### 500-Level Statistics Courses (500-535)

**Statistics 500: Statistical Learning I: Regression**

The course covers concepts and methods for regression analysis and applications. Topics

include estimation, inference, interpretation of results, diagnostics, lack of fit, robust procedures, weighting and transformations, and model selection. The response variable could be continuous, binary or counts. More advanced techniques (splines, principal components analysis, and shrinkage estimators including ridge regression and Lasso) will also be covered. While there will be some theory, the emphasis will be on applications and data analysis. (3 Credits)

*Pre-requisite:* Linear Algebra (at the level of Math 214 or equivalent) AND

Theoretical Statistics (at the level of Stats 426 or equivalent)

**Statistics 501: Applied Statistics II**

Generalized linear models including logistics regression, Poisson regression, contingency tables. Random effects and repeated measures. Modern regression techniques. Regression and classification trees. Neural networks. *(3 Credits)*

*Pre-requisite:* STATS 500

**Statistics 503: Statistical Learning II: Multivariate Analysis**

The course covers methods for modern multivariate data analysis and statistical

learning, including both their theoretical foundations and practical applications. Topics include principal component analysis and other dimension reduction techniques, classification (discriminant analysis, decision trees, nearest neighbor classifiers, logistic partitioning methods, model-based methods), and categorical data analysis. There will be a significant data analysis component. *(4 Credits)*

*Pre-requisite: *STATS 500 or equivalent.

**Statistics 504: Practice and Communication in Applied Statistics**

This course provides students with hands-on experience using a variety of techniques from modern applied statistics through case studies involving data drawn from various fields. Lectures provide background on case studies, along with reviews of relevant methodology. Students then conduct independent data analyses for each case study and produce written reports. Evaluation is based on attaining insight from the data, effective communication of findings, and appropriate use of statistical methodology, as well as active participation in class discussions.* (3 credits)*.

This course is restricted to Master in Applied Statistics and Masters in Data Science students only.

*Pre-requisite:* STATS 500 and 503.

**Statistics 505: Econometric Analysis I (ECON 671)**

Econ 671 and 672 form the 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. *(3 Credits)*

Permission of instructor required to register.

**Statistics 506: Computational Methods and Tools in Statistics**

Selected topics in computational statistics including: managing and processing large data sets, parallel and distributed programming, simulation and Monte Carlo methods, interactive statistical methods, and optimization. (3 Credits)

Pre-requisite: STATS Master's Standing or stats 500.

**STATS 507: Data Science and Analytics using Python**

This course surveys some of the tools and frameworks currently popular among data scientists and machine learning practitioners in academia and industry. The first half of the course consists of an accelerated introduction to the Python programming language, including brief introductions to object-oriented and functional programming styles as well as tools for code optimization. The second half of the course will survey tools for handling structured data (regular expressions, HTML/JSON, databases), data visualization, numerical and symbolic computing, interacting with the UNIX/Linux command line, and large-scale distributed computing. Several modern inferential techniques arising in machine learning and applied statistics will be reviewed. *(3 credits)*

Advisory pre-requisite: STATS 500

**Statistics 509: Statistical Models and Methods for Financial Data**

This course will cover statistical models and methods relevant to the analysis of financial data. Topics covered will include modeling and estimation of data from heavy-tailed distributions, models and inference with multivariate copulas, linear and non-linear time series analysis, and statistical portfolio modeling. Applications from finance will be used to illustrate the methods. (3 Credits)

Pre-requisite: Stat 500 and 510, or equivalent

**Statistics 510: Probability and Distribution Theory**

Essential concepts of probability and distribution theory that are important for statistical inference including: random variables, probability, conditional probability, distribution functions, independence, modeling dependence, transformations, quantiles, order statistics, laws of large numbers, central limit theorem, and sampling distributions. (3 Credits)

*Pre-requisite:* Math 215 (Calculus III) or equivalent

**Statistics 511: Statistical Inference**

This is a graduate-level introductory course to key concepts, methods and theory in statistical inference. The topics covered will include univariate and multivariate families of distributions, likelihood principle, point estimation, confidence regions, hypothesis tests, large sample properties, and other selected topics in contemporary methods. (3 Credits)

