| course | number | instructor | level | time |
|---|---|---|---|---|
| Introduction to Statistics | 101-106a | Reuning-Scherer & Staff | intro, no prereqs | T,Th 1:00-2:15 |
| Probability and Statistics for Scientists | 238a | Chang | intro | M,W,F 2:30-3:20 |
| Probability Theory with Applications | 241/541a | Pollard |
intro, with calculus | M,W,F 9:30-10:20 |
| Linear Models | 312/612a | Leeb |
intermediate | T,Th 9:00-10:15 |
| Data Analysis | 361/661a | Hartigan |
intermediate | M, W 2:30-3:45 |
| [Stochastic Calculus] | 603a | Pollard | N/A |
|
| [Foundations of
Statistics] |
605a | Hartigan | N/A |
|
| Statistical Inference | 610a | Zhou | intro grad | T,Th 10:30-11:45 |
| Statistical Case Studies | 625a | Emerson | intermediate grad | T,Th 2:30-3:45 |
| Monte Carlo Methods |
636a |
Chang |
||
| Bayes Theory |
653a |
Hartigan |
TBA |
|
| Internship in Statistical Research | 695a | Hartigan |
||
| Introductory Statistics |
100b |
Emerson |
intro |
M,W,F
10:30 - 11:20 |
| Introductory Data Analysis | 230/530b | Leeb |
intro | M,W 2:30-3:45 |
| Theory of Statistics | 242/542b | Zhou | intro, with calculus | M,W,F 9:30-10:20 |
| Stochastic Processes | 251/551b | Madiman |
intermediate | M,W 1:00-2:15 |
| Advanced Probability | 330/600b | Pollard | adv. undergrad/ intermediate grad |
T,Th 2:30-3:45 |
| Information Theory | 364/664b | Barron |
intermediate | T,Th 9:00-10:15 |
| Data Mining and Machine Learning | 365/665b | Leeb | M,W 11:30-12:45 | |
| Applied Math Senior Seminar | AM490b | Barron | W 3:30 - 5:20 | |
| Markov Processes and
Random Fields |
606b |
Pollard |
T,Th 10:30-11:45 |
|
| [Inequalities
for Probability & Statistics] |
607b |
Pollard |
N/A |
|
| Practical Work | 626b | Emerson | adv. grad | 1:00-2:00 |
| Statistical Consulting | 627b | Emerson | T 2:30 - 3:45, F 1:00 - 4:00 |
|
| Statistical Methods in Genetics and Bioinformatics | 645b | Chang | T, TH 10:30 - 11:20, F 2:00 - 2:50 |
|
| Multivariate Methods for the
Social Sciences |
660b | Reuning-Scherer | T, TH 1:00 - 2:15 | |
| [Probabilistic Networks, Algorithms, and
Applications] |
667b |
Tatikonda |
N/A |
|
| Information and
Probability |
668a |
Barron/Madiman |
TBA |
|
| Nonparametric Statistics |
680b |
Zhou |
TBA |
STAT 101a / E&EB 210aG / MCDB
215a,
Introduction to Statistics: Life Sciences.
Instructor: Mr. Jonathan Reuning-Scherer
/ Mr. Gunter Wagner
Statistical and probabilistic analysis of
biological problems presented with a unified foundation in basic
statistical theory. Problems are drawn from genetics, ecology,
epidemiology, and bioinformatics.
STAT 102a / EP&E 203a / PLSC
425a,
Introduction to Statistics: Political Science.
Instructor: Mr. Jonathan Reuning-Scherer
/ Mr. Donald Green
Statistical analysis of politics and quantitative
assessments of public policies. Problems presented with reference to a
wide array of examples: public opinion, campaign finance, racially
motivated crime, and health policy.
[STAT 104a / PSYC 201a,
Introduction to
Statistics: Psychology. Not
offered this semester.]
STAT 105a, Introduction to
Statistics: Medicine.
