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Department of Statistical Science (STA)
Professor Gelfand, Chair; Professor of the Practice Stangl, Associate Chair and Director of Undergraduate Studies;
Professor West, Director of Graduate Studies; Professors Berger, Clark, Clyde, Dunson, Winkler, and Wolpert;
Associate Professors , Hartemink, Hauser, Mattingly, Reiter and Schmidler,; Assistant Professors Li, Mukherjee,
and Tokdar; Professors Emeriti Burdick and Sacks; Professor of the Practice Banks; Assistant Professors of the
Practice Cetinkaya and Lock, Associate Research Professor Iversen; Assistant Research Professor Lucas; Adjunct
Professor Bayarri and Smith Visiting Assistant Professor Manolopoulou
A major or a minor is available in this department.
The Department of Statistical Science coordinates teaching and research in the statistical sciences at Duke
University. In its teaching and research, the department's faculty members emphasize modern statistical methods
involving computationally intensive stochastic modeling, coupled with interdisciplinary applications in many fields.
The department also offers courses in basic statistical methods and advanced mathematical statistics.
20. General Statistics. Credit for Advanced Placement on the basis of College Board Examination in statistics. One
course.
30. Basic Statistics and Quantitative Literacy. QS Statistical concepts involved in making inferences, decisions,
and predictions from data. Emphasis on applications, not formal technique. Prerequisite: Must have taken placement
test and placed in Statistical Science 30. Not open to students who have Statistical Science 20 or 100-level statistics
course. Instructor: Staff. One course.
89S. First-Year Seminar. QS Topics vary each semester offered. Instructor: Staff. One course.
101. Data Analysis and Statistical Inference. QS, R, STS Introduction to statistics as a science of understanding
and analyzing data. Major themes include data collection, exploratory analysis, inference, and modeling. Focus on
principles underlying quantitative research in social sciences, humanities, and public policy. Research projects teach
the process of scientific discovery and synthesis and critical evaluation of research and statistical arguments.
Readings give perspective on why in 1950, Samuel Wilks said "Statistical thinking will one day be as necessary a
qualification for efficient citizenship as the ability to read and write." Prerequisites: placement exam. Not open to
students with credit for Statistics 102 or above. Instructor: Staff. One course. C-L: Information Science and
Information Studies
102. Introductory Biostatistics. QS, R, STS Reading and interpretation of statistical analysis from life and health
sciences. Topics include: basic concepts and tools of probability, estimation, inference, decisions analysis, and
modeling. Emphasizes role of biostatistics in modern society. Prerequisites: placement test. Not open to students
who have credit for another 100-level STA course. Instructor: Stangl. One course. C-L: Information Science and
Information Studies
103. Statistics in the Courtroom. QS Reading and interpretation of statistical analyses from court cases.
Conceptual bases for using data and understanding uncertainty when making legal decisions. Includes reading and
discussion of articles about legal cases. Topics include: basic concepts and tools of probability and conditional
probability, and of statistical analysis including estimation, inference, prediction, and decision analysis.
Prerequisites: Must have taken Statistical Science 30, Statistical Science 20 or taken statistics placement test and
placed in Statistical Science 103. Instructor: Stangl. One course.
110FS. Focus Program - Introductory Special Topics in Statistics. QS This is a seminar course for focus
students. Topics vary every semester. Mathematics 21 is a prerequisite. Instructor: Banks. One course.
Proof for the 2012-2013 Duke University Bulletin of Undergraduate Instruction, p. 2
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111. Probability and Statistical Inference. QS Basic laws of probability - random events, independence and
dependence, expectations, Bayes theorem. Discrete and continuous random variables, density, and distribution
functions. Binomial and normal models for observational data. Introduction to maximum likelihood estimation and
Bayesian inference. One- and two-sample mean problems, simple linear regression, multiple linear regression with
two explanatory variables. Applications in economics, quantitative social sciences, and natural sciences emphasized.