*Pre-requisite: Stat 510 or equivalent*

**STATS 513: (Regression and Data Analysis)**

The course is designed for graduate students interested in quantitative research to learn about regression models for data analysis. Topics include estimation and inference, diagnostics, model selection, and interpretation of results associated with linear models and general linear models. Additional topics may vary with the instructor. *(3 Credits)*

*Advisory Pre-Requisites: Linear Algebra (at the level of MATH 214 or equivalent) AND Statistics (at the level of STATS 412 or STATS 426)*

*No credit granted to those who have completed or are enrolled in STATS 413 and/or STATS 500*

**Statistics 520: Mathematical Methods in Statistics**

This course provides the mathematical background for theoretical Ph.D.-level courses in statistics and probability. The course reviews basic notions from matrix algebra and real analysis. It then introduces students to measure theory and integration. In particular, the content covers definition of measures and measurable functions, convergence theorems, Lebesgue integration, Lp spaces, signed measures, Radon-Nikodym theorem, and integration on product spaces.* (3 Credits)*

*Pre-requisite:* MATH 451 or equivalent course in real analysis.

**Statistics 525: Probability Theory (MATH 525)**

This course covers axiomatic probability; combinatorics; random variables and their distributions; special distributions; joint, marginal and conditional distributions; expectation; the mean, variance, and moment generating function; induced distributions; sums of independent random variables; the law of large numbers; the central limit theorem. Optional topics drawn from: random walks, Markov chains, and/or martingales. *(3 Credits)*

*Advisory Pre-requisite: *MATH 451 (strongly recommended) or 450. STATS 425 would be helpful.

**Statistics 526: Discrete State Stochastic Processes (MATH 526)**

Review of discrete distributions; generating functions; compound distributions, renewal theorem; modeling of systems as Markov chains; first properties; Chapman-Kolmogorov equations; return and first passage times; classification of states and periodicity; absorption probabilities and the forward equation; stationary distributions and the backward equation; ergodicity; limit properties; application to branching and queueing processes; examples from engineering, biological and social sciences; Markov chains in continuous time; embedded chains; the M/G/1 queue; Markovian decision processes; application to inventory problems; other topic at instructor's discretion. *(3 Credits)*

*Pre-requisite: *STATS 525 or EECS 501

**Statistics 531: Analysis of Time Series**

Decomposition of series; trends and regression as a special case of time series; cyclic components; smoothing techniques; the variate difference method; representations including spectrogram, periodogram, etc.; stochastic difference equations autoregressive schemes, moving averages; large sample inference and prediction; covariance structure and spectral densities; hypothesis testing and estimation and applications and other topics. *(3 Credits)*

*Pre-requisite:* STATS 426

**Statistics 535: Reliability (IOE 562)**

This course covers the important reliability concepts and methodology that arise in modeling, assessing, and improving product reliability and in analyzing field and warranty data. Topics are selected from the following: Basic reliability concepts, common parametric models for component reliability, censoring schemes, analysis of time-to-failure data, accelerated testing for reliability assessment, modeling and analyzing repairable systems reliability, analysis of warranty and field-failure data, maintenance policies and availability, reliability improvement through experimentation.* (3 Credits)*

*Pre-requisite: *STATS 425 and 426 (or IOE 316 and 366)

### 500-Level Statistics Courses (545-580)

**Statistics 545: Data Analysis in Molecular Biology (BIOSTAT 646, BIOINFORMATICS 545)**

The course will cover statistical methods used to analyze data in experimental molecular biology, with an emphasis on gene and protein expression array data. Topics: Data acquisition; databases; low level processing; normalization; quality control; statistical inference (group comparisons, cyclicity, survival); multiple comparisons; statistical learning algorithms; clustering; visualization; and case studies. *(3 Credits)*

*Pre-requisite: *Graduate standing and STATS 400 (or equivalent) or permission of instructor.

*Advisory Pre-requisite: *Students should have a strong preparation in either biology or some branch of quantitative analysis (mathematics, statistics, or computer science), but not necessarily in both domains.

