Course Catalog

Numbers and Reason

Surveys the standard ways in which "arithmetic turns into understanding" across examples from the natural and the social sciences. Main concepts include abduction (inference to the best explanation), consilience (numerical agreement across multiple measurement levels), bell curves, linear models, and the likelihood of hypothesis. Offered: A.

Lectures in Applied Statistics

Weekly lectures illustrating the importance of statisticians in a variety of fields, including medicine and the biological, physical, and social sciences. Credit/no-credit only. Offered: jointly with BIOST 111; Sp.

Introduction to Data Science

Survey course introducing the essential elements of data science: data collection, management, curation, and cleaning; summarizing and visualizing data; basic ideas of statistical inference, machine learning. Students will gain hands-on experience through computing labs. Offered: AWSp.

Statistical Reasoning

Introduces statistical reasoning. Focuses primarily on the what and why rather than the how. Helps students gain an understanding of the rationale behind many statistical methods, as well as an appreciation of the use and misuse of statistics. Encourages and requires critical thinking. May only receive credit for one of STAT 220, or STAT 221/CS&SS 221/SOC 221, or STAT 290. Offered: AWSpS.

Statistical Concepts and Methods for the Social Sciences

Develops statistical literacy. Examines objectives & pitfalls of statistical studies; study designs, data analysis, inference; graphical & numerical summaries of numerical &categorical data; correlation and regression; estimation, confidence intervals, & significance tests. Emphasizes social science examples and cases. May only receive credit for one of STAT 220, STAT 221/CS&SS 221/SOC 221, or STAT 290. Offered: jointly with CS&SS 221/SOC 221; AWSp.

Advanced Placement (AP) Statistics

Course awarded based on Advanced Placement (AP) score. Consult the Admissions Exams for Credit website for more information.

BASIC STATISTICS WITH APPLICATIONS

Statistical Computing

An introduction to the foundations of statistical computing and data analysis. Topics include programming fundamentals, data cleaning, data visualization, debugging, and version control. Topics are motivated by methods in statistics and machine learning. Taught using the R programming language. Prerequisite: either STAT 290, STAT 311, STAT 390, STAT 391, or Q SCI 381; recommended: experience with R programming language. Offered: AWSpS.

Introduction to the Ethics of Algorithmic Decision Making

Ethical and social implications of design, implementation, and interpretation of statistical decision-making algorithms. Examples from medicine, education, and criminal justice. Examines how algorithms interact with social categories including race, class, and gender - preserving or reshaping existing inequities. Evaluates statistical frameworks for balancing fairness and privacy with efficiency.

Elements of Statistical Methods

Elements of good study design. Descriptive statistics including correlation and regression. Introductory concepts of probability and sampling; binomial and normal distributions. Basic concepts of hypothesis testing, estimation, and confidence intervals; t-tests and chi-square tests. Experience with computer software. Prerequisite: either STAT 220, STAT 221/CS&SS 221/SOC 221, STAT 290, MATH 120, MATH 124, MATH 125, MATH 126, MATH 134, MATH 135, MATH 136, QMETH 201, Q SCI 190, Q SCI 291, or Q SCI 292. Offered: AWSpS.

Design of Experiments

Introduction to the analysis of data from planned experiments. Analysis of variance for multiple factors and applications of orthogonal arrays and linear graphs for fractional factorial designs to product and process design optimization. Regression analysis with applications in engineering. Prerequisite: either IND E 315, STAT 341, or STAT 390. Offered: jointly with IND E 316; W.

Evaluating Social Science Evidence

A critical introduction to the methods used to collect data in social science: surveys, archival research, experiments, and participant observation. Evaluates "facts and findings" by understanding the strengths and weaknesses of the methods that produce them. Case based. Offered: jointly with CS&SS 320/SOC 320.

Data Science and Statistics for Social Sciences I

Introduction to applied data analysis for social scientists. Focuses on using programming to prepare, explore, analyze, and present data that arise in social science research. Data science topics include loading, cleaning, and exploring data, basic visualization, reproducible research practices. Statistical topics include measurement, probability, modeling, assessment of statistical evidence. Lectures intermixed with programming and lab sessions. Offered: jointly with CS&SS 321/SOC 321; W.

Case-Based Social Statistics II

Continuation of CS&SS 321/SOC 321/STAT 321. Progresses to questions of assessing the weight of evidence and more sophisticated models including regression-based methods. Built around cases investigating the nature and content of statistical principles and practice. Hands-on approach: weekly data analysis laboratory. Prerequisite: CS&SS 321/SOC 321/STAT 321, or permission of instructor. Offered: jointly with CS&SS 322/SOC 322.

