, assumptions, and problem-solving. Topics include: commonly used statistical methods for gene identification, association mapping and other related problems. Focus on statistical tools for gene expression studies and association studies, multiple comparison procedures, likelihood inference and preparation for advanced study in the areas of bioinformatics and statistical genetics. Pre: (MATH 2224 or MATH 2224H or MATH 2204 or MATH 2204H or MATH 2406H or CMDA 2005), (STAT 3104 or STAT 4105 or STAT 4705 or CMDA 2006), (STAT 3006 or STAT 3616 or STAT 4706 or CMDA 2006). (3H,3C)

4444: APPLIED BAYESIAN STATISTICS

Introduction to Bayesian methodology with emphasis on applied statistical problems: data displaying, prior distribution elicitation, posterior analysis, models for proportions, means and regression. Pre: (MATH 2224 or MATH 2224H or MATH 2204 or MATH 2204H or MATH 2406H or CMDA 2005), (STAT 3104 or STAT 4105 or STAT 4705 or CMDA 2006), STAT 3006 or STAT 3616 or STAT 4 706 or CMDA 2006. (3H,3C)

4504: APPLIED MULTIVARIATE ANALYSIS

Non-mathematical study of multivariate analysis. Multivariate analogs of univariate test and estimation procedures. Simultaneous inference procedures. Multivariate analysis of variance, repeated measures, inference for dispersion and association parameters, principal components analysis, discriminate analysis, cluster analysis. Use of SAS. Pre: 3006 or 4706 or CMDA 2006 or STAT 3616. (3H,3C)

4514: CONTINGENCY TABLE ANALYSIS

Statistical techniques for frequency data. Goodness-of-fit. Tests and measures of association for two-way tables. Log-linear models for multidimensional tables. Parameter estimation, model selection, incomplete tables, ordinal categories, logistic regression. Use of SAS and SPSSx. Pre: 3006 or 3616 or 4106 or 4706 or 5606 or 5616. (3H,3C)

4524: SAMPLE SURVEY METHODS

Statistical methods for the design and analysis of survey sampling. Fundamental survey designs. Methods of randomization specific to various survey designs. Estimation of population means, proportions, totals, variances, and mean squared errors. Design of questionnaires and organization of a survey. Pre: 3006 or 3616 or 4106 or 4706 or 5606 or 5616. (3H,3C)

4534: APPLIED STATISTICAL TIME SERIES ANALYSIS

Applied course in time series analysis methods. Topics include regression analysis, detecting and address autocorrelation, modeling seasonal or cyclical trends, creating stationary time series, smoothing techniques, forecasting and forecast errors, and fitting autoregressive integrated moving average models. Pre: 3006 or 4104 or 4706 or 4714 or 3616 or BIT 2406 or CMDA 2006. (3H,3C)

4584 (MATH 4584): ADVANCED CALCULUS FOR STATISTICS

Introduction to those topics in advanced calculus and linear algebra needed by statistics majors. Infinite sequences and series. Orthogonal matrices, projections, quadratic forms. Extrema of functions of several variables. Multiple integrals, including convolution and nonlinear coordinate changes. Pre: (MATH 1114 or MATH 2114 or MATH 2114H or MATH 2405H), (MATH 1205 or MATH 1225), (MATH 1206 or MATH 1226), (MATH 2224 or MATH 2204 or MATH 2204H or MATH 2406H or CMDA 2005). (3H,3C)

4604: STATISTICAL METHODS FOR ENGINEERS

Introduction to statistical methodology with emphasis on engineering applications: probability distributions, estimation, hypothesis testing, regression, analysis of variance, quality control. Only one of the courses 4604, 4705, and 4714 may be taken for credit. STAT 4604 partially duplicates STAT 3005, STAT 3615, STAT 3006, STAT 3616 and STAT 4706. Only one may be taken for credit. Pre: MATH 1206 or MATH 1226. (3H,3C)

4654 (CMDA 4654) (CS 4654): INTERMEDIATE DATA ANALYTICS AND MACHINE LEARNING

A technical analytics course. Covers supervised and unsupervised learning strategies, including regression, generalized linear models, regularization, dimension reduction methods, tree-based methods for classification, and clustering. Upper-level analytical methods shown in practice: e.g., advanced naive Bayes and neural networks. Pre: (3654 or CMDA 3654 or CS 3654), (STAT 3104 or STAT 4706 or CMDA 2006). (3H,3C)

4664 (CMDA 4664): COMPUTATIONAL INTENSIVE STOCHASTIC MODLEING

Stochastic modeling methods with an emphasis in computing are taught. Select concepts from the classical and Bayesian paradigms are explored to provide multiple perspectives for how to learn from complex, datasets. There is particular focus on nested, spatial, and time series models. Pre: (4106 or CMDA 3605), (CS 1114 or CS 1064 or STAT 2005). (3H,3C)

4705-4706: PROBABILITY AND STATISTICS FOR ENGINEERS

Basic concepts of probability and statistics with emphasis on engineering applications. 4705: Probability, random variables, sampling distributions, estimation, hypothesis testing, simple linear regression correlation, one-way analysis of variance. 4706: Multiple regression, analysis of variance, factorial and fractional experiments. Only one of the courses 3704, 4604, 4705, 4714, and 4724 may be taken for credit. Pre: MATH 2224 or MATH 2204 or MATH 2204H or MATH 2406H for 4705; 4705 or 4105 for 4706. (3H,3C)

4714: PROBABILITY AND STATISTICS FOR ELECTRICAL ENGINEERS

Introduction to the concepts of probability, random variables, estimation, hypothesis testing, regression, and analysis of variance with emphasis on application in electrical engineering. Only one of the courses 3704, 4604, 4705, 4714 and 4724 may be taken for credit. Pre: MATH 2224 or MATH 2204 or MATH 2204H or MATH 2406H. (3H,3C)

4804 (AAEC 4804): ELEMENTARY ECONOMETRICS

Economic applications of mathematical and statistical techniques: regression, estimators, hypothesis testing, lagged variables, discrete variables, violations of assumptions, simultaneous equations. Pre: (3005 or 3604 or CMDA 2006), (AAEC 1006). (3H,3C)

4964: FIELD STUDY

Pass/Fail only. Variable credit course.

4974: INDEPENDENT STUDY

Variable credit course.

4974H: INDEPENDENT STUDY

Honors section. Variable credit course.

4984: SPECIAL STUDY

Variable credit course.

4994: UNDERGRADUATE RESEARCH

Variable credit course.

4994H: UNDERGRADUATE RESEARCH

Honors section. Variable credit course.