**Statistics 547: Probabilistic Modeling in Bioinformatics (Math 547)**

Probabilistic models of proteins and nucleic acids. Analysis of DNA/RNA and protein sequence data. Algorithms for sequence alignment, statistical 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. *(3 Credits)*

*Pre-requisite: *STATS 425 or BIOL 427 or BIOL CHEM 415; basic programming skills desirable. Graduate standing and permission of instructor.

**Statistics 548: Computations in Probabilistic Modeling in Bioinformatics (MATH 548)**

This will be a computational laboratory course designed in parallel with Math/Stat 547. Weekly hands-on problems will be presented on the algorithms presented in the course, the use of public sequence databases, the design of hidden Markov models. Concrete examples of homology, gene finding, structure analysis. *(1 Credit)*

*Pre-requisite: *STATS 425 or BIOL 427 or BIOL CHEM 415; basic programming skills desirable. Graduate standing and permission of instructor.

**Statistics 550: Bayesian Decision Analysis (IOE 560)**

Axiomatic foundations for personal probability and utility; interpretation and assessment of personal probability and utility; formulation of Bayesian decision problems; risk functions, admissibility; likelihood principle and properties of likelihood functions; natural conjugate prior distributions; improper and finitely additive prior distributions; examples of posterior distributions, including the general regression model and contingency tables; Bayesian credible intervals and hypothesis tests; applications to a variety of decision-making situations. *(3 Credits)*

*Pre-requisite:* STATS 425

**Statistics 551: Topics in Bayesian modeling and computation**

This course provides basic concepts and several modern techniques of Bayesian modeling and computation. Foundational topics include decision theoretic characterization of Bayesian inference and its relation to frequentist methods, de Finetti-type theorems and the existence of priors, conjugate priors and other notions of objective prior distributions, and Bayesian model selection. The course covers a number of advanced modeling techniques, both classical and modern, which belong to the class of hierarchical models, spatiotemporal models, dynamics models and Bayesian nonparametric models. A substantial part of the course is devoted to computational algorithms based on Markov Chain Monte Carlo sampling for complex models, sequential Monte Carlo methods, and deterministic methods such as variational approximation. A key component of the course would involve data analysis with Bayesian techniques.

*Advisory Prerequisites: *statistics and probability background at the level of STATS 510, which may be taken concurrently. Experience with data analysis techniques at the level of STATS 500 and STATS 503 will be helpful.

**Statistics 553: Conceptual Foundations of Statistical Inference (PHIL 553)**

This course will focus on conceptual issues in the foundations of probability theory and statistics. It is intended for graduate students with modest prior background in statistics. Probability theory will be reviewed, and elementary statistical techniques will be discussed. Course will evaluate the main philosophical interpretations of the probability calculus and resulting paradigms of statistical inference.* (3-4 Credits)*

*Pre-requisite: *A course in statistical theory (e.g. PSYCH 613, ECON 405) and graduate or advanced undergraduate standing, or permission of instructor.

**Statistics 560: Introduction to Nonparametric Statistics (BIOS 685)**

Confidence intervals and tests for quantiles, tolerance regions, and coverages; estimation by U statistics and linear combination or order statistics; large sample theory for U statistics and order statistics; the sample distribution and its uses including goodness-of-fit tests; rank and permutation tests for several hypotheses including a discussion of locally most powerful rank and permutation tests; and large sample and asymptotic efficiency for selected tests. *(3 Credits)*

*Pre-requisite: *STATS 426

**Statistics 570: Design of Experiments (IOE 570)**

Basic topics and ideas in the design of experiments: randomization and randomization tests; the validity and analysis of randomized experiments; randomized blocks; Latin and Graeco-Latin squares; plot techniques; factorial experiments; the use of confounding and response surface methodology; weighing designs, lattice and incomplete block and partially balanced in complete block designs. *(3 Credits)*

*Pre-requisite: *STATS 500 or background in regression. Graduate standing.