Introduction to Probability and Mathematical Statistics I

Fundamentals of probability for statistics; axioms of probability, conditional and joint probability, independence; random variables, univariate and multivariate distributions and densities, moments, and moment generating functions; binomial, negative binomial, geometric, Poisson, uniform, normal, exponential distributions; and transformations of a random variable. Prerequisite: either MATH 126 or MATH 136; and either STAT 311, STAT 390/MATH 390, or Q SCI 381. Offered: A.

Introduction to Probability and Mathematical Statistics II

Brief review of: sample spaces, random variables, probability. Distribution: binomial, normal, Poisson, geometric. Followed by: expectation, variance, central limit theorem. Basic concepts of estimation, testing, and confidence intervals. Maximum likelihood estimators and likelihood ratio tests, efficiency. Introduction to regression. Prerequisite: STAT 340 or MATH 394/STAT 394; and STAT 311 or STAT 390. Offered: W.

Introduction to Probability and Mathematical Statistics III

Brief review of: sample spaces, random variables, probability. Distribution: binomial, normal, Poisson, geometric. Followed by: expectation, variance, central limit theorem. Basic concepts of estimation, testing, and confidence intervals. Maximum likelihood estimators and likelihood ratio tests, efficiency. Introduction to regression. Prerequisite: STAT 341. Offered: Sp.

Statistical Methods in Engineering and Science

Concepts of probability and statistics. Conditional probability, independence, random variables, distribution functions. Descriptive statistics, transformations, sampling errors, confidence intervals, least squares and maximum likelihood. Exploratory data analysis and interactive computing. Cannot be taken for credit if credit received for STAT509/CS&SS 509/ECON 580. Prerequisite: either MATH 126 or MATH 136. Offered: AWSpS.

Quantitative Introductory Statistics for Data Science

The basic concepts of statistics, machine learning and data science, as well as their computational aspects. Statistical models, likelihood, maximum likelihood and Bayesian estimation, regression, classification, clustering, principal component analysis, model validation, statistical testing. Practical implementation and visualization in data analysis. Assumes knowledge of basic probability, mathematical maturity, and ability to program. Prerequisite: either CSE 312 or MATH 394/STAT 394. Offered: W.

Probability I

Axiomatic definitions of probability; random variables; conditional probability and Bayes' theorem; expectations and variance; named distributions: binomial, geometric, Poisson, uniform (discrete and continuous), normal and exponential; normal and Poisson approximations to binomial. Transformations of a single random variable. Markov and Chebyshev's inequality. Weak law of large numbers for finite variance. Prerequisite: either a minimum grade of 2.0 in MATH 126, or a minimum grade of 2.0 in MATH 136. Offered: jointly with MATH 394; AWSpS.

Probability II

Jointly distributed random variables; conditional distributions and densities; conditional expectations and variance; covariance, correlation, and Cauchy-Schwarz inequality; bivariate normal distribution; multivariate transformations; moment generating functions; sums of independent random variables; Central Limit Theorem; Chernoff's inequality; Jensen's inequality. Prerequisite: either a minimum grade of 2.0 in MATH 394/STAT 394, or a minimum grade of 2.0 in STAT 340. Offered: jointly with MATH 395; WSpS.

Finite Markov Chains and Monte-Carlo Methods

Finite Markov chains; stationary distributions; time reversals; classification of states; classical Markov chains; convergence in total variation distance and L2; spectral analysis; relaxation time; Monte Carlo techniques: rejection sampling, Metropolis-Hastings, Gibbs sampler, Glauber dynamics, hill climb and simulated annealing; harmonic functions and martingales for Markov chains. Prerequisite: a minimum grade of 2.0 in MATH 208; and either a minimum grade of 2.0 in MATH 394/STAT 394 and STAT 395/MATH 395, or a minimum grade of 2.0 in STAT 340 and STAT 341, or a minimum grade of 2.0 in STAT 340 and STAT 395/MATH 395. Offered: jointly with MATH 396; Sp.

Introduction to Resampling Inference

Introduction to computer-intensive data analysis for experimental and observational studies in empirical sciences. Students design, program, carry out, and report applications of bootstrap resampling, rerandomization, and subsampling of cases. Experience programming in R is beneficial. Cannot be taken for credit if credit received for STAT 503/QMETH 503. Prerequisite: either STAT 311, STAT 341, STAT 390, STAT 391, or Q SCI 381 and Q SCI 482. Offered: jointly with Q SCI 403; Sp.