Prerequisites: Mathematics 21 or equivalent. Not open to students who have credit for another 100-level statistics
course. Instructor: Staff. One course. C-L: Information Science and Information Studies
130. Probability and Statistics in Engineering. QS Introduction to probability, independence, conditional
independence, and Bayes' theorem. Discrete and continuous, univariate and multivariate distributions. Linear and
nonlinear transformations of random variables. Classical and Bayesian inference, decision theory, and comparison
of hypotheses. Experimental design, statistical quality control, and other applications in engineering. Not open to
students who have taken Statistical Science 250 or 611. Prerequisite: Mathematics 212 or equivalent. Instructor:
Mukherjee. One course. C-L: Information Science and Information Studies, Modeling Biological Systems
210. Regression Analysis. QS, R, W Extensive study of regression modeling. Multiple regression, weighted least
squares, logistic regression, log-linear models, analysis of variance, model diagnostics and selection. Emphasis on
applications. Examples drawn from a variety of fields. Prerequisite: 100-level statistics course. Permission of
Director of Undergraduate Studies required for courses outside Statistical Science. Instructor: Reiter, Stangl, Clyde.
One course.
230. Probability. QS One course. C-L: see Mathematics 230; also C-L: Information Science and Information
Studies, Modeling Biological Systems
250. Statistics. QS An introduction to the concepts, theory, and application of statistical inference, including the
structure of statistical problems, probability modeling, data analysis and statistical computing, and linear regression.
Inference from the viewpoint of Bayesian statistics, with some discussion of sampling theory methods and
comparative inference. Applications to problems in various fields. Prerequisite: Mathematics 221 or equivalent and
Mathematics 230/Statistical Science 230. Instructor: Wolpert. One course. C-L: Mathematics 342, Information
Science and Information Studies
320. Design and Analysis of Causal Studies. QS Design of randomized experiments and observational studies.
Role of randomization, block designs, factorial designs, fractional factorial designs, matching. Analysis of variance,
contrasts, propensity score matching, instrumental variables. Prerequisites: Statistical Science 210 or Economics
208D. Instructor: Banks. One course.
321. Design and Analysis of Surveys. QS Design and analysis of surveys, including random sampling,
stratification, clustering, and multi-stage sampling. Design-based and model-based inference. Methods for handling
missing data. Prerequisites: Statistical Science 210 or Economics 208D. Instructor: Reiter. One course.
340. Introduction to Statistical Decision Analysis. QS Quantitative methods for decision making under
uncertainty. Probability theory, personal probabilities and utilities, decision trees, ROC curves, sensitivity analysis,
dominant strategies, Bayesian networks and influence diagrams, Markov models and time discounting, costeffectiveness analysis, multi-agent decision making, game theory. Prerequisite: Statistics 230. Instructor: Schmidler,
Berger. One course.
350S. Statistical Methods in Bioinformatics. QS, R Statistical and analytical tools for bioinformatics and
genomics. Methods for comparison, database search, and functional inference for DNA, RNA, and protein
sequences; analysis of families of molecular sequences and structures; inference in genetic pedigrees and basic
linkage analysis; analysis of gene expression experiments. Topics include: sequence comparison algorithms and
Karlin-Altschul statistics; Hidden Markov models of families; statistics of protein structure threading; visualization
and comparative analyses for oligonucleotide array datasets. Statistical Science 230/Mathematics 230 required.
Statistical Science 250/Mathematics 342 suggested. Computer programming and molecular biology required.
Instructor: Mukherjee, Schmidler. One course.
360. Bayesian Inference and Modern Statistical Methods. QS Principles of data analysis and advanced statistical
modeling. Bayesian inference, prior and posterior distributions, multi-level models, model checking and selection,
stochastic simulation by Markov Chain Monte Carlo. Prerequisites: Statistical Science 210 or Economics 208D,
Statistical Science 230, and Statistical Science 250. Instructor: Clyde, Reiter, or Stangl. One course. C-L: Modeling
Biological Systems
393. Research Independent Study. R Individual research in a field of special interest, under the supervision of a
faculty member, resulting in a substantive paper or written report containing significant analysis and interpretation
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of a previously approved topic. Consent of instructor and director of undergraduate studies required. Instructor:
Staff. One course.