**Statistics 580: Methods and Theory of Sample Design (SOC 717/BIOS 617)**

Theory underlying sample designs and estimation procedures commonly used in survey practice. Simple random sampling, stratification systematic sampling, cluster sampling, multistage sampling, sampling with probability proportional to size, replicated sampling, multiphase sampling. Post-stratification, ratio, regression and difference estimation. Variance estimation with complex sample designs: Taylor series method, repeated replications, jackknife repeated replications. Nonresponse weighting adjustments and imputation. *(3 Credits)*

*Pre-requisite: *Three or more courses in Statistics and preferably a course in methods of survey sampling.

### 600-Level Statistics Courses (Effective Fall 2020)

**Statistics 600: Regression Analysis**

This is an advanced introduction to regression modeling and prediction, including traditional and modern computationally-intensive methods. It includes a comprehensive treatment of linear models for independent observations using least squares estimation; non least-squares approaches including penalization methods for variable selection; regression methods for dependent data, including generalized least squares, estimating equations, and mixed models; generalized linear models and generalized estimating equations; quantile regression, dimension reduction regression, and smoothing-based methods. It also covers issues related to data collection, study design, and interpretation of findings, including missing data, non-representative samples, causality, and designed experiments. (4 credits).

*Prerequisites*: linear algebra; regression at the level of STATS 413; probability and statistical theory at the level of STATS 425/426.

**Statistics 601: Statistical Learning**

This course is an advanced introduction to modern statistical learning. Topics include dimension reduction techniques, including principal component analysis, factor analysis, multidimensional scaling and manifold learning; conceptual framework of classification including cost functions, Bayes classifiers, overfitting and generalization; specific classification methods including logistic regression, naive Bayes, discriminant analysis, support vector machines, kernel-based methods, generalized additive models, tree-based methods, boosting, neural networks; clustering methods including K-means, model-based clustering algorithms, mixture models, latent variable models, hierarchical models; and algorithms such as the EM algorithm, Gibbs sampling, and variational inference methods. Additional topics that may be covered include categorical data analysis, graphical models, and deep learning. (4 credits)

*Prerequisite*: STATS 600

**Statistics 604: Statistical Practice**

This course studies the process of statistical investigation. Students will learn to formulate scientific and statistical questions, analyze relevant data, and clearly communicate their findings. The emphasis is not on specific methods, but rather on scientific reasoning, collaboration, communication, and critical evaluation of findings. The course will be project based, using case studies from collaborative research and consulting. Key components of the course include: question formulation, data collection and study design, data cleaning and exploratory data analysis, model selection and validation, assessment of findings, post-hoc analysis, and conclusions, writing, communication and critical assessment, and reproducibility and replicability. (4 credits).

*Prerequisite*: STATS 600

**Statistics 605: Advanced Topics in Modeling and Data Analysis**

This course covers recent developments in statistical modeling and data analysis. Topics vary by instructor.

*Prerequisite*: STATS 601

**Statistics 606: Computation and Optimization Methods in Statistics**

This course is an introduction to mathematical optimization with emphasis on theory and algorithms relevant to statistical practice. The course covers algorithms for large-scale matrix computations, majorization-minimization methods, Newton-type methods, and stochastic approximation. It also covers optimality conditions, Lagrange duality for convex optimization problems, and convergence analysis. *(3 Credits)*

*Advisory prerequisites: *MATH 451, STATS 425, STATS 426. Computer programming experience is recommended.

**Statistics 608: Monte Carlo Methods in Statistics**

This course is an introduction to Monte Carlo sampling and integration methods that arise in statistics. Course topics include: basic Monte Carlo methods (random number generators, variance reduction techniques, importance sampling and its generalizations), an introduction to Markov chains and Markov Chain Monte Carlo (Metropolis-Hastings and Gibbs samplers, data-augmentation techniques, convergence diagnostics). Optional topics include: sequential Monte Carlo, Hamiltonian Monte Carlo, advanced computational methods (approximate Bayesian computation, variational inference) for complex statistical models such as latent variable and hierarchical or nonparametric Bayesian models.* (3 Credits)*

*Advisory prerequisites: *MATH 451, STATS 425, STATS 426. Computer programming experience is recommended.

