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STATISTICS

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**STAT 100 Numbers and Reason (5) QSR*** Bookstein*

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.

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**STAT 111 Lectures in Applied Statistics (1) NW**

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.

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**STAT 220 Basic Statistics (5) NW, QSR**

Objectives and pitfalls of statistical studies. Structure of data sets, histograms, means, and standard deviations. Correlation and regression. Probability, binomial and normal. Interpretation of estimates, confidence intervals, and significance tests. (Students may receive credit for only one of STAT 220, STAT 221, STAT 311, and ECON 311.) Offered: AWSpS.

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**STAT 221 Statistical Concepts and Methods for the Social Sciences (5) NW, QSR*** Morita*

Develops statistical literacy. Examines objectives and pitfalls of statistical studies; study designs, data analysis, inference; graphical and numerical summaries of numerical and categorical data; correlation and regression; and estimation, confidence intervals, and significance tests. Emphasizes social science examples and cases. (Students may receive credit for only one of STAT 220, STAT 221, STAT 311, STAT 221/CS&SS 221/SOC 221, and ECON 311.) Offered: jointly with CS&SS 221/SOC 221; AWSp.

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**STAT 302 Statistical Software and Its Applications (3)*** Morita*

Introduction to data structures and basics of implementing procedures in statistical computing packages, selected from but not limited to R, SAS, STATA, MATLAB, SPSS, and Minitab. Provides a foundation in computation components of data analysis. Prerequisite: either STAT 311/ECON 311 or STAT 390/MATH 390. Offered: W.

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**STAT 311 Elements of Statistical Methods (5) NW, QSR**

Elementary concepts of probability and sampling; binomial and normal distributions. Basic concepts of hypothesis testing, estimation, and confidence intervals; t-tests and chi-square tests. Linear regression theory and the analysis of variance. (Students may receive credit for only one of STAT 220, STAT 221, STAT 311, and ECON 311.) Prerequisite: either MATH 111, MATH 120, MATH 124, MATH 127, or MATH 144. Offered: AWSpS.

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**STAT 316 Design of Experiments and Regression Analysis (4) NW*** Kapur*

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: IND E 315. Offered: jointly with IND E 316; W.

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**STAT 320 Evaluating Social Science Evidence (5) I&S, QSR**

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.

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**STAT 321 Case-Based Social Statistics I (5) I&S, QSR**

Introduction to statistical reasoning for social scientists. Built around cases representing in-depth investigations into the nature and content of statistical and social-science principles and practice. Hands-on approach: weekly data-analysis laboratory. Fundamental statistical topics: measurement, exploratory data analysis, probabilistic concepts, distributions, assessment of statistical evidence. Offered: jointly with CS&SS 321/SOC 321; W.

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**STAT 322 Case-Based Social Statistics II (5) I&S, QSR**

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; Sp.

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**STAT 340 Introduction to Probability and Mathematical Statistics I (4) QSR*** Morita*

Covers the fundamentals of probability and mathematical statistics; axioms of probability, conditional and joint probability, random variables, univariate and multivariate distributions and densities, and moments; bionomial, negative binomial, geometric, Poisson, normal, exponential distributions, and central limit theorem; and basic estimation and hypothesis testing theory. Prerequisite: either STAT 311/ECON 311 or STAT 390/MATH 390; either a minimum grade of 2.5 in MATH 327 or MATH 136. Offered: A.

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**STAT 341 Introduction to Probability and Statistical Inference I (4) NW**

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: either STAT 340 or STAT/MATH 394 and STAT/MATH 395; either STAT/ECON 311 or STAT/MATH 390; either a minimum grade of 2.5 in MATH 136 or MATH 327. Offered: W.

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**STAT 342 Introduction to Probability and Statistical Inference II (4) NW**

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.

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**STAT 390 Probability and Statistics in Engineering and Science (4) NW**

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. Students may receive credit for only one of STAT 390, STAT 481/ECON 481, and ECON 580. Prerequisite: either MATH 126 or MATH 136. Offered: jointly with MATH 390; AWSpS.

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**STAT 391 Probability and Statistics for Computer Science (4) NW**

Fundamentals of probability and statistics from the perspective of the computer scientist. Random variables, distributions and densities, conditional probability, independence. Maximum likelihood, density estimation, Markov chains, classification. Applications in computer science. Prerequisite: minimum grade of 2.5 in MATH 126; 2.5 in MATH 308; either CSE 326, CSE 332, CSE 373, CSE 417, or CSE 421. Offered: Sp.

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**STAT 394 Probability I (3) NW**

Sample spaces; basic axioms of probability; combinatorial probability; conditional probability and independence; binomial, Poisson, and normal distributions. Prerequisite: minimum grade of 2.0 in either MATH 126 or MATH 136; recommended: either MATH 324 or MATH 327. Offered: jointly with MATH 394; AWS.

