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Courses in LSA Statistics
Statistics (STATS)
STATS 401. Applied Statistical Methods II
MATH 115, and STATS 250 (350) or 400 or 405, or ECON 405, or NRE 438. (4). (BS). (QR/1). May not be repeated for credit. No credit granted to those who have completed or are enrolled in STATS 413.

An intermediate course in applied statistics which assumes knowledge of STAT 350/400-level material. Covers a range of topics in modeling and analysis of data including: review of simple linear regression, two-sample problems, one-way analysis of variance; multiple linear regression, diagnostics and model selection; two-way analysis of variance, multiple comparisons, and other selected topics.

STATS 403. Introduction to Quantitative Research Methods
MATH 115, one of STATS 250 (350), 280, 400, 412. (4). (BS). May not be repeated for credit.

This course introduces methods for planning, executing, and evaluating research studies based on experiments, surveys, and observational datasets. In addition to learning a toolset of methods, students will read and report on recent research papers to learn how study design and data analysis are handled in different fields.

STATS 404. Effective Communication in Statistics
STATS 470 or 480. (2). (BS). May not be repeated for credit. May not be used in the Statistics or Applied Statistics academic minor. Rackham credit requires additional work.

This course will focus on the principles of good written and oral communication of statistical information and data analyses. Participants will study communication principles and apply them in writing assignments and oral presentations of statistical analyses. Topics will include giving constructive feedback and rewriting to improve clarity and technical correctness.

STATS 406. Introduction to Statistical Computing
STATS 401 AND MATH 215; or STATS 403 and MATH 215; or STATS 412; or MATH 425. (Prerequisites enforced at registration.) (4). (BS). May not be repeated for credit. F.

Selected topics in statistical computing, including basic numerical aspects, iterative statistical methods, principles of graphical analyses, simulation and Monte Carlo methods, generation of random variables, stochastic modeling, importance sampling, numerical and Monte Carlo integration.

STATS 408. Statistical Principles for Problem Solving: A Systems Approach
High school algebra. (4). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in STATS 170.

Our purpose is to help you use quantitative reasoning to facilitate learning. Specifically, we introduce statistical and mathematical principles, and then use these as analogues in a variety of real world situations. The notion of a system, a collection of components that come together repeatedly for a purpose, provides an excellent framework to describe many real world phenomena and provides a way to view the quality of an inferential process.

STATS 412. Introduction to Probability and Statistics
Prior or concurrent enrollment in MATH 215. (3). (BS). (QR/1). May not be repeated for credit. No credit granted to those who have completed or are enrolled in ECON 405, STATS 280, 400, or IOE 265. One credit granted to those who have completed or are enrolled in STATS 250. May not be used in the Statistics or Applied Statistics academic minor. F, W, Sp.

An introduction to probability theory; statistical models, especially sampling models; estimation and confidence intervals; testing statistical hypotheses; and important applications, including the analysis of variance and regression.

STATS 414. Special Topics in Statistics
Consent of department required. Varies by term and instructor. (3 - 4). May be elected twice for credit. May be elected more than once in the same term. Rackham credit requires additional work.

A course in exploring topics of current interest in statistics, probability and/or data science. Content varies by term and instructor.

STATS 415. Data Mining and Statistical Learning
MATH 215 and 217, and one of STATS 401, 406, 412 or 426. (4). (BS). May not be repeated for credit.

This course covers the principles of data mining, exploratory analysis and visualization of complex data sets, and predictive modeling. The presentation balances statistical concepts (such as over-fitting data, and interpreting results) and computational issues. Students are exposed to algorithms, computations, and hands-on data analysis in the weekly discussion sessions.

STATS 425 / MATH 425. Introduction to Probability
MATH 215. (3). (BS). May not be repeated for credit. F, W, Sp, Su.

STATS 426. Introduction to Theoretical Statistics
STATS 425 and prior or concurrent enrollment in MATH 217, 412 or 451. (3). (BS). May not be repeated for credit.

An introduction to theoretical statistics for students with a background in probability. Probability models for experimental and observational data, normal sampling theory, likelihood-based and Bayesian approaches to point estimation, confidence intervals, tests of hypotheses, and an introduction to regression and the analysis of variance. This course serves as a prerequisite for many graduate-level statistics courses.

STATS 430. Applied Probability
STATS 425 or equivalent. (3). (BS). May not be repeated for credit.

