Statistics and Data Science (S&DS)

S&DS 100b, Introductory StatisticsEthan Meyers

An introduction to statistical reasoning. Topics include numerical and graphical summaries of data, data acquisition and experimental design, probability, hypothesis testing, confidence intervals, correlation and regression. Application of statistical concepts to data; analysis of real-world problems. May not be taken after S&DS 101106 or 109.  QR
TTh 9am-10:15am

S&DS 101a / E&EB 210a, Introduction to Statistics: Life SciencesJonathan Reuning-Scherer

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.  QR
TTh 1pm-2:15pm

S&DS 102a / EP&E 203a / PLSC 452a, Introduction to Statistics: Political ScienceJonathan Reuning-Scherer

Statistical analysis of politics, elections, and political psychology. Problems presented with reference to a wide array of examples: public opinion, campaign finance, racially motivated crime, and public policy.  QR
TTh 1pm-2:15pm

S&DS 103a / EP&E 209a / PLSC 453a, Introduction to Statistics: Social SciencesJonathan Reuning-Scherer

Descriptive and inferential statistics applied to analysis of data from the social sciences. Introduction of concepts and skills for understanding and conducting quantitative research.  QR
TTh 1pm-2:15pm

S&DS 105a, Introduction to Statistics: MedicineJonathan Reuning-Scherer

Statistical methods used in medicine and medical research. Practice in reading medical literature competently and critically, as well as practical experience performing statistical analysis of medical data.  QR
TTh 1pm-2:15pm

S&DS 106a, Introduction to Statistics: Data AnalysisJonathan Reuning-Scherer

An introduction to probability and statistics with emphasis on data analysis.  QR
TTh 1pm-2:15pm

S&DS 108a, Introduction to Statistics: Advanced FundamentalsJonathan Reuning-Scherer

Introductory statistical concepts beyond those covered in high school AP statistics.   Includes additional concepts in regression, an introduction to multiple regression, ANOVA, and logistic regression. This course is intended as a bridge between AP statistics and courses such as S&DS 230, Data Exploration and Analysis. Meets for the second half of the term only. Prerequisites: A previous statistics course in high school. May not be taken after S&DS 100, S&DS 101106, PSYC 100, or any other full semester Yale introductory statistics courses. Students should consider S&DS 103 or both S&DS 108, 109.  ½ Course cr
TTh 1pm-2:15pm

S&DS 109a, Introduction to Statistics: FundamentalsJonathan Reuning-Scherer

General concepts and methods in statistics. Meets for the first half of the term only. May not be taken after S&DS 100 or 101106.  ½ Course cr
TTh 1pm-2:15pm

S&DS 123b / CPSC 123b / PLSC 351b / S&DS 523b, YData: An Introduction to Data ScienceEthan Meyers

Computational, programming, and statistical skills are no longer optional in our increasingly data-driven world; these skills are essential for opening doors to manifold research and career opportunities. This course aims to dramatically enhance knowledge and capabilities in fundamental ideas and skills in data science, especially computational and programming skills along with inferential thinking. YData is an introduction to Data Science that emphasizes the development of these skills while providing opportunities for hands-on experience and practice. YData is accessible to students with little or no background in computing, programming, or statistics, but is also engaging for more technically oriented students through extensive use of examples and hands-on data analysis. Python 3, a popular and widely used computing language, is the language used in this course. The computing materials will be hosted on a special purpose web server.  QR
TTh 2:30pm-3:45pm

* S&DS 160b / AMTH 160b / MATH 160b, The Structure of NetworksStaff

Network structures and network dynamics described through examples and applications ranging from marketing to epidemics and the world climate. Study of social and biological networks as well as networks in the humanities. Mathematical graphs provide a simple common language to describe the variety of networks and their properties.  QR

* S&DS 172a / EP&E 328a / PLSC 347a, YData: Data Science for Political CampaignsJoshua Kalla

Political campaigns have become increasingly data driven. Data science is used to inform where campaigns compete, which messages they use, how they deliver them, and among which voters. In this course, we explore how data science is being used to design winning campaigns. Students gain an understanding of what data is available to campaigns, how campaigns use this data to identify supporters, and the use of experiments in campaigns. This course provides students with an introduction to political campaigns, an introduction to data science tools necessary for studying politics, and opportunities to practice the data science skills presented in S&DS 123, YData.
W 1:30pm-3:20pm

S&DS 230a or b, Data Exploration and AnalysisStaff

Survey of statistical methods: plots, transformations, regression, analysis of variance, clustering, principal components, contingency tables, and time series analysis. The R computing language and Web data sources are used. Prerequisite: a 100-level Statistics course or equivalent, or with permission of instructor.  QR