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**STAT 395 Probability II (3) NW**

Random variables; expectation and variance; laws of large numbers; normal approximation and other limit theorems; multidimensional distributions and transformations. Prerequisite: minimum grade of 2.0 in STAT/MATH 394. Offered: jointly with MATH 395; WSpS.

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**STAT 396 Probability III (3) NW**

Characteristic functions and generating functions; recurrent events and renewal theory; random walk. Prerequisite: minimum grade of 2.0 in either MATH 395 or STAT 395. Offered: jointly with MATH 396; Sp.

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**STAT 403 Introduction to Resampling Inference (4) NW**

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. Credit allowed for STAT 403 or STAT 503 but not both. Prerequisite: either STAT 311/ECON 311, STAT 341, STAT 390/MATH 390, STAT 481/ECON 481, or Q SCI 381 and Q SCI 482; recommended: Q SCI 483, which may be taken concurrently. Offered: jointly with Q SCI 403; Sp.

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**STAT 421 Applied Statistics and Experimental Design (4) NW**

Computer-aided data analyses using comparisons between batches, analysis of variance and regression. Evaluation of assumptions, data transformation, reliability of statistical measures (jackknife, bootstrap). Fisher-Gosset controversy. Prerequisite: either STAT 342 or STAT 481/ECON 481; recommended: MATH 308. Offered: A.

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**STAT 423 Applied Regression and Analysis of Variance (4) NW**

Regression analysis. Problems in interpreting regression coefficients. Estimation, including two-stage least squares. Guided regression: building linear models, selecting carriers. Regression residuals. Analysis of variance. Nonparametric regression. Factorial designs, response surface methods. Prerequisite: either STAT 342, STAT 421, or STAT 481/ECON 481; recommended: MATH 308. Offered: W.

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**STAT 425 Introduction to Nonparametric Statistics (3) NW**

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: STAT 390/MATH 390. Offered: jointly with BIOST 425.

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**STAT 427 Introduction to Analysis of Categorical Data (4) NW**

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: either STAT 342, STAT 362, or STAT 421.

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**STAT 428 Multivariate Analysis for the Social Sciences (4) NW**

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.

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**STAT 480 Sampling Theory for Biologists (3) NW*** Skalski*

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; recommended: Q SCI 483. Offered: jointly with Q SCI 480; W, odd years.

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**STAT 486 Experimental Design (4) NW*** Conquest*

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; recommended: Q SCI 483. Offered: jointly with Q SCI 486; W, even years.

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**STAT 491 Introduction to Stochastic Processes (3) NW**

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 either MATH 395 or STAT 395. Offered: jointly with MATH 491; A.

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**STAT 492 Stochastic Calculus for Option Pricing (3) NW**

Introductory stochastic calculus mathematical foundation for pricing options and derivatives. Basic stochastic analysis tools, including stochastic integrals, stochastic differential equations, Ito's formula, theorems of Girsanov and Feynman-Kac, Black-Scholes option pricing, American and exotic options, bond options. Prerequisite: either MATH 394 or STAT 394; either MATH 395 or STAT 395. Offered: jointly with MATH 492; W.

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**STAT 495 Service Learning: K-12 Tutoring Experience (1-5, max. 5)*** Morita*

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

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**STAT 498 Special Topics (1-5, max. 15) NW**

Reading and lecture course intended for special needs of students.

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**STAT 499 Undergraduate Research (1-5, max. 15)**

Offered: AWSpS.

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**STAT 502 Design and Analysis of Experiments (4)**

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, MATH 390/STAT 390, ECON 481/STAT 481, ECON 580 or equivalent; MATH 308 or equivalent. Offered: A.

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**STAT 503 Practical Methods for Data Analysis (4)**

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. Departmental credit allowed for only one of 403 and 503. Prerequisite: B A 500 or QMETH 500 or equivalent or permission of instructor. Offered: jointly with QMETH 503.

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**STAT 504 Applied Regression (4)**

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 481/ECON 481, or SOC 425; recommended: MATH 308. Offered: jointly with CS&SS 504.

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**STAT 506 Applied Probability and Statistics (4)**

Discreet 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. Offered: jointly with AMATH 506.

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**STAT 509 Introduction to Mathematical Statistics: Econometrics I (5) NW**

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. (Credit allowed for only one of STAT 390, STAT 481, and ECON 580.) Prerequisite: STAT 311/ECON 311; either MATH 136 or MATH 126 with either MATH 308 or MATH 309; recommended: MATH 324. Offered: jointly with CS&SS 509/ECON 580; A.