Research Design and Statistics for HIHIM

Explores healthcare and research statistics. Addresses hospital statistics, used to calculate usage levels of heathcare resources and outcomes of clinical operations, and research statistics, used to summarize and describe significant characteristics of a data set, and to make inferences about a population based on data collected from a sample. In addition, principles of research are described, including the Institutional Review Board process. Offered: jointly with BIOST 406/HIHIM 425.

Introduction to Machine Learning

Provides practical introduction to machine learning. Modules include regression, classification, clustering, retrieval, recommender systems, and deep learning, with a focus on an intuitive understanding grounded in real-world applications. Intelligent applications are designed and used to make predictions on large, complex datasets. Prerequisite: either CSE 123, CSE 143, CSE 160, or CSE 163; and either STAT 311, STAT 390, STAT 391, IND E 315, MATH 394/STAT 394, STAT 395/MATH 395, or Q SCI 381. Offered: jointly with CSE 416.

Applied Statistics and Experimental Design

Experimental designs, including completely randomized, blocked, Latin Square, factorial, 2 to the k, fractional, nested, and split-plot; fixed effects and random effects models; confounding and aliasing. Analyses of real data, to illustrate concepts. Prerequisite: STAT 342. Offered: A.

Applied Regression and Analysis of Variance

Least squares; simple/multiple linear regression including interpretation; variable selection; analysis of covariance; assumptions and diagnostics/remedies; weighting and generalized least squares; hypothesis testing. Analyses of real data to illustrate concepts. Prerequisite: STAT 342, which may be taken concurrently. Offered: W.

Introduction to Nonparametric Statistics

Overview of nonparametric methods, such as rank tests, goodness of fit tests, 2 x 2 tables, nonparametric estimation. Useful for students with only a statistical methods course background. Prerequisite: Either STAT 311 and STAT 340, STAT 390, or STAT 391. Offered: jointly with BIOST 425.

Introduction to Analysis of Categorical Data

Techniques for analysis of count data. Log-linear models, logistic regression, and analysis of ordered response categories. Illustrations from the behavioral and biological sciences. Computational procedures. Prerequisite: STAT 391 or STAT 423.

Multivariate Analysis for the Social Sciences

Multivariate techniques commonly used in the social and behavioral sciences. Linear models for dependence analysis (multivariate regression, MANOVA, and discriminant analysis) and for interdependence analysis (principal components and factor analysis). Techniques applied to social science data using computer statistical packages. Prerequisite: either STAT 342, STAT 362, or STAT 421.

Introduction to Statistical Machine Learning

Introduces the theory and application of statistical machine learning. Topics may include supervised versus unsupervised learning; cross-validation; the bias-variance trade-off; regression and classification; regularization and shrinkage approaches; non-linear approaches; tree-based methods; and support vector machines. Includes applications in R. Prerequisite: either STAT 341or STAT 391; recommended: MATH 208. Offered: Sp.

Multivariate Statistical Methods

Introduces statistical methods for analysis of multidimensional data. Methods include tools for exploratory analysis of high-dimensional data, statistical modeling approaches to parameter estimation and hypothesis testing, and nonparametric methods for classification and clustering. Includes applications in R. Prerequisite: MATH 208; and either STAT 341, STAT 390/MATH 390, or STAT 391. Offered: W.

Visualizing Data

Visual representations of data to discover patterns, answer questions, convey findings, drive decisions, and provide persuasive evidence. Students create visualizations using high-level programming languages such as Python and R. Prerequisite: either CSE123, CSE163, or STAT 302. Offered: W.

Sampling Theory for Biologists

Theory and applications of sampling finite populations including: simple random sampling, stratified random sampling, ratio estimates, regression estimates, systematic sampling, cluster sampling, sample size determinations, applications in fisheries and forestry. Other topics include sampling plant and animal populations, sampling distributions, estimation of parameters and statistical treatment of data. Prerequisite: Q SCI 482. Offered: jointly with Q SCI 480; W, odd years.

Experimental Design

Emphasizes data modeling using structured means resulting from choice of experimental and treatment design. Examines experimental designs, including crossed, nested designs; block; split-plot designs; and covariance analysis. Also covers multiple comparisons, efficiency, power, sample size, and pseudo-replication. Prerequisite: Q SCI 482. Offered: jointly with Q SCI 486; W, even years.