Review of probability theory; introduction to random walks; counting and Poisson processes; Markov chains in discrete and continuous time; equations for stationary distributions; introduction to Brownian motion. Selected applications such as branching processes, financial modeling, genetic models, the inspection paradox, inventory and queuing problems, prediction, and/or risk analysis.

STATS 470. Introduction to the Design of Experiments
STATS 401 or 412 or 425, or MATH 425. (Prerequisites enforced at registration.) (4). (BS). May not be repeated for credit. F.

Introduces students to basic concepts for planning experiments and to efficient methods of design and analysis. Topics covered include concepts such as randomization, replication and blocking; analysis of variance and covariance and the general linear model; factorial and fractional factorial designs, blocked designs, and split-plot designs.

STATS 480. Survey Sampling Techniques
STATS 401 or 412 or 425 or MATH 425. (Prerequisites enforced at registration.) (4). (BS). May not be repeated for credit. W.

Introduces students to basic ideas in survey sampling, moving from motivating examples to abstraction to populations, variables, parameters, samples and sample design, statistics, sampling distributions, Horvitz-Thompson estimators, basic sample design (simple random, cluster, systematic, multiple stage), various errors and biases, special topics.

STATS 500. Applied Statistics I
MATH 217, 417, or 513; and STATS 250 (350) or 426. (3). (BS). May not be repeated for credit. F.

Linear models; definitions, fitting, identifiability, collinearity, Gauss-Markov theorem, variable selection, transformation, diagnostics, outliers and influential observations. ANOVA and ANCOVA. Common designs. Applications and real data analysis are stressed, with students using the computer to perform statistical analyses.

STATS 503. Applied Multivariate Analysis
STATS 500 or permission of instructor. (3). (BS). May not be repeated for credit. F.

STATS 504. Statistical Consulting
STATS 401 or 500. (3). (BS). May be repeated for a maximum of 9 credits.

The goal of this course is to introduce students to key aspects of statistical consulting and data analysis activities. Students will be involved in problem solving and real applications individually or in groups, analyze data, write reports, and make presentations.

STATS 505 / ECON 671. Econometric Analysis I
Graduate standing and permission of instructor. (3). (BS). May not be repeated for credit.

This course is the first in two-course block that forms that basic required sequence in econometrics for all doctoral students. Their purpose is to provide Ph.D. students with the training needed to do the basic quantitative analysis generally understood to be part of the background of all modern economists. This includes: the theory and practice of testing hypotheses, statistical estimation theory, the basic statistical theory underlying the linear model, an introduction to econometric methods, and the nature of the difficulties which arise in applying statistical procedures to economic research problems.

STATS 509. Statistical Models and Methods for Financial Data
STATS 500 and STATS 510. (3). May not be repeated for credit.

This course will cover statistical models and methods relevant to financial data analysis. These include modeling and estimation of heavy tailed distributions, modeling and inference with multivariate copulas, linear and non-linear time series analysis, and statistical portfolio modeling. Data examples from financial applications will be used to illustrate the methods.

STATS 510. Mathematical Statistics I
MATH 215 or equivalent. (3). May not be repeated for credit.

This course introduces the essential concepts of probability and emphasizes topics that are important for statistical theory. Topics include counting, probability and conditional probability, independence, random variables, distribution functions, modeling dependence, transformations, quintiles, order statistics, laws of large numbers, central limit theorem, sampling distributions.

STATS 511. Mathematics Statistics II
STATS 425 or MATH 425 or STATS 510 or equivalent courses in probability. (3). May not be repeated for credit.

This is an introductory course to statistical estimation and inference. It is designed to give students sufficient mathematical statistics background so that they can utilize the theory in practice. The course will cover the following topics: univariate and multivariate families of distributions; sampling distributions and relevant properties; likelihood principles; point estimation; inference procedures; large sample properties, and selected topics in contemporary statistical methods.

STATS 525 / MATH 525. Probability Theory
MATH 451 (strongly recommended). MATH 425/STATS 425 would be helpful. (3). (BS). May not be repeated for credit.

STATS 526 / MATH 526. Discrete State Stochastic Processes
MATH 525 or STATS 525 or EECS 501. (3). (BS). May not be repeated for credit.

STATS 535 / IOE 562. Reliability
STATS 425 and 426 (or IOE 316 and 366). (3). (BS). May not be repeated for credit.

STATS 545 / BIOINF 545 / BIOSTAT 646. High Throughput Molecular Genomic and Epigenomic Data Analysis
STATS 400 (or equivalent) and graduate standing: or permission of instructor. Students should have a strong preparation in either biology or some branch of quantitative analysis (mathematics, statistics, or computer science). (3). (BS). May not be repeated for credit.