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**STAT 512 Statistical Inference (4)**

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. Introduction to decision theory. Prerequisite: STAT 395 and STAT 421, STAT 423, STAT 504, or BIOST 512 (concurrent registration permitted for these three). Offered: A.

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**STAT 513 Statistical Inference (4)**

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. Introduction to decision theory. Prerequisite: STAT 512. Offered: W.

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**STAT 516 Stochastic Modeling of Scientific Data (3-)**

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 or STAT 396. Offered: A.

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**STAT 517 Stochastic Modeling of Scientific Data (-3)**

Covers Markov random fields; continuous-tie 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.

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**STAT 518 Stochastic Modeling Project (3)**

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.

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**STAT 519 Time Series Analysis (3)**

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. Offered: A.

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**STAT 520 Spectral Analysis of Time Series (4)**

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. The parametric autoregressive spectral density estimate for single and multiple stationary time series. Spectral analysis of nonstationary random processes and for randomly sampled processes. Techniques of robust spectral analysis. Prerequisite: one of STAT 342, STAT 390, STAT 481, or IND E 315. Offered: jointly with E E 520; W.

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**STAT 521 Advanced Probability (3)**

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.

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**STAT 522 Advanced Probability (3)**

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.

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**STAT 523 Advanced Probability (3)**

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.

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**STAT 524 Design of Medical Studies (3)**

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.

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**STAT 527 Nonparametric Regression and Classification (3)*** Minin, Raftery, Richardson, Wakefield*

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.

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**STAT 528 Applied Statistics Capstone (3)*** McCormick, Sampson, Wakefield*

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.

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**STAT 529 Sample Survey Techniques (3)**

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.

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**STAT 530 Wavelets: Data Analysis, Algorithms, and Theory (3)**

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: some Fourier theory and linear algebra; Math or STAT 390, ECON or STAT 481, or STAT 513; or IND E 315. Offered: jointly with E E 530; Sp.

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**STAT 533 Theory of Linear Models (3)**

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; and STAT 513, BIOST 515, and a course in matrix algebra. Offered: jointly with BIOST 533; Sp.

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**STAT 534 Statistical Computing (3)**

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.

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**STAT 535 Statistical Learning: Modeling, Prediction, and Computing (3)**

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.

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**STAT 536 Analysis of Categorical and Count Data (3)**

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: SOC 504, SOC 505, SOC 506, or equivalent; recommended: CS&SS 505 and CS&SS 506, or equivalent. Offered: jointly with CS&SS 536/SOC 536; A.

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**STAT 538 Statistical Learning: Modeling, Prediction, and Computing (3)**

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.

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**STAT 539 Statistical Learning: Modeling, Prediction and Computing (3)*** Meila*

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

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**STAT 542 Multivariate Analysis (3)**

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. Offered: WSp.

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**STAT 544 Bayesian Statistical Methods (3)**

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.

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**STAT 547 Options and Derivatives (4)**

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; recommended: ECON 424.

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**STAT 548 Machine Learning for Big Data (4)*** Fox, Guestrin*

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.

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**STAT 549 Statistical Methods for Portfolios (4)**

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.

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**STAT 550 Statistical Genetics I: Mendelian Traits (3)**

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; A.

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**STAT 551 Statistical Genetics II: Quantitative Traits (3)**

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.

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**STAT 552 Statistical Genetics III: Design and Analysis (3)**

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.

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**STAT 560 Hierarchical Modeling for the Social Sciences (4)**

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; recommended: CS&SS 505, CS&SS 506 or equivalent. Offered: jointly with CS&SS 560/SOC 560.

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**STAT 561 Special Topics in Applied Statistics (1-5, max. 15)**

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

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**STAT 562 Special Topics in Applied Statistics (1-5, max. 15)**

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

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**STAT 564 Bayesian Statistics for the Social Sciences (4)**

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; recommended: CS&SS 505; CS&SS 506. Offered: jointly with CS&SS 564.

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**STAT 566 Causal Modeling (4)**

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; recommended: CS&SS 505, CS&SS 506, or equivalent. Offered: jointly with CS&SS 566.

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**STAT 567 Statistical Analysis of Social Networks (4)**

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; recommended: CS&SS 505; CS&SS 506. Offered: jointly with CS&SS 567.

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**STAT 570 Advanced Regression Methods for Independent Data (3)**

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: STAT 512 and STAT 513;BIOST/STAT 533 or STAT 421/STAT 502 and STAT 423/STAT 504; a course in matrix algebra. Offered: jointly with BIOST 570; A.

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**STAT 571 Advanced Regression Methods for Dependent Data (3)**

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.