**Statistics 610: Statistical Theory I**

This course covers core topics in statistical theory. It starts with a brief review of necessary probability concepts such as types of convergence and background on exponential families and related topics. The core topics include sample and asymptotic variance bounds, maximum likelihood estimation and likelihood ratio theory, asymptotic relative efficiency, the EM algorithm, M-estimation, robustness, multiple testing, fundamentals of decision theory and Bayesian inference, empirical Bayes and Steinian shrinkage. (3 Credits)

*Prerequisites*: STATS 510 and 511 or equivalent, real analysis (Math 451 or equivalent).

**Statistics 611: Statistical Theory II**

This course continues Stats 611, covering nonparametrics (nonparametric regression, splines, kernel methods, density estimation, risk, generalization bounds, overfitting); resampling and data splitting methods (cross-validation, stability selection, data splitting, parametric and nonparametric bootstrap), statistical problems in high dimensions (white noise model, classical nonparametrics, Stein’s paradox, the Lasso and related algorithms and penalties. Additional topics will be selected by the instructor and may include post-selection inference, adaptive inference and sequential learning, empirical processes with applications to statistics, minimaxity, and Bayesian inference. (3 credits).

*Prerequisite*: STATS 610

**Statistics 612: Advanced Topics in Theoretical Statistics**

This course covers recent developments in statistical theory. Topics vary by instructor.

*Prerequisite*: STATS 611

**Statistics 617: Advanced Topics in Quantitative Methodology**

This course explores and critiques advanced methods for conducting quantitative research in the social sciences. A special topic is chosen for a particular semester, with relevant methods drawn from a wide variety of disciplines, including economics, education, epidemiology, psychology, sociology, and statistics. Particular attention is paid to quasi-experimental and observational research design. *(3 Credits)*

*Pre-requisites: *Graduate level courses in Statistics at the level of 500 and 501 or permission of instructor.

**Statistics 620: Applied Probability and Stochastic Modeling**

The bulk of this course focuses on 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. Topics covered include Markov chains in discrete and continuous time, Poisson processes, Brownian motion, random walks, and their applications in key scientific and engineering areas. Additional topics in modern probability theory chosen by the instructor are covered in the last few weeks of the course. (3 Credits)

Prerequisites: STATS 510 or equivalent, real analysis (Math 451 or equivalent).

**Statistics 621: Probability Theory**

The course is a self-contained rigorous measure-theoretic introduction to probability theory. Topics covered include measure and probability spaces, random variables, independence, expectation, convergence, laws of large numbers, convergence in distribution, central limit theorems, conditional expectation and martingales. (3 Credits)

*Prerequisites*: STATS 510 or equivalent, real analysis (Math 451 or equivalent).

**Statistics 626: Probability and Random Processes II (MATH 626)**

Selected topics from among: diffusion theory and partial differential equations; spectral analysis; stationary processes, and ergodic theory; information theory; martingales and gambling systems; theory of partial sums. *(3 Credits)*

*Pre-requisites: *STATS 625. Graduate standing.

**Statistics 630: Topics in Applied Probability**

Advanced topics in applied probability, such as queueing theory, inventory problems, branching processes, stochastic difference and differential equations, etc. The course will study one or two advanced topics in detail. *(3 Credits)*

*Pre-requisites: *Permission of instructor.

**Statistics 631: Advanced Time Series Analysis**

*Pre-requisites:* STATS 500, 610, 611. Graduate standing.

Statistics 640: Multivariate Statistical Models (BIOS 890)

Wishart distribution, multivariate linear models, multivariate regression, Hotelling's T-square and its applications, discriminant analysis, canonical correlations, principal components analysis, growth curves.* (3 Credits)*

*Pre-requisites: *MATH 417 and either STATS 611 or BIOSTAT 602. Graduate standing and permission of instructor.