S&DS 238a, Probability and StatisticsJoseph Chang

Fundamental principles and techniques of probabilistic thinking, statistical modeling, and data analysis. Essentials of probability, including conditional probability, random variables, distributions, law of large numbers, central limit theorem, and 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 for calculations, simulations, and analysis of data. After or concurrently with MATH 118 or 120.  QR
TTh 1pm-2:15pm

S&DS 240a, An Introduction to Probability TheoryElisa Celis

Introduction to probability theory. Topics include probability spaces, random variables, expectations and probabilities, conditional probability, independence, discrete and continuous distributions, central limit theorem, Markov chains, and probabilistic modeling. This course counts towards the Data Science certificate but not the Statistics and Data Science major. Prerequisite: MATH 115.  QR
MW 2:30pm-3:45pm

S&DS 241a / MATH 241a, Probability TheoryYihong Wu

Introduction to probability theory. Topics include probability spaces, random variables, expectations and probabilities, conditional probability, independence, discrete and continuous distributions, central limit theorem, Markov chains, and probabilistic modeling. After or concurrently with MATH 120 or equivalent.  QR
MW 9am-10:15am

S&DS 242b / MATH 242b, Theory of StatisticsZhou Fan

Study of the principles of statistical analysis. Topics include maximum likelihood, sampling distributions, estimation, confidence intervals, tests of significance, regression, analysis of variance, and the method of least squares. Some statistical computing. After S&DS 241 and concurrently with or after MATH 222 or 225, or equivalents.  QR
MW 9am-10:15am

S&DS 262b / AMTH 262b / CPSC 262b, Computational Tools for Data ScienceRoy Lederman

Introduction to the core ideas and principles that arise in modern data analysis, bridging statistics and computer science and providing students the tools to grow and adapt as methods and techniques change. Topics include principal component analysis, independent component analysis, dictionary learning, neural networks and optimization, as well as scalable computing for large datasets. Assignments include implementation, data analysis and theory. Students require background in linear algebra, multivariable calculus, probability and programming. Prerequisites: after or concurrently with MATH 222225, or 231; after or concurrently with MATH 120230, or ENAS 151; after or concurrently with CPSC 100112, or ENAS 130; after S&DS 100-108 or S&DS 230 or S&DS 241 or S&DS 242. Enrollment is limited; requires permission of the instructor.  QR

S&DS 265a, Introductory Machine LearningJohn Lafferty

This course covers the key ideas and techniques in machine learning without the use of advanced mathematics. Basic methodology and relevant concepts are presented in lectures, including the intuition behind the methods. Assignments give students hands-on experience with the methods on different types of data. Topics include linear regression and classification, tree-based methods, clustering, topic models, word embeddings, recurrent neural networks, dictionary learning and deep learning. Examples come from a variety of sources including political speeches, archives of scientific articles, real estate listings, natural images, and several others. Programming is central to the course, and is based on the Python programming language. Prerequisites: Two of the following courses: S&DS 230, 238, 240, 241 and 242; previous programming experience (e.g., R, Matlab, Python, C++), Python preferred.  QR
TTh 9am-10:15am

S&DS 312a, Linear ModelsHarrison Zhou

The geometry of least squares; distribution theory for normal errors; regression, analysis of variance, and designed experiments; numerical algorithms, with particular reference to the R statistical language. After S&DS 242 and MATH 222 or 225.  QR
MW 11:35am-12:50pm

S&DS 351b / EENG 434b / MATH 251b, Stochastic ProcessesAmin Karbasi

Introduction to the study of random processes including linear prediction and Kalman filtering, Poison counting process and renewal processes, Markov chains, branching processes, birth-death processes, Markov random fields, martingales, and random walks. Applications chosen from communications, networking, image reconstruction, Bayesian statistics, finance, probabilistic analysis of algorithms, and genetics and evolution. Prerequisite: S&DS 241 or equivalent.  QR
MW 1pm-2:15pm

S&DS 352b / MB&B 452b / MCDB 452b, Biomedical Data Science, Mining and ModelingMark Gerstein

Techniques in data mining and simulation applied to bioinformatics, the computational analysis of gene sequences, macromolecular structures, and functional genomics data on a large scale. Sequence alignment, comparative genomics and phylogenetics, biological databases, geometric analysis of protein structure, molecular-dynamics simulation, biological networks, microarray normalization, and machine-learning approaches to data integration. Prerequisites: MB&B 301 and MATH 115, or permission of instructor.  SC
MW 1pm-2:15pm