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**STAT 572 Advanced Regression Methods: Project (3)**

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

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**STAT 573 Statistical Methods for Categorical Data (3)**

Advanced topics in generalized linear models and the analysis of categorical data: overdispersion, quasilikelihood, parameters in link and variance functions, exact conditional inference, random effects, saddlepoint approximations. Prerequisite: BIOST 571 and STAT 582. Credit/no-credit only. Offered: jointly with BIOST 573; Sp.

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**STAT 574 Multivariate Statistical Methods (3)**

Use of multivariate normal sampling theory, linear transformations of random variables, one- and two-sample tests, profile analysis, partial and multiple correlation, multivariate ANOVA and least squares, discriminant analysis, principal components, factor analysis, robustness, and some special topics. Some computer use included. Prerequisite: BIOST 570 or permission of instructor. Offered: jointly with BIOST 574.

MyPlan Course Details: STAT 574 (student access only)

**STAT 576 Statistical Methods for Survival Data (3)**

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.

MyPlan Course Details: STAT 576 (student access only)

**STAT 577 Advanced Design and Analysis of Experiments (3)**

Concepts important in experimental design and analyzing data from planned experiments. Multi-way layouts, randomized block designs, incomplete block designs, Lating and Graeco-Latin squares, factorial and fractional designs, split-plot designs, optimal design theory, response surface experiments. Prerequisite: either BIOST 515, BIOSTAT 533, STAT 502, STAT 504, STAT 533, or permission of instructor. Offered: jointly with BIOST 577.

MyPlan Course Details: STAT 577 (student access only)

**STAT 578 Special Topics in Advanced Biostatistics (*, max. 30)**

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

MyPlan Course Details: STAT 578 (student access only)

**STAT 579 Data Analysis and Reporting (2, max. 8)**

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 or permission of instructor. Offered: jointly with BIOST 579; AWSp.

MyPlan Course Details: STAT 579 (student access only)

**STAT 581 Advanced Theory of Statistical Inference (3)**

Limit theorems, asymptotic methods, asymptotic efficiency and efficiency bounds for estimation, maximum likelihood estimation, Bayes methods, asymptotics via derivatives of functionals, sample-based estimates of variability: (bootstrap and jackknife); robustness; estimation for dependent data, nonparametric estimation and testing. Prerequisite: STAT 513; either MATH 426 or MATH 576. Offered: A.

MyPlan Course Details: STAT 581 (student access only)

**STAT 582 Advanced Theory of Statistical Inference (3)**

Limit theorems, asymptotic methods, asymptotic efficiency and efficiency bounds for estimation, maximum likelihood estimation, Bayes methods, asymptotics via derivatives of functionals, sample-based estimates of variability: (bootstrap and jackknife); robustness; estimation for dependent data, nonparametric estimation and testing. Prerequisite: STAT 581. Offered: W.

MyPlan Course Details: STAT 582 (student access only)

**STAT 583 Advanced Theory of Statistical Inference (3)**

Limit theorems, asymptotic methods, asymptotic efficiency and efficiency bounds for estimation, maximum likelihood estimation, Bayes methods, asymptotics via derivatives of functionals, sample-based estimates of variability: (bootstrap and jackknife); robustness; estimation for dependent data, nonparametric estimation and testing. Prerequisite: STAT 582. Offered: Sp.

MyPlan Course Details: STAT 583 (student access only)

**STAT 590 Statistics Seminar (*, max. 15)**

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

MyPlan Course Details: STAT 590 (student access only)

**STAT 591 Special Topics in Statistics (1-5, max. 15)**

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.

MyPlan Course Details: STAT 591 (student access only)

**STAT 592 Special Topics in Statistics (1-5, max. 15)**

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: W.

MyPlan Course Details: STAT 592 (student access only)

**STAT 593 Special Topics in Statistics (1-5, max. 15)**

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.

MyPlan Course Details: STAT 593 (student access only)

**STAT 598 Techniques of Statistical Consulting (1)**

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.

MyPlan Course Details: STAT 598 (student access only)

**STAT 599 Statistical Consulting (*, max. 12)**

Consulting experience in data analysis, applied statistics. Student required to provide consulting services to students and faculty three hours per week. Prerequisite: permission of Graduate Program Coordinator. Credit/no-credit only. Offered: AWSpS.

MyPlan Course Details: STAT 599 (student access only)

**STAT 600 Independent Study or Research (*-)**

Prerequisite: permission of Graduate Program Coordinator. Offered: AWSpS.

MyPlan Course Details: STAT 600 (student access only)

**STAT 700 Master's Thesis (*-)**

Prerequisite: permission of Graduate Program Coordinator. Offered: AWSpS.

MyPlan Course Details: STAT 700 (student access only)

**STAT 800 Doctoral Dissertation (*-)**

Prerequisite: permission of Graduate Program Coordinator. Offered: AWSpS.

MyPlan Course Details: STAT 800 (student access only)