Instructor: Mr. Jonathan
Reuning-Scherer / Mr. David Salsburg
Statistical methods relied upon in medicine and
medical research. Practice in reading medical literature
competently and critically, as well as practical experience performing
statistical analysis of medical data.
STAT 106a, Introduction to
Statistics:
Data Analysis.
Instructor: Mr. Andrew Barron
Time:
Tues, Thurs 2:30-3:20 An introduction
to Probability and Statistics with emphasis on data analysis.
STAT
238a / STAT 538a,
Probability and Statistics for Scientists
Instructor: Mr. Joseph Chang
Time: Mon, Wed, Fri 2:30-3:20
Fundamental principles and techniques that help
scientists think probabilistically, develop statistical models, and
analyze data. Essentials of probability:
conditional probability, random variables, distributions, law of large
numbers, central limit theorem, Markov chains. Statistical
inference with emphasis on the Bayesian approach: parameter
estimation, likelihood, prior and posterior distributions, Bayesian
inference using Markov chain Monte Carlo. Introduction to
regression and linear models. Computers are used throughout for
calculations, simulations, and analysis of data. After MATH
118a or b or 120a or b. Some
acquaintance with matrix algebra and computing assumed.
STAT
241a / STAT 541a,
Probability Theory with Applications
Instructor: Mr. David Pollard
Time: Mon, Wed, Fri 9:30 - 10:20
A first course in probability theory:
probability spaces, random variables, expectations and probabilities,
conditional probability, independence, some discrete and continuous
distributions, central limit theorem, law of large numbers. After or concurrent with Mathematics 120a
or b or equivalents.
STAT
242b / STAT 542b / Mathematics 242b, Theory of Statistics
Instructor: Mr. Harrison Zhou
Time: Mon, Wed, Fri 9:30 - 10:20
Principles
of statistical analysis: maximum
likelihood, sampling distributions, estimation, confidence intervals,
tests of significance, regression, analysis of variance, and the method
of least squares. After Statistics
241a; after or concurrent with Mathematics 222.
[MORE
COURSE
INFORMATION]
STAT
251b / STAT 551b, Stochastic Processes
Instructor: Mr. Mokshay Madiman
Time: Mon, Wed 1 - 2:15
Introduction
to the study of random processes,
including Markov chains, Markov random fields, martingales, random
walks, Brownian motion and diffusions. Tecniques in probability, such
as coupling and large deviations. Applications to image reconstruction,
Bayesian statistics, finance, probabilistic analysis of algorithms,
genetics and evolution. After Statistics
241a or equivalent.
STAT
312a / STAT 612a,
Linear Models
Instructor: Mr. Hannes Leeb
Time: Tues, Thurs 9:00-10:15
The geometry of least squares; distribution
theory for normal errors; regression, analysis of variance, and
designed experiments; numerical algorithms (with particular reference
to Splus); alternatives to least squares. Generalized linear models. Linear algebra and some acquaintance with
statistics assumed.
STAT
361a STAT 661a, Data Analysis
Instructor: Mr. John Hartigan
Time: Mon, Wed 2:30 - 3:45
Through analysis of data sets using the Splus
statistical computing language, study of a selection of statistical
topics such as linear and nonlinear models, maximum likelihood,
resampling methods, curve estimation, model selection, classification
and clustering. After Statistics
242 and Mathematics 222b or 225a or b, or equivalents.
STAT
364b / STAT 664b, Information Theory
Instructor: Mr. Andrew Barron
Time: Tue, Thu 9:00 - 10:15
Foundations of information theory in
mathematical communications, statistical inference, statistical
mechanics, probability, and algorithmic complexity. Quantities of
information and their properties: entropy, conditional entropy,
divergence, redundancy, mutual information, channel capacity. Basic
theorems of data compression, data summarization, and channel coding.
Applications in statistics and finance. After Statistics 241.