470S. Introduction to Statistical Consulting. QS, R Participation by students in data analysis projects from the
DSS Statistical Consulting Center. Projects led and directed by DSS faculty. Prerequisites: Statistical Science 360.
Instructor: Lucas. One course.
471S. Computational Data Analysis. QS Data analysis, exploration, and representation. Scientific modeling and
computation. Data mining for large datasets, algebraic decomposition methods, stochastic simulation for temporal
models of dynamic processes, graphical and network data, computational methods development. Problems and data
drawn from ISDS research projects. Prerequisites: Statistical Science 360, some computer programming expertise.
Instructor: Dunson. One course. C-L: Modeling Biological Systems
490S. Special Topics in Statistics. QS, R Special topics not covered in core courses and more advanced topics
related to current research directions in statistics. Consent of instructor required. Instructor: Staff. One course.
497S. Research Seminar in Statistical Science I. QS, R Statistical and mathematical underpinnings of
methodological research in statistical science. Student presentations of their statistical research in collaboration with,
and under the supervision of, an DSS faculty mentor. Offered only in fall semesters. Permission of department
required. Instructor: Stangl or West. One course.
498S. Research Seminar in Statistical Science II. QS, R, W Continuation of Statistical Science 497S. Statistical
and mathematical underpinnings of methodological research in statistical science. Student presentations of their
statistical research in collaboration with, and under the supervision of, a DSS faculty mentor. Consent of department
required. Instructor: Stangl or West. One course.
504. Statistical Genetics. One course. C-L: see Computational Biology and Bioinformatics 541; also C-L: Genome
Sciences and Policy
505. Computational Gene Expression Analysis. QS C-L: see Computational Biology and Bioinformatics 521; also
C-L: Molec Genetics & Microbiology 521
601. Bayesian and Modern Statistical Data Analysis. QS Principles of data analysis and modern statistical
modeling. Exploratory data analysis. Introduction to Bayesian inference, prior and posterior distributions, predictive
distributions, hierarchical models, model checking and selection, missing data, introduction to stochastic simulation
by Markov Chain Monte Carlo using a higher level statistical language such as R or Matlab. Applications drawn
from various disciplines. Not open to students with credit for Statistics 360. Prerequisite: Statistics 611 or Instructor
consent. Instructor: Clyde or Reiter. One course.
611. Introduction to Statistical Methods. QS Emphasis on classical techniques of hypothesis testing and point and
interval estimation, using the binomial, normal, t, F, and chi square distributions. Not open to students who have had
Statistical Science 250 or Mathematics 342. Prerequisite: Mathematics 212 (may be taken concurrently) or
equivalent, or consent of instructor. Instructor: Li. One course.
612. Numerical Analysis. QS, R One course. C-L: see Computer Science 520; also C-L: Mathematics 565,
Modeling Biological Systems
613. Statistical Methods for Computational Biology. One course. C-L: see Computational Biology and
Bioinformatics 540
614. Computational Structural Biology. QS, R One course. C-L: see Computer Science 664; also C-L:
Computational Biology and Bioinformatics 550
621. Applied Stochastic Processes. QS One course. C-L: see Mathematics 541
622. Statistical Data Mining. QS Introduction to data mining, including multivariate nonparametric regression,
classification, and cluster analysis. Topics include the Curse of Dimensionality, the bootstrap, cross-validation,
search (especially model selection), smoothing, the backfitting algorithm, and boosting. Emphasis on regression
methods (e.g., neural networks, wavelets, the LASSO, and LARS), classifications methods (e.g., CART, Support
vector machines, and nearest-neighbor methods), and cluster analysis (e.g., self-organizing maps, D-means
clustering, and minimum spanning trees). Theory illustrated through analysis of classical data sets. Prerequisites:
Statistical Science 250. Instructor: Banks. One course. C-L: Computer Science 579
623. Statistical Decision Theory. QS Formulation of decision problems; criteria for optimality: maximum expected
utility and minimax. Axiomatic foundations of expected utility; coherence and the axioms of probability (the Dutch
Book theorem). Elicitation of probabilities and utilities. The value of information. Estimation and hypothesis testing
as decision problems: risk, sufficiency, completeness and admissibility. Stein estimation. Bayes decision functions
and their properties. Minimax analysis and improper priors. Decision theoretic Bayesian experimental design.