Introduction to Stochastic Processes

Random walks, Markov chains, branching processes, Poisson process, point processes, birth and death processes, queuing theory, stationary processes. Prerequisite: minimum grade of 2.0 in MATH 394/STAT 394 and MATH 395/STAT 395, or minimum grade of 2.0 in STAT 340 and STAT 341 and MATH 396/STAT 396. Offered: jointly with MATH 491; A.

Introduction to Stochastic Processes II

Introduces elementary continuous-time discrete/continuous-state stochastic processes and their applications. Covers useful classes of continuous-time stochastic processes (e.g., Poisson process, renewal processes, birth and birth-and-death processes, Brownian motion, diffusion processes, and geometric Brownian motion) and shows how useful they are for solving problems of practical interest. Prerequisite: a minimum grade of 2.0 in MATH 491/STAT 491. Offered: jointly with MATH 492.

Service Learning: K-12 Tutoring Experience

Tutoring mathematics in local K-12 schools. Offered: AWSp.

Special Topics

Reading and lecture course intended for special needs of students.

Undergraduate Research

Offered: AWSpS.

Design and Analysis of Experiments

Design of experiments covering concepts such as randomization, blocking, and confounding. Analysis of experiments using randomization tests, analysis of variance, and analysis of covariance. Prerequisite: either STAT 342, STAT 390/MATH 390, or STAT 509/CS&SS 509/ECON 580; and MATH 208. Offered: A.

Practical Methods for Data Analysis

Basic exploratory data analysis with business examples. Data summaries, multivariate data, time series, multiway tables. Techniques include graphical display, transformation, outlier identification, cluster analysis, smoothing, regression, robustness. Cannot be taken for credit if credit received for STAT 403/Q SCI 403. Prerequisite: B A 500 or QMETH 500. Offered: jointly with QMETH 503.

Applied Regression

Least squares estimation. Hypothesis testing. Interpretation of regression coefficients. Categorical independent variables. Interactions. Assumption violations: outliers, residuals, robust regression; nonlinearity, transformations, ACE, CART; nonconstant variance. Variable selection and model averaging. Prerequisite: either STAT 342, STAT 390/MATH 390, STAT 421, STAT 509/CS&SS 509/ECON 580, or SOC 505. Offered: jointly with CS&SS 504.

Applied Probability and Statistics

Discrete and continuous random variables, independence and conditional probability, central limit theorem, elementary statistical estimation and inference, linear regression. Emphasis on physical applications. Prerequisite: some advanced calculus and linear algebra.

Econometrics I: Introduction to Mathematical Statistics

Examines methods, tools, and theory of mathematical statistics. Covers, probability densities, transformations, moment generating functions, conditional expectation. Bayesian analysis with conjugate priors, hypothesis tests, the Neyman-Pearson Lemma. Likelihood ratio tests, confidence intervals, maximum likelihood estimation, Central limit theorem, Slutsky Theorems, and the delta-method. Prerequisite: STAT 311/ECON 311; either MATH 136 or MATH 126 with either MATH 308 or MATH 309. (Credit allowed for only one of STAT 390, STAT 481, and ECON 580.) Offered: jointly with CS&SS 509/ECON 580.

Statistical Inference

Review of random variables; transformations, conditional expectation, moment generating functions, convergence, limit theorems, estimation; Cramer-Rao lower bound, maximum likelihood estimation, sufficiency, ancillarity, completeness. Rao-Blackwell theorem. Hypothesis testing: Neyman-Pearson lemma, monotone likelihood ratio, likelihood-ratio tests, large-sample theory. Contingency tables, confidence intervals, invariance. Decision theory. Prerequisite: STAT 395 and STAT 421, STAT 423, STAT 504, or BIOST 512 (concurrent registration permitted for these three). Offered: A.

Statistical Inference

Review of random variables; transformations, conditional expectation, moment generating functions, convergence, limit theorems, estimation; Cramer-Rao lower bound, maximum likelihood estimation, sufficiency, ancillarity, completeness. Rao-Blackwell theorem. Hypothesis testing: Neyman-Pearson lemma, monotone likelihood ratio, likelihood-ratio tests, large-sample theory. Contingency tables, confidence intervals, invariance. Decision theory. Prerequisite: STAT 512. Offered: W.

Stochastic Modeling of Scientific Data

Covers discrete-time Markov chain theory; inference for discrete-time Markov chains; Monte Carlo methods; missing data; hidden Markov models; and Gaussian Markov random fields. Prerequisite: either STAT 342, MATH 396/STAT 396, or STAT 391. Offered: A.