STAT 365b / STAT
665b, Data
Mining
and Machine Learning
Instructor: Mr. Hannes Leeb
Time: Mon, Wed 11:30 - 12:45
Techniques for data mining and machine
learning
are covered from both a statistical and a computational perspective,
including support vector machines, bagging, boosting, neural networks,
and other nonlinear and nonparametric regression methods. The
course will give the basic ideas and intuition behind these methods, a
more formal understanding of how and why they work, and opportunities
to experiment with machine learning algorithms and apply them to data. After
STAT 242b.
AM490b,
Applied Math Senior Seminar and Project
Instructor: Mr. Andrew Barron
Time: Wed 2:30 - 3:20
Under the supervision of a member of the
faculty, each student works on an independent project. Students
participate in seminar meetings at which they speak on the progress of
their projects. Some meetings are devoted to talks by visiting
applied mathematicians.
STAT
600b / 330b, Advanced Probability
Instructor: Mr. David Pollard
Time: Tues, Thurs 2:30 - 3:45
Measure
theoretic probability, conditioning,
laws of large numbers, convergence in distribution, characteristic
functions, central limit theorems, martingales. Some knowledge of real
analysis is assumed.
[MORE
COURSE
INFORMATION]
STAT
606b, Markov Proceesses and Random Fields
Instructor: David Pollard
Markov chains on general state spaces;diffusions;Markov random
fields;Gibbs measures; percolations. After STAT 600.
[STAT
607b, Inequalities for Probability & Statistics]
STAT 610a,
Statistical Inference
Instructor: Mr. Harrison Zhou
Time: Tues, Thurs 10:30-11:45 am
A
systematic development of the mathematical
theory of statistical inference covering methods of estimation,
hypothesis testing, and confidence intervals. An introduction to
statistical decision theory. Undergraduate probability at the level of Statistics
241a assumed.
STAT
625a,
Statistical Case Studies
Instructor: Mr. John Emerson and Mr. John
Hartigan.
Time: Tues, Thurs 2:30-3:45 pm
Statistical
analysis of a variety of problems including the value of a baseball
player, the
fairness of real estate taxes, how to win the Tour de France, energy
consumption in Yale buildings, and interactive questionnaires for
course
evaluations. We will emphasize methods
of choosing data, acquiring data, and assessing data quality.
Computations will use R.
STAT
626b, Practical Work
Instructor: Mr. John Emerson
Time: contact instructor
Place: contact instructor
Individual one-semester projects, with students
working on studies outside the Department, under the guidance of a
statistician.
STAT
627b, Statistical Consulting
Instructor:
Jay Emerson
Time: TBA
Statistical
consulting and
collaborative research projects often require statisticians to explore
new
topics outside their area of expertise. This course exposes students to
real
problems, requiring them to draw on their expertise in probability,
statistics,
and data analysis. Students complete the course with individual
projects
supervised jointly by faculty outside the department and by one of the
instructors.
STAT 636a,
Monte Carlo Methods.
Instructor:
Joseph Chang.
Theory
and practice of Monte Carlo methods,
with emphasis on Markov chain Monte Carlo and statistical applications.
Generation of random variables, importance sampling, Metropolis
Hastings,
Gibbs sampling, variable dimension methods and model selection,
multilevel and
population based methods, convergence diagnostics. Markov chains in
general
state spaces and rates of convergence. Applications in Bayesian
inference,
simulation, and optimization.
STAT
645b, Statistical Methods in Genetics and Bioinformatics
Instructor: Mr. Joseph Chang
Time: TBA
Stochastic
modeling and statistical methods
applied to problems such as mapping quantitative trait loci, analyzing
gene expression data, sequence alignment, and reconstructing
evolutionary trees. Statistical methods include maximu likelihood,
Bayesian inference, Monte Carlo Markov chains, and some methods of
classification and clustering. Models introduced include variance
components, hidden Markov models, Bayesian networks, and coalescent.
Recommended background: Stat 541, Stat 542. Prior knowledge of biology
is not required.
STAT 653a, Bayes Theory
Instructor: Mr. John Hartigan
Time: TBA
Axioms and interpretations of probability. Construction of probablilty
distributions. Optimality of Bayes procedures. Martingales.