This course will cover statistical methods used to analyze data in experimental molecular biology. The course will primarily cover topics relating to gene expression data analysis, but other types of data such as genome sequence and epigenomics data that is sometimes analyzed in concert with expression data will also be covered.

STATS 547 / BIOINF 547 / MATH 547. Probabilistic Modeling in Bioinformatics
MATH,Flexible, due to diverse backgrounds of intended audience. Basic probability (level of MATH/STATS 425), or molecular biology (level of BIOLOGY 427), or biochemistry (level of CHEM/BIOLCHEM 451), or basic programming skills desireable or permission. (3). (BS). May not be repeated for credit.

Probabilistic models of proteins and nucleic acids. Analysis of DNA/RNA and protein sequence data. Algorithms for sequence alignment, statsistical analysis of similarity scores, hidden Markov models. Neural networks, training, gene finding, protein family profiles, multiple sequence alignment, sequence comparison and structure prediction. Analysis of expression array data.

STATS 560 / BIOSTAT 685. Introduction to Nonparametric Statistics
STATS 426 or permission of instructor. (3). (BS). May not be repeated for credit.

STATS 570 / IOE 570. Experimental Design
STATS 500 or background in regression and Graduate standing. (3). (BS). May not be repeated for credit.

Basic design principles, review of analysis of variance, block designs, two-level and three-level factorial and fractional factorial experiments, designs with complex aliasing, data analysis techniques and case studies, basic response surface methodology, variation reduction and introductory robust parameter designs.

STATS 575 / ECON 678. Advanced Econometrics I
MATH 417, and MATH 425/STATS 425; or ECON 671, 672, and 600. (3). (BS). May not be repeated for credit. F.

This course in econometric theory stressing the statistical foundation of the general linear model and the asymptotic distribution theory of nonlinear models. The course involves a development of the required theory in mathematical statistics and derivations and proofs of the main results associated with statistical inference in econometric models. Asymptotic distribution theory is studies in some detail.

STATS 576 / ECON 679. Advanced Econometrics II
ECON 678/STATS 575 or equivalent. (3). (BS). May not be repeated for credit.

This course continues from ECON 678. Includes a thorough treatment of statistical problems in econometrics, cross section data, times series data, panel data, development of simultaneous equation techniques, generalized method of moments, and formulation and estimation of special models. Selected current research topics depend on time and interest.

STATS 580 / BIOSTAT 617 / SOC 717 / SURVMETH 617. Methods and Theory of Sample Design
Three or more courses in statistics and preferably a course in methods of survey sampling. (3). (BS). May not be repeated for credit.

This course is concerned with the theory underlying the methods of survey sampling widely used in practice. It covers the basic techniques of simple random sampling, stratification, systematic sampling, cluster and multi-stage sampling, and probability proportional to size sampling. It also examines methods of variance estimation for complex sample designs, including the Taylor series expansion method, balanced repeated replications, and jackknife methods.

STATS 600. Linear Models
Knowledge of linear algebra; STATS 425 and STATS 426 or equivalent courses in probability and statistics. (3). May be repeated for a maximum of 6 credits.

This is an advanced introduction to regression modeling and prediction, including traditional and modern computationally-intensive methods. The following topics will be covered: 1) Theory and practice of linear models, including the relevant distribution theory, estimation, confidence and prediction intervals, testing, models and variable selection generalized least squares, robust fitting, and diagnostics; 2) Generalized linear models, including likelihood formulation, estimation and inference, diagnostics, and analysis of deviance; and 3) Large and small-sample inference as well as inference via the bootstrap, cross-validation, and permutation tests.

STATS 601. Analysis of Multivariate and Categorical Data
STATS 600. (3). May be repeated for a maximum of 6 credits.

This is an advanced introduction to the analysis of multivariate and categorical data. Topics include: 1) dimensional reduction techniques, including principal component analysis, multidimensional scaling and extensions; 2) classification, starting with a conceptual framework developed from cost functions, Bayes classifiers, and issues of over-fitting and generalization, and continuing with a discussion of specific classification methods, including LDA, QDA, and KNN; 3) discrete data analysis, including estimation and testing for log-linear models and contingency tables; 4) large-scale multiple hypothesis testing, including Bonferroni, Westphal-Young and related approaches, and false discovery rates; 5) shrinkage and regularization, including ridge regression, principal component regression, partial least squares, and the lasso; 6) clustering methods, including hierarchical methods, partitioning methods, K-means, and model based clustering.