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Combining evidence and group decisions. Prerequisite: Statistical Science 732 or consent of instructor. Instructor:
Berger or Schmidler. One course.
690. Special Topics in Statistics. Prerequisite: Statistical Science 611 or consent of instructor. Pass/Fail grading
only. Instructor: Staff. One course.
711. Probability and Measure Theory. QS Introduction to probability spaces, the theory of measure and
integration, random variables, and limit theorems. Distribution functions, densities, and characteristic functions;
convergence of random variables and of their distributions; uniform integrability and the Lebesgue convergence
theorems. Weak and strong laws of large numbers, central limit theorem. Prerequisite: elementary real analysis and
elementary probability theory. Instructor: Mukherjee, Wolpert. One course.
721. Linear Models. QS Multiple linear regression and model building. Exploratory data analysis techniques,
variable transformations and selection, parameter estimation and interpretation, prediction, Bayesian hierarchical
models, Bayes factors and intrinsic Bayes factors for linear models, and Bayesian model averaging. The concepts of
linear models from Bayesian and classical viewpoints. Topics in Markov chain Monte Carlo simulation introduced
as required. Prerequisite: Statistical Science 611 and 601 or equivalent. Instructor: Clyde. One course. C-L:
Mathematics 543
732. Statistical Inference. QS Classical, likelihood, and Bayesian approaches to statistical inference. Foundations
of point and interval estimation, and properties of estimators (bias, consistency, efficiency, sufficiency, robustness).
Testing: Type I and II errors, power, likelihood ratios; Bayes factors, posterior probabilities of hypotheses. The
predictivist perspective. Applications include estimation and testing in normal models; model choice and criticism.
Prerequisite: Statistical Science 611 and 831 or consent of instructor. Instructor: Li, Wolpert. One course.
790. Special Topics in Statistics. Prerequisite: Statistical Science 611 or consent of instructor. Pass/Fail grading
only. Instructor: Staff. One course.
790-40. Topics in Probability Theory. QS One course. C-L: see Mathematics 690-40
811. Probability. QS One course. C-L: see Mathematics 641
831. Probability and Statistical Models. QS Theory, modeling, and computational topics in probability and
statistics: distribution theory and modeling, simulation and applied probability models in statistics, generation of
random variables. Monte Carlo method and integration; Markov Chain Monte Carlo methods; applied stochastic
processes including Markov process theory, linear systems theory, and AR models. Latent variable probability
models, i.e., mixture models, hidden Markov models, and missing data problems. Discrete and continuous
multivariate distributions; linear, multinormal, and graphical models; tools of linear algebra and probability calculus.
Statistical computing using Matlab/R. Prerequisite: Statistical Science 601, 721, and 732. Instructor: Schmidler or
West. One course.
841. Generalized Linear Models. QS Likelihood-based and Bayesian inference of binomial, ordinal, and Poisson
regression models, and the relation of these models to item response theory and other psychometric models. Focus
on latent variable interpretations of categorical variables, computational techniques of estimating posterior
distributions on model parameters, and Bayesian and likelihood approaches to case analyses and goodness-of-fit
criterion. Theory and practice of modern regression modeling within the unifying context of generalized linear
models. A brief review of hierarchical linear models. Students expected to use several software packages and to
customize functions in these packages to perform applied analyses. Prerequisite: Statistical Science 611 and 721 or
consent of instructor. Instructor: Dunson. One course.