Asymptotics. Markov sampling. Robustness against violations in the
assumed distributions. Choice among models.
STAT 660b,
Multivariate
Statistics for Social Sciences
Instructor:
Mr. Jonathan Reuning-Scherer
Time:; Tues, Thur 1:00 pm - 2:15 pm
A practical introduction to the analysis of
multivariate data as applied to
examples from the social sciences. Topics to include multivariate
analysis of variance (MANOVA),
principle components analysis, cluster analysis (hierarchical
clustering, k-means), canonical correlation,
multidimensional scaling, factor analysis, discriminant analysis, and
structural equations modeling.
Emphasis is placed on practical application of multivariate techniques
to a variety of examples in the
social sciences. There are regular homework assignments and a final
project. Regular use of some
statistical software package (students may choose among SAS, SPSS, and
MINITAB). A complete
syllabus will be available on the classes server.
STAT
667b / ENAS 503, Probabilistic
Networks, Algorithms, and Applications
Instructor:
Mr. Sekhar Tatikonda
Time:
Tues, Thurs 11:30 - 12:45
This course examines
probabilistic and computational methods for the statistical modeling of complex data.
The emphasis will be on the unifying framework provided by graphical models,
a formalism that merges aspects of graph theory and probability
theory. Graphical models: Markov random fields, Bayesian networks, and factor
graphs. Algorithms: filtering, smoothing,
belief-propagation, sum-product,
and junction tree. Variational techniques: mean-field and convex
relaxations. Markov processes on graphs: MCMC, factored HMMs, and Glauber
dynamics. Some statistical physics techniques: cavity and replica methods.
Applications to error-correcting codes, computer vision, bio-informatics, and
combinatorial optimization.
[MORE
COURSE INFORMATION]
STAT
668a
Information and Probability. Andrew Barron, Mokshay Madiman
TBA.
Study of several key results in probability
using ideas and methods from information theory. Topics include entropy
and its
relationship to Fisher information, the law of large numbers, central
limit
theorem (normal approximation), law of small numbers (Poisson
approximation),
large deviations, martingales, Markov chains, and information
projection. The
approach we take quantitifies the increase in entropy or more generally
the
drop in information distance from an approximating distribution.
Interpretations from statistics, physics, and finance.
STAT 680b,
Nonparametric Statistics. Harrison
Zhou.
Introduction
to nonparametric methods such as kernel estimation, Fourier basis
estimation,
wavelet estimation. Optimal minimax convergence rates and constants for
function spaces, with connections to information theory. Adaptive
estimators
(e.g., adaptive shrinkage estimation). If time permits: high
dimensional
function estimation, functional data estimation, classification, or
nonparametric asymptotic equivalence. Applications to real data. Some
knowledge
of statistical theory at the level of STAT
610a
is assumed.
STAT 695a, Internship in
Statistical Research (1 credit)
Instructor: Mr. John Hartigan
The Internship is designed to give students an
opportunity to gain practical exposure to problems in the analysis of
statistical data, as part of a research group within industries such
as: medical and pharmaceutical research, financial, information
technologies, telecommunications, public policy, and others. The
Internship experience often serves as a basis for the Ph.D.
dissertation. Students will work with the Director of Graduate
Studies and other faculty advisors to select suitable placements.
Students
will submit a one-page description of their Internship plans to the DGS
by May 1st, which will be evaluated by the DGS and other faculty
advisors by May 15th. Upon completion of the Internship, students
shall submit a written report of their work to the DGS, no later than
October 1st. The Internship will be graded on a Satisfactory/
Unsatisfactory basis, and will be based on the student's written report
and an oral presentation.
This course is an elective requirement for the
Ph.D. degree.
STAT 699, Research Seminar in Statistics
Instructor: Mr. Sekhar
Tatikonda / Mr. David Pollard
Time: Friday, 10:00 - 12:00
Course lists for prior years may be found here. Please note these older pages are not being updated, and as such, some of the links may no longer be working.