STATS 605. Advanced Topics in Modeling and Data Analysis
STATS 601. (3). May be repeated for a maximum of 6 credits.

This course covers recent developments in statistical modeling and data analysis. Topics include: 1) classification and machine learning, including support vector machines, recursive partitioning, and ensemble methods; 2) methods for analyzing sets of curves, surfaces and images, including functional data analysis, wavelets, independent component analysis, and random field models; 3) modern regression, including splines and generalized additive models; 4) methods for analyzing structured dependent data, including mixed effects models, hierarchical models, graphical models, and Bayesian networks; and 5) clustering detection, and dimension reduction methods, including manifold learning, spectral clustering, and bump hunting.

STATS 607. Programming and Numerical Methods in Statistics
Consent of department required. STATS 425, STATS 426. Computer Programming experience recommended. (3; 1.5 in the half-term). May be elected twice for credit.

This course is ad advanced introduction to modern programming (Part I) and numerical analysis (Part 11) techniques used in statistics, modeling and data analysis. Part I course topics include: basic data structures, structured data formats, iteration and recursion, functional programming, classes and object-oriented programming, memory management, strategies for documenting and debugging code. This part of the course will cover programming fundamentals relevant for research on statistical methodology, and for working with large and complex data sets. Part II course topics include: sorting and binary searches, root finding in one dimension, interpolation techniques, low-dimensional numerical integration, solving triangular systems, basic matrix factorizations (LU, Cholesky, QR), Schur and singular value decompositions, sparse matrices. This part of the course will cover elementary algorithms that are useful for numerical analysis and programming with data.

STATS 608. Optimization Methods in Statistics
Consent of department required. MATH 451, STATS 425, STATS 426. Comp programming experience recommended. (3; 1.5 in the half-term). May be elected twice for credit.

This course is an advanced introduction to deterministic (Part I) and stochastic (Part II) optimization techniques. Part I course topics include: basic result's from mathematical analysis, role of convexity in optimization, Karush-Kuhn-Tucker conditions in constrained optimization, majoration algorithms and their applications (EM algorithm), Newton's method and extensions, convergence results, convex programming and duality. The material covers both theoretical and implementation issues, as well as application to statistical models. Part II course topics include: basic Monte Carlo methods (random number generators, variance reductions techniques), an introduction to Markov chains (irreducibility, recurrence, ergodicity), Markov Chain Monte Carlo methods (Metropolis-Hastings and Gibbs sampling algorithms, data-augmentation techniques, convergence diagnostics), and stochastic optimization (simulated annealing and stochastic approximation). This part of the course covers both theory and applications to complex statistical models.

STATS 610. Statistical Inference
STATS,MATH 451, STATS 425, and 426 or equivalent courses in probability, statistics and real analysis. (3). May be repeated for a maximum of 6 credits.

This course introduces students to the theory of statistical inference. It starts with a review of topics in probability theory including densities, expectation, random vectors and covariance matrices, independence, and conditioning. It then introduces exponential families and sufficiency and develops the theory of point estimation including unbiased and Bayesian estimation, conditional distributions, variance bounds and information. The theory of hypothesis testing is also covered, including uniformly most powerful tests and the duality between testing and interval estimation. Additional topics that may be covered include curved exponential families, equivariant estimation, and empirical Bayes and shrinkage estimators.

STATS 611. Large Sample Theory
STATS 610; and Graduate standing. (3). May be repeated for a maximum of 6 credits.

This course covers topics in large sample theory that are central for statistical inference, including: 1) modes of convergence, central limit theorems for averages and medians, and asymptotic relative efficiency; 2) estimating equations including the law of large numbers for random functions, consistency and asymptotic normality for maximum likelihood and M-estimators, the E-M algorithm, and asymptotic confidence intervals; 3) large sample theory for likelihood ratio tests. In addition, simulations inference and nonparametric regression are also covered. Other possible topics include theory for two sided tests and tests for higher dimensions.

STATS 612. Advanced Topics in Theoretical Statistics
STATS,STATS 520 or equivalent course in measure theory and STATS 611. (3). May be repeated for a maximum of 6 credits.

This course deals with selected topics in theoretical statistics at an advanced level. Topics include stochastic convergence in metric spaces, empirical processes including the empirical distribution function, functional delta method and applications including large sample theory for nonparametric density estimation, and the large sample theory for bootstrap methods. Other possible topics include semi-parametric models and efficiency issues.