Stochastic Modeling of Scientific Data

Covers Markov random fields; continuous-time Markov chains; birth-death and branching processes; and point processes and cluster models. Procedures for inference for these stochastic processes, including Likelihood methods and estimating equations. Prerequisite: STAT 516. Offered: W.

Stochastic Modeling Project

Student in-depth analyses, oral presentations, and discussion of selected research articles focusing on stochastic modeling of, and inference for, scientific data. Prerequisite: STAT 517 and permission of instructor. Offered: Sp.

Time Series Analysis

Descriptive techniques. Stationary and nonstationary processes, including ARIMA processes. Estimation of process mean and autocovariance function. Fitting ARIMA models to data. Statistical tests for white noise. Forecasting. State space models and the Kalman filter. Robust time series analysis. Regression analysis with correlated errors. Statistical properties of long memory processes. Prerequisite: STAT 513.

Spectral Analysis of Time Series

Estimation of spectral densities for single and multiple time series. Nonparametric estimation of spectral density, cross-spectral density, and coherency for stationary time series, real and complex spectrum techniques. Bispectrum. Digital filtering techniques. Aliasing, prewhitening. Choice of lag windows and data windows. Use of the fast Fourier transform. Prerequisite: either STAT 342, STAT 390, STAT 509/CS&SS 509/ECON 580, or IND E 315. Offered: jointly with E E 520.

Advanced Probability

Measure theory and integration, independence, laws of large numbers. Fourier analysis of distributions, central limit problem and infinitely divisible laws, conditional expectations, martingales. Prerequisite: either MATH 426 or MATH 576. Offered: jointly with MATH 521; A.

Advanced Probability

Measure theory and integration, independence, laws of large numbers. Fourier analysis of distributions, central limit problem and infinitely divisible laws, conditional expectations, martingales. Prerequisite: either MATH 426 or MATH 576. Offered: jointly with MATH 522; W.

Advanced Probability

Measure theory and integration, independence, laws of large numbers. Fourier analysis of distributions, central limit problem and infinitely divisible laws, conditional expectations, martingales. Prerequisite: either MATH 426 or MATH 576. Offered: jointly with MATH 523; Sp.

Design of Medical Studies

Design of medical studies, with emphasis on randomized controlled clinical trials. Bias elimination, controls, treatment assignment and randomization, precision, replication, power and sample size calculations, stratification, and ethics. Suitable for graduate students in biostatistics and for research-oriented graduate students in other scientific fields. Prerequisite: BIOST 511 or equivalent, and one of BIOST 513, BIOST 518, STAT 421, STAT 423, STAT 512, or EPI 512; or permission of instructor. Offered: jointly with BIOST 524; Sp.

Nonparametric Regression and Classification

Covers techniques for smoothing and classification including spline models, kernel methods, generalized additive models, and the averaging of multiple models. Describes measures of predictive performance, along with methods for balancing bias and variance. Prerequisite: either STAT 502 and STAT 504 or BIOST 514 and BIOST 515. Offered: jointly with BIOST 527; Sp.

Applied Statistics Capstone

Covers technical and non-technical aspects of applied statistics work, building on methods taught in prerequisite courses. Key elements include: study design, determining the aim of the analysis, choosing an appropriate method, and report writing. Prerequisite: STAT 502; STAT 504; STAT 536; STAT 570. Offered: W.

Sample Survey Techniques

Design and implementation of selection and estimation procedures. Emphasis on human populations. Simple, stratified, and cluster sampling; multistage and two-phase procedures; optimal allocation of resources; estimation theory; replicated designs; variance estimation; national samples and census materials. Prerequisite: either STAT 421, STAT 423, STAT 504, QMETH 500, BIOST 511, or BIOST 517, or equivalent; or permission of instructor. Offered: jointly with BIOST 529/CS&SS 529.

Wavelets: Data Analysis, Algorithms, and Theory

Review of spectral analysis. Theory of continuous and discrete wavelets. Multiresolution analysis. Computation of discrete wavelet transform. Time-scale analysis. Wavelet packets. Statistical properties of wavelet signal extraction and smoothers. Estimation of wavelet variance. Prerequisite: college-level coursework in Fourier theory and linear algebra; and either STAT 390/MATH 390, STAT 509/CS&SS 509/ECON 580, STAT 513, or IND E 315. Offered: jointly with E E 530; Sp.

Theory of Linear Models

Examines model structure; least squares estimation; Gauss-Markov theorem; central limit theorems for linear regression; weighted and generalized least squares; fixed and random effects; analysis of variance; blocking and stratification; and applications in experimental design. Prerequisite: STAT 421 or STAT 423 or BIOST 515; and STAT 513; and a course in matrix algebra. Offered: jointly with BIOST 533; Sp.