941. Modern Nonparametric Theory and Methods. QS Modern nonparametric approaches for exploring and
drawing inferences from data. Topics may include: resampling methods, nonparametric density estimation,
nonparametric regression and classification, bootstrapping, kernel methods, splines, local regression, wavelets,
support vector machines, nonparametric modeling for random distributions. Classical and Bayesian perspectives.
Consent of instructor required. Instructor: Dunson. One course.
944. Spatial Statistics. QS Modeling data with spatial structure;point-referenced (geo-statistical)data, areal (lattice)
data, and point process data; stationarity, valid covariance functions; Gaussian processes and generalizations;
kriging; Markov random fields (CAR and SAR); hierarchical modeling for spatial data; misalignment; multivariate
spatial data, space/time data specification. Theory and application. Some assignments will involve computing and
data analysis. Consent of instructor required. Instructor: Gelfand. One course.
THE MAJOR
The major in statistical science provides students with exposure to modern statistical reasoning and the skills
needed to develop, analyze and utilize statistical techniques for addressing quantitative, data-based problems in the
natural and social sciences. The course of study exposes students to a broad range of statistical methods using tools
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from mathematical and computational sciences. Students who complete the major in statistical science will be well
prepared for careers in business, where they must appreciate and accommodate uncertainty in their decision-making,
and for further study and embarking on research in science, law, business, or other fields.
As part of the course of study, majors in statistical science complete a research project under the supervision of
a faculty member. These projects can involve the analysis of complex data, the development of new methods or
theory, or the extension and evaluation of existing techniques. The director of undergraduate studies links majors to
a research mentor, who works with students to develop and complete the research project. Students earn credit for
their research by taking Statistics 497S and Statistics 498S.
For the A.B. Degree
Prerequisites. Mathematics 21 (or 111L), 122 (or 112L), 212, and 221 (or216).
Major Requirements. Statistics 230/Mathematics 230. Statistics 250/Mathematics 342, or Statistics 611.
Statistics 210. Statistics 360, 497S, and 498S. Two additional courses above Statistics 250 (excluding 540 and 611).
Only one independent study in statistical science can be used towards the major. Up to one statistical course from
other departments can be used towards the major, provided the course is pre-approved by the director of
undergraduate studies.
For the B.S. Degree
Prerequisites. Mathematics 21 (or 111L), 122 (or 112L), 212, and 221 (or 216).
Major Requirements. Statistics 230/Mathematics 230. Statistics 250/Mathematics 342, or Statistics 611.
Statistics 210. Statistics 360, 497S, and 498S. Three additional courses above Statistics 250 (excluding 540 and
611). Only one independent study in statistical science can be used towards the major. Up to two statistical courses
above Statistics 250 from other departments can be used towards the major, provided the courses are pre-approved
by the director of undergraduate studies. One 300-level or higher course in an applied quantitative area other than
statistical science, such as engineering, mathematics, one of the natural sciences, or one of the quantitative social
sciences.
THE MINOR
The minor is designed to provide students in other disciplines with opportunities for exposure and skill
development in advanced statistical methods. These are useful for conducting research in applied subjects, and they
are appealing to employers and graduate schools seeking students with quantitative skills. The minor is flexible, so
that students from most majors can find a path to the minor that serves their needs. The director of undergraduate
studies assists students in selecting courses for the minor.
Prerequisites. Mathematics 21 (or 111L) and 122 (or 112fL).
Requirements. Five additional courses in statistical science above the 100 level, only one of which can be from
Statistics 101,102, 103, 111, or 130. Up to two courses above Statistics 250 from other departments can be used
towards the major, provided the courses are pre-approved by the director of undergraduate studies.