STATS 620. Applied Probability and Stochastic Modeling
STATS,MATH 451, STATS 425, and 426 or equivalent courses in probability, statistics and real analysis. (3). May be repeated for a maximum of 6 credits.

This course in an introduction to stochastic models that capture the evolution in time of various random phenomena and/or dynamical systems. Such phenomena/systems arise extensively in diverse areas of research, ranging from biology, to data networks and production planning. Emphasis is placed on modeling aspects as well as development of the underlying theory. Topics covered include: markov chains in discrete and continuous time, Poisson and renewal processes, Brownian motion. Applications of these models in key scientific and engineering areas, such as genetics, and epidemics, computational algorithms, computers, and communication networks, inventory systems financial and risk management, are discussed.

STATS 621. Probability Theory
STATS,STATS 520 or equivalent course in measure theory, STATS 620. (3). May be repeated for a maximum of 6 credits.

This course is an introduction to measure-theoretic probability theory, with emphasis on rigorous treatment of the various topics discussed in the course. Topics to be covered include: 1) constructions of probability spaces, Kolmogorov's consistency theorem; independence of families of random variables, Borel-Cantelli lemmas and 0-1 laws; 2) various modes of convergence (inprobability, almost surely, in Lp, in distribution) and properties of weak convergence; 3) laws of large numbers; 4) central limit theorems for sequences and triangular arrays; 5) conditional expectations and distributions and 6) discrete time martingale theory. In addition, Brownian motion, continuous time martingales and elements of ergodic theory may be covered.

STATS 625 / MATH 625. Probability and Random Processes I
MATH 597 and Graduate standing. (3). (BS). May not be repeated for credit.

STATS 626 / MATH 626. Probability and Random Processes II
MATH 625/STATS 625 and Graduate standing. (3). (BS). May not be repeated for credit.

STATS 700. Special Topics in Applied Statistics I
STATS 501 and graduate standing. (1.5 - 3). May be repeated for a maximum of 12 credits.

This course covers selected special topics in applied statistics. It could be offered as a full-term course with a more extended coverage of multiple topics under one focus or as two half-terms that each term consists of its own special focus. The goal behind this course is to raise students' exposures to the modern research topics in applied statistics.

STATS 711. Special Topics in Theoretical Statistics II
Graduate standing and permission of instructor. (3). May not be repeated for credit.

STATS 750. Directed Reading
Consent of instructor required. Graduate standing. (1 - 6). (INDEPENDENT). May be elected five times for credit. May be elected more than once in the same term.

Designed for individual students who have an interest in a specific topic (usually that has stemmed from a previous course). An individual instructor must agree to direct such a reading, and the requirements are specified when approval is granted.

STATS 808. Seminar in Applied Statistics I
Graduate standing. (1). May be elected once for a maximum of 5 credits.

STATS 809. Seminar in Applied Statistics II
Graduate standing. (1). May be repeated for credit.

STATS 810. Literature Proseminar I
Consent of instructor required. Graduate standing. (2). May not be repeated for credit.

STATS 811. Literature Proseminar II
Consent of instructor required. Graduate standing. (2). May not be repeated for credit.

STATS 817 / EDUC 817 / PSYCH 817 / SOC 810. Interdisciplinary Seminar in Quantitative Social Science Methodology
Graduate standing, and Graduate-level course in STATS at the level of STAT 500 and 501. (1). May be repeated for a maximum of 6 credits. This course has a grading basis of "S" or "U".

This seminar will meet to consider methodological issues that arise in research in the social sciences. Themes for each meeting will arise from ongoing research projects at the University of Michigan. Visiting researchers will provide a brief account of their aims and data before defining the methodological challenge for which they desire discussion.

STATS 990. Dissertation/Precandidate
Election for dissertation work by doctoral student not yet admitted as a Candidate. Graduate standing. (1 - 8; 1 - 4 in the half-term). (INDEPENDENT). May be repeated for credit. This course has a grading basis of "S" or "U".

STATS 993. Graduate Student Instructor Training Program
Graduate standing. (1). May not be repeated for credit. This course has a grading basis of "S" or "U".

STATS 995. Dissertation/Candidate
Graduate School authorization for admission as a doctoral Candidate. (Prerequisites enforced at registration.) (8; 4 in the half-term). (INDEPENDENT). May be repeated for credit. This course has a grading basis of "S" or "U".

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