Statistical Computing

Introduction to scientific computing. Includes programming tools, modern programming methodologies, (modularization, object oriented design), design of data structures and algorithms, numerical computing and graphics. Uses C++ for several substantial scientific programming projects. Prerequisite: experience with programming in a high level language. Offered: jointly with BIOST 534; Sp.

Statistical Learning: Modeling, Prediction, and Computing

Covers statistical learning over discrete multivariate domains, exemplified by graphical probability models. Emphasizes the algorithmic and computational aspects of these models. Includes additional topics in probability and statistics of discrete structures, general purpose discrete optimization algorithms like dynamic programming and minimum spanning tree, and applications to data analysis. Prerequisite: experience with programming in a high level language. Offered: A.

Analysis of Categorical and Count Data

Analysis of categorical data in the social sciences. Binary, ordered, and multinomial outcomes, event counts, and contingency tables. Focuses on maximum likelihood estimations and interpretations of results. Prerequisite: either SOC 504, SOC 505, SOC 506/CS&SS 507, STAT 423, or STAT 504/CS&SS 504. Offered: jointly with CS&SS 536/SOC 536.

Statistical Learning: Modeling, Prediction, and Computing

Reviews optimization and convex optimization in its relation to statistics. Covers the basics of unconstrained and constrained convex optimization, basics of clustering and classification, entropy, KL divergence and exponential family models, duality, modern learning algorithms like boosting, support vector machines, and variational approximations in inference. Prerequisite: experience with programming in a high level language. Offered: W.

Statistical Learning: Modeling, Prediction and Computing

Supervised, applied project in statistical modeling, prediction, and computing. Prerequisite: STAT 535; STAT 538; computer programming at intermediate level. Offered: Sp.

Multivariate Analysis

Multivariate normal distribution; partial and multiple correlation; Hotelling's T2; Bartlett's decomposition; various likelihood ratio tests; discriminant analysis; principal components; graphical Markov models. Prerequisite: STAT 582 or permission of instructor.

Bayesian Statistical Methods

Statistical methods based on the idea of a probability distribution over the parameter space. Coherence and utility. Subjective probability. Likelihood principle. Conjugate families. Structure of Bayesian inference. Limit theory for posterior distributions. Sequential experiments. Exchangeability. Bayesian nonparametrics. Empirical Bayes methods. Prerequisite: STAT 513 or permission of instructor.

Options and Derivatives

Covers theory, computation, and statistics of options and derivatives pricing, including options on stocks, stock indices, futures, currencies, and interest rate derivatives. Prerequisite: STAT 506 or permission of instructor.

Machine Learning for Big Data

Covers machine learning and statistical techniques for analyzing datasets of massive size and dimensionality. Representations include regularized linear models, graphical models, matrix factorization, sparsity, clustering, and latent factor models. Algorithms include sketching, random projections, hashing, fast nearest-neighbors, large-scale online learning, and parallel learning (Map-Reduce, GraphLab). Prerequisite: either STAT 535 or CSE 546. Offered: jointly with CSE 547; W.

Statistical Methods for Portfolios

Covers the fundamentals of modern statistical portfolio construction and risk measurement, including theoretical foundations, statistical methodology, and computational methods using modern object-oriented software for data analysis, statistical modeling, and numerical portfolio optimization. Prerequisite: ECON 424 or equivalent, or permission of instructor.

Statistical Genetics I: Mendelian Traits

Mendelian genetic traits. Population genetics; Hardy-Weinberg, allelic variation, subdivision. Likelihood inference, information and power; latent variables and EM algorithm. Pedigree relationships and gene identity. Meiosis and recombination. Linkage detection. Multipoint linkage analysis. Prerequisite: STAT 390 and STAT 394, or permission of instructor. Offered: jointly with BIOST 550; Sp.

Statistical Genetics II: Quantitative Traits

Statistical basis for describing variation in quantitative traits. Decomposition of trait variation into components representing genes, environment and gene-environment interaction. Methods of mapping and characterizing quantitative trait loci. Prerequisite: STAT/BIOST 550; STAT 423 or BIOST 515; or permission of instructor. Offered: jointly with BIOST 551; A.

Statistical Genetics III: Design and Analysis

Overview of probability models, inheritance models, penetrance. Association and linkage. The lod score method. Affected sib method. Fitting complex inheritance models. Design mapping studies; multipoint, disequilibrium, and fine-scale mapping. Ascertainment. Prerequisite: STAT/BIOST 551; GENOME 371; or permission of instructor. Offered: jointly with BIOST 552; W.