**Statistics 642: Linear Statistical Models I (BIOS 851)**

Gauss-Markov theorem; one-way, two-way analysis of variance, and complete higher-way layouts; regression; the general linear model and hypothesis; least squares theory; analysis of covariance; missing observations; multiple comparisons procedures; incomplete blocks, split plot designs, and Latin squares; variance component models, mixed models; treatment of residuals; robustness of the methods. Special topics in the second semester. *(3 Credits)*

*Pre-requisites: *MATH 417 and either STATS 611 or BIOSTAT 602. Graduate standing.

**Statistics 670: Advanced Design and Analysis of Experiments**

This is an advanced course on the design and analysis of experiments. It will cover topics from orthogonal arrays, optimal designs, minimum aberration designs, parameter design, response surface methodology, computer experiments, and experiments with split-plot structure. Emphasis will be placed on new concepts/tools and recent advances. *(3 Credits)*

*Pre-requisites: *STATS 570 or permission of instructor.

**Statistics 680: Theory of Sampling**

Recent developments in the foundations and methodology of sampling finite populations. Identifiability of units, likelihood of units, likelihood functions, admissibility of standard estimators, randomization, use of prior information in design and inference. Models for non-sampling errors including bias, response error and non-response. Other topics of current interest. *(3 Credits)*

*Pre-requisites: *STATS 426 and 575. Graduate standing.

### 700-Level Statistics Courses

**Statistics 700: Special Topics in Applied Statistics I**

Selected topics in applied statistics.

*Pre-requisite: *STATS 501 and graduate standing.

**Statistics 701: Special Topics in Applied Statistics II**

Selected topics in applied statistics.

*Pre-requisite: * STATS 501 and graduate standing.

**Statistics 710: Special Topics in Theoretical Statistics I**

Selected topics in theoretical statistics.

*Pre-requisite: * Graduate standing and permission of instructor.

**Statistics 711: Special Topics in Theoretical Statistics II**

Selected topics in theoretical statistics.

*Pre-requisite: *Graduate standing and permission of instructor.

**Statistics 725: Topics in Advanced Probability I (MATH 725)**

*Pre-requisite: *STATS 626. Graduate standing

**Statistics 726: Topics in Advanced Probability II (MATH 726)**

*Pre-requisite: *STATS 626, 725; MATH 725. Graduate standing.

**Statistics 750: Directed Reading**

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.

*Pre-requisite: *Graduate standing (INDEPENDENT).

### 800-Level Statistics Courses

**Statistics 808: Seminar in Applied Statistics I**

*Pre-requisite:* Graduate standing.

**Statistics 809: Seminar in Applied Statistics II**

*Pre-requisite:*Graduate standing.

**Statistics 810: Literature Proseminar I**

This course is designed to acquaint students with classical papers in mathematics and applied statistics and probability theory, to encourage them in critical independent reading and to permit them to gain pedagogical experience during the course of their graduate training.

*Pre-requisite:* Graduate standing and permission of instructor.

**Statistics 811: Literature Proseminar II**

This course is designed to acquaint students with classical papers in mathematics and applied statistics and probability theory, to encourage them in critical independent reading and to permit them to gain pedagogical experience during the course of their graduate training.

*Pre-requisite: *Graduate standing and permission of instructor.

**Statistics 816: Interdisciplinary Seminar in the Physical Sciences**

The seminar will consider statistical questions that arise in the physical sciences. Topics will be drawn from current research projects, will vary each semester. Meetings will feature lectures by faculty from the University and selected visitors. Students will be expected to complete a course project and present to group.

*Pre-requisite: *Graduate standing and permission of instructor.

**Statistics 817: Interdisciplinary Seminar in Quantitative Social Science Methodology (EDUC 817/PSYCH 817/SOC 810)**

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.

*Pre-requisite:* Graduate level courses in Statistics at the level of STATS 500 and 501 or permission of instructor.

**Statistics 818: Seminar in Theoretical Statistics I**

*Pre-requisite:* Graduate standing.

**Statistics 819: Seminar in Theoretical Statistics II**

*Pre-requisite:* Graduate standing.

### 900-Level Statistics Courses

**Statistics 990: Dissertation/Precandidate**

**Statistics 995: Dissertation/Candidate**