S&DS 361b / AMTH 361b, Data AnalysisBrian Macdonald

Selected topics in statistics explored through analysis of data sets using the R statistical computing language. Topics include linear and nonlinear models, maximum likelihood, resampling methods, curve estimation, model selection, classification, and clustering. After S&DS 242 and MATH 222 or 225, or equivalents.  QR
TTh 9am-10:15am

S&DS 363b, Multivariate Statistics for Social SciencesJonathan Reuning-Scherer

Introduction to the analysis of multivariate data as applied to examples from the social sciences. Topics include principal components analysis, factor analysis, cluster analysis (hierarchical clustering, k-means), discriminant analysis, multidimensional scaling, and structural equations modeling. Extensive computer work using either SAS or SPSS programming software. Prerequisites: knowledge of basic inferential procedures and experience with linear models.  QR
TTh 1pm-2:15pm

S&DS 364b / AMTH 364b / EENG 454b, Information TheoryAndrew Barron

Foundations of information theory in 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 STAT 241.  QR
TTh 11:35am-12:50pm

S&DS 365a, Intermediate Machine LearningJohn Lafferty

S&DS 365 is a second course in machine learning at the advanced undergraduate or beginning graduate level. The course assumes familiarity with the basic ideas and techniques in machine learning, for example as covered in S&DS 265. The course treats methods together with mathematical frameworks that provide intuition and justifications for how and when the methods work. Assignments give students hands-on experience with machine learning techniques, to build the skills needed to adapt approaches to new problems. Topics include nonparametric regression and classification, kernel methods, risk bounds, nonparametric Bayesian approaches, graphical models, attention and language models, generative models, sparsity and manifolds, and reinforcement learning. Programming is central to the course, and is based on the Python programming language and Jupyter notebooks. Prerequisites: a background in probability and statistics at the level of S&DS 242; familiarity with the core ideas from linear algebra, for example through Math 222; and computational skills at the level of S&DS 265 or CPSC 200.  QR
MW 9am-10:15am

S&DS 400a / MATH 330a, Advanced ProbabilitySekhar Tatikonda

Measure theoretic probability, conditioning, laws of large numbers, convergence in distribution, characteristic functions, central limit theorems, martingales. Some knowledge of real analysis assumed.  QR
TTh 2:30pm-3:45pm

S&DS 410a, Statistical InferenceZhou Fan

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.  Prerequisite: level of S&DS 241.
TTh 11:35am-12:50pm

* S&DS 425a or b, Statistical Case StudiesBrian Macdonald

Statistical analysis of a variety of statistical problems using real data. Emphasis on methods of choosing data, acquiring data, assessing data quality, and the issues posed by extremely large data sets. Extensive computations using R statistical software. Prerequisites: prior course work in probability and statistics, and a data analysis course at the level of STAT 361, 363, or 365 (or STAT 220, 230 if supported by other course work).  QR

S&DS 431a / AMTH 431a, Optimization and ComputationYang Zhuoran

This course is designed for students in Statistics & Data Science who need to know about optimization and the essentials of numerical algorithm design and analysis. It is an introduction to more advanced courses in optimization. The overarching goal of the course is teach students how to design algorithms for Machine Learning and Data Analysis (in their own research). This course is not open to students who have taken S&DS 430.  Prerequisites: Knowledge of linear algebra, multivariate calculus, and probability. Linear Algebra, by MATH 222, 223 or 230 or 231; Graph Theory, by MATH 244 or CPSC 365 or 366; and comfort with proof-based exposition and problem sets, such as is gained from MATH 230 and 231, or CPSC 366.
TTh 1pm-2:15pm

S&DS 432b, Advanced Optimization TechniquesSekhar Tatikonda

This course covers fundamental theory and algorithms in optimization, emphasizing convex optimization. Topics covered include convex analysis; duality and KKT conditions; subgradient methods; interior point methods; semidefinite programming; distributed methods; stochastic gradient methods; robust optimization; and an introduction to nonconvex optimization.   Applications accepted from statistics & data science, economics, engineering, and the sciences. Prerequisites: Knowledge of linear algebra, such as MATH 222, 225; multivariate calculus, such as MATH 120;  probability, such as S&DS 241/541; optimization, such as S&DS 431/631; and, comfort with proof-based exposition and problem sets.
TTh 1pm-2:15pm

* S&DS 480a or b, Individual StudiesSekhar Tatikonda

Directed individual study for qualified students who wish to investigate an area of statistics not covered in regular courses. A student must be sponsored by a faculty member who sets the requirements and meets regularly with the student. Enrollment requires a written plan of study approved by the faculty adviser and the director of undergraduate studies.

S&DS 491a and S&DS 492b, Senior ProjectStaff

Individual research that fulfills the senior requirement. Requires a faculty adviser and DUS permission. The student must submit a written report about results of the project.