Courses
Sta 114/Math 136- Statistical inference
Sayan Mukherjee, Spring 2008 M-W 2:50pm – 4:05pm
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.
Sta 180S- Statistical Methods in Bioinformatics
Sayan Mukherjee, Spring 2009 Tu-Th 10:05am – 11:20amm
Explore statistical models and analytical tools for bioinformatics and genomics. Topics include functional inference for DNA, RNA, and protein sequences, and the analysis of genetic pedigrees, gene expression experiments, and families of molecular sequences and structures.
Sta 113- Probability/Statistics in engineering
Sayan Mukherjee, Fall 2006, 2007, 2008, 2009 Tu-Th 1:15pm – 2:30pm
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.
STA 205- Probability and measure theory
Sayan Mukherjee, Fall 2009 Tu-Th 11:40am – 12:55pm
This is a course about random variables, especially about their convergence and conditional expectations, providing an introduction to the foundations of \
modern Bayesian statistical inference.
Students are expected to know real analysis at the level of W. Rudin's Principles of Mathematical Analysis or M. Reed's Fundamental Ideas of Analysis--- t\
he topology of R^n, convergence in metric spaces (especially uniform convergence of functions on R^n), infinite series, countable and uncountable sets, co\
mpactness and convexity, and so forth. Students without this background should take or at least co-register with Duke's Math 203, Basic Analysis I. More a\
dvanced mathematical topics from real analysis, including parts of measure theory, Fourier and functional analysis, are introduced as needed to support a \
deep understanding of probability and its applications. Topics of later interest in statistics (e.g., regular conditional density functions) are given spe\
cial emphasis.
Math 288- Topics in probability: random graphs and statistical inference
Sayan Mukherjee and Jonathan Mattingly, Fall 2007 M-W 2:50pm – 4:05pm
Probabilistic and statistical aspects of random graphs. Specifically structure of random
graphs and statistical inference on graphs.
CBB 240/STA 270- Statistical methods in computational biology
Sayan Mukherjee, Spring 2006, 2007, 2009 M-W 2:50pm – 4:05pm
Methods of statistical inference and stochastic modeling with application to functional genomics and computational molecular biology. Topics include: statistical theory underlying sequence analysis and database searching; Markov models; elements of Bayesian and likelihood inference; multivariate high-dimensional regression models, applied linear regress analysis; discrete data models; multivariate data decomposition methods (PCA, clustering, multi-dimensional scaling); software tools for statistical computing.
STA 293- Topics in statistics: statistical learning - theory and algorithms
Sayan Mukherjee, Spring & Fall 2005 Tu-Th 1:15pm – 2:30pm
Mathematical and computational development of statistical machine learning.