Statistical Methods for Spatial Data

Motivates the need for, and describes methods for, the analysis of spatial data. Topics: Clustering, cluster detection, spatial regression, modeling neighborhood effects, geographical information systems. Point and aggregated data considered and data from complex surveys. Offered: jointly with CS&SS 554/SOC 534; W.

Introduction to Statistics and Probability

Overview of probability; conditional probability and independence; Bayes Theorem; discrete and continuous random variables including jointly distributed; key distributions including the normal and its spin offs; properties of expectation and variance; conditional expectation; covariance and correlation; Central Limit Theorem; law of large numbers; Parameter Estimation. Offered: jointly with BIOST 556/DATA 556; A.

Applied Statistics and Experimental Design

Inferential statistical methods for discrete and continuous random variables including tests for difference in means and proportions; linear and logistic regression; causation versus correlation; confounding; resampling methods; study design. Prerequisite: either STAT 556/BIOST 556/DATA 556 or permission of instructor. Offered: jointly with BIOST 557/DATA 557; W.

Statistical Machine Learning for Data Scientists

Bias-variance trade-off; training versus test error; overfitting; cross-validation; subset selection methods; regularized approaches for linear/logistic regression: ridge and lasso; non-parametric regression: trees, bagging, random forests; local regression and splines; generalized additive models; support vector machines; k-means and hierarchical clustering; principal components analysis. Prerequisite: STAT/BIOST/DATA 557, or permission of instructor. Offered: jointly with BIOST 558/DATA 558; Sp.

Measure Theory

Measures: Caratheodory Extension Theorem. Measurable functions: Riesz Theorem, Slutsky Theorem. Integration: Fatou's lemma, MCT, DCT; Helly-Bray, Mann-Wald and Skorokhod theorems. Derivatives via signed measures. Measures and processes on products. Distribution and quantile functions. Independence and conditional distributions. Prerequisite: either MATH 424 and MATH 425, or MATH 574 and MATH 575. Offered: Sp.

Hierarchical Modeling for the Social Sciences

Explores ways in which data are hierarchically organized, such as voters nested within electoral districts that are in turn nested within states. Provides a basic theoretical understanding and practical knowledge of models for clustered data and a set of tools to help make accurate inferences. Prerequisite: SOC 504, SOC 505, SOC 506 or equivalent. Offered: jointly with CS&SS 560/SOC 560.

Special Topics in Applied Statistics

Data analysis, spectral analysis or robust estimation. Prerequisite: permission of instructor.

Special Topics in Applied Statistics

Data analysis, spectral analysis or robust estimation. Prerequisite: permission of instructor.

Statistical Demography

Statistical methods and models for estimating and forecasting population quantities. Topic: Demographic rates; Population projection; Leslie matrix; modeling age-specific patterns; probabilistic population projections and Bayesian hierarchical models; estimating past and present fertility, mortality, migration and population; big data in demography. Prerequisite: Either STAT 509/CS&SS 509/ECON 509, STAT 513, or permission from the instructor. Offered: jointly with CS&SS 563/SOC 563; Sp.

Bayesian Statistics for the Social Sciences

Statistical methods based on the idea of probability as a measure of uncertainty. Topics covered include subjective notion of probability, Bayes' Theorem, prior and posterior distributions, and data analysis techniques for statistical models. Prerequisite: SOC 504, SOC 505, SOC 506 or equivalent. Offered: jointly with CS&SS 564.

Causal Modeling

Construction of causal hypotheses. Theories of causation, counterfactuals, intervention vs. passive observation. Contexts for causal inference: randomized experiments; sequential randomization; partial compliance; natural experiments, passive observation. Path diagrams, conditional independence, and d-separation. Model equivalence and causal under-determination. Prerequisite: course in statistics, SOC 504, SOC 505, SOC 506, or equivalent. Offered: jointly with CS&SS 566.

Statistical Analysis of Social Networks

Statistical and mathematical descriptions of social networks. Topics include graphical and matrix representations of social networks, sampling methods, statistical analysis of network data, and applications. Prerequisite: SOC 504, SOC 505, SOC 506, or equivalent. Offered: jointly with CS&SS 567.

Advanced Regression Methods for Independent Data

Covers linear models, generalized linear and non-linear regression, and models. Includes interpretation of parameters, including collapsibility and non-collapsibility, estimating equations; likelihood; sandwich estimations; the bootstrap; Bayesian inference: prior specification, hypothesis testing, and computation; comparison of approaches; and diagnostics. Prerequisite: either STAT 512 and STAT 513, or BIOST 522 and BIOST 523; and either STAT 502 and STAT 504/CS&SS 504, or BIOST 514 and BIOST 515; recommended: matrix algebra from a course at the level of BIOST 533/STAT 533. Offered: jointly with BIOST 570; A.

Advanced Regression Methods for Dependent Data

Covers longitudinal data models, generalized linear and non-linear mixed models; marginal versus conditional models; generalized estimating equations, likelihood-based inference, REML, BLUP, and computation of integrals; Bayesian inference: Markov chain Monte Carlo; covariance models, including models for split plot designs; comparison of approaches; and diagnostics. Prerequisite: BIOST570/STAT 570. Offered: jointly with BIOST 571; W.

Preparation for Research Prelim

Student presentations and discussion on selected methodological research articles focusing on regression modeling. Prerequisite: BIOST 571/STAT 571. Offered: jointly with BIOST 572; Sp.

Statistical Methods for Survival Data

Statistical methods for censored survival data arising from follow-up studies on human or animal populations. Parametric and nonparametric methods, Kaplan-Meier survival curve estimator, comparison of survival curves, log-rank test, regression models including the Cox proportional hazards model, competing risks. Prerequisite: STAT 581 and either BIOST 515, STAT 473, or equivalent. Offered: jointly with BIOST 576.

Special Topics in Advanced Biostatistics

Advanced-level topics in biostatistics offered by regular and visiting faculty. Prerequisite: permission of instructor. Offered: jointly with BIOST 578; AWSpS.

Data Analysis and Reporting

Analysis of real data to answer scientific questions. Common data-analytic problems. Sensible approaches to complex data. Graphical and tabular presentation of results. Writing reports for scientific journals, research collaborators, consulting clients. Graduate standing in statistics or biostatistics. Credit/no-credit only. Offered: jointly with BIOST 579; SpS.

Advanced Theory of Statistical Inference I

Foundations of parametric statistics: elementary decision theory, Bayesian methods, modes of convergence, central limit theorems, delta method, maximum likelihood estimation, regularity, hypothesis testing under fixed and local alternatives, parametric efficiency theory. Prerequisite: STAT 513. ; recommended: mathematical analysis from a course at the level of either MATH 426 or STAT 559. Offered: jointly with BIOST 583; A.

Advanced Theory of Statistical Inference II

Semiparametric and nonparametric estimation of irregular parameters: minimax rates of convergence, kernel methods, bias-variance tradeoff, concentration inequalities, empirical risk minimization, Rademacher complexity, Vapnik-Chervonenkis dimension, covering and bracketing numbers, empirical process theory (Glivenko-Cantelli results). Prerequisite: STAT 581/BIOST 583. ; recommended: mathematical analysis from a course at the level of either MATH 426 or STAT 559. Offered: jointly with BIOST 584; W.

Advanced Theory of Statistical Inference III

Semiparametric and nonparametric estimation of regular parameters: weak convergence, empirical process theory (Donsker results), asymptotic linearity, estimating equations, U-statistics, functional delta method, efficiency theory, construction of efficient estimators. Prerequisite: STAT 582/BIOST 584. ; recommended: mathematical analysis from a course at the level of either MATH 426 or STAT 559. Offered: jointly with BIOST 585; Sp.

Statistics Seminar

Prerequisite: permission of graduate program coordinator. Credit/no-credit only. Offered: AWSp.

Special Topics in Statistics

Distribution-free inference, game and decision theory, advanced theory of estimation (including sequential estimation), robustness, advanced probability theory, stochastic processes or empirical processes. Prerequisite: permission of instructor. Offered: A.

Special Topics in Statistics

Advanced topics in statistics and probability. Content varies by quarter. Prerequisite: permission of instructor. Offered: AWSpS.

Special Topics in Statistics

Distribution-free inference, game and decision theory, advanced theory of estimation (including sequential estimation), robustness, advanced probability theory, stochastic processes or empirical processes. Prerequisite: permission of instructor. Offered: Sp.

Techniques of Statistical Consulting

Seminar series covering technical and non-technical aspects of statistical consulting, including skills for effective communication with clients, report writing, statistical tips and rules of thumb, issues in survey sampling, and issues in working as a statistical consultant in academic, industrial, and private-practice settings. Prerequisite: entry code. Offered: jointly with BIOST 598; ASp.