The Department of Statistics at U-M has a growing reputation as an international leader in statistical education and research. While there will be some theory, the emphasis will be on applications and data analysis. 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. This course is restricted to Master in Applied Statistics and Masters in Data Science students only. endobj Analysis of DNA/RNA and protein sequence data. Statistics 625: Probability and Random Processes I (MATH 625), Axiomatics; measures and integration in abstract spaces. Topics to be covered include: (i) constructions of probability spaces, Kolmogorov's consistency theorem; independence of families of random variables, Borel-Cantelli lemmas and 0-1 laws; (ii) various modes of convergence (in probability, almost surely, in Lp, in distribution) and properties of weak convergence, (iii) laws of large numbers, (iv) central limit theorems for sequences and triangular arrays, (v) conditional expectations and distributions and (vi) discrete time martingale theory. 585.3 831.4 831.4 892.9 892.9 708.3 917.6 753.4 620.2 889.5 616.1 818.4 688.5 978.6 endobj Knowledge of probability at the level of BIOSTAT 601 or MATH 525. (3 Credits). 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. 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. >> Statistics 605: Advanced Topics in Modeling and Data Analysis. /Widths[277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 Prerequisites: STATS 510 and 511 or equivalent,  real analysis (Math 451 or equivalent). Statistics 548: Computations in Probabilistic Modeling in Bioinformatics (MATH 548), This will be a computational laboratory course designed in parallel with Math/Stat 547. (3 Credits), 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. Statistics 610: Homework 1 September 16, 2008 Announcement: The homework carries 140 points but the maximum you can score is 110 points. This course covers core topics in statistical theory. 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 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. 777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 /BaseFont/FCATPY+CMEX10 (4 Credits), Statistics 504: Practice and Communication in Applied Statistics. Prerequisites: STATS 510 and 511 or equivalent,  real analysis (Math 451 or equivalent). /FirstChar 33 This is an advanced introduction to regression modeling and prediction, including traditional and modern computationally-intensive methods. 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), Statistics 604: Statistical Investigations in a Consulting Framework, Statistical Investigations in a Consulting Framework --- This course provides graduate students with a variety of modeling and data analysis opportunities through consultations with other researchers. Statistics 631: Advanced Time Series Analysis. Pre-requisite: STATS Master's Standing or stats 500. Pre-requisite: Three or more courses in Statistics and preferably a course in methods of survey sampling. Pre-requisite: STATS 626, 725; MATH 725. 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. Statistics 601: Analysis of Multivariate and Categorical Data, This is an advanced introduction to the analysis of multivariate and categorical data. Pre-requisite: Graduate level courses in Statistics at the level of STATS 500 and 501 or permission of instructor. The course will be project based, using case studies from collaborative research and consulting. 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. 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 Pre-requisites: STATS 500, 610, 611. Pre-requisite: Graduate standing and permission of instructor. 10 0 obj /FirstChar 33 Variance estimation with complex sample designs: Taylor series method, repeated replications, jackknife repeated replications. Pre-requisite: Graduate standing (INDEPENDENT). (3 Credits). Pre-requisites: MATH 451, STATS 425, and STATS 426 or equivalent courses in probability, statistics and real analysis. /Subtype/Type1 (4 Credits), Statistics 504: Practice and Communication in Applied Statistics. 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). (4 credits). 843.3 507.9 569.4 815.5 877 569.4 1013.9 1136.9 877 323.4 569.4] /Encoding 7 0 R Statistics 608: Monte Carlo Methods in Statistics, This course is an introduction to Monte Carlo sampling and integration methods that arise in statistics. Graduate standing. (3 Credits), Statistics 612: Advanced Topics in Theoretical Statistics, This course deals with selected topics in theoretical statistics at an advanced level. /Subtype/Type1 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. /LastChar 196 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. 25 0 obj 506.3 632 959.9 783.7 1089.4 904.9 868.9 727.3 899.7 860.6 701.5 674.8 778.2 674.6 Several modern inferential techniques arising in machine learning and applied statistics will be reviewed. Pre-requisite: Graduate standing and STATS 400 (or equivalent) or permission of instructor. << Pre-requisites: STATS 570 or permission of instructor. Computer programming experience is recommended. Advisory Pre-requisite: MATH 451 (strongly recommended) or 450. Advisory prerequisites: MATH 451, STATS 425, STATS 426. (3 Credits), Pre-requisite: Linear Algebra (at the level of Math 214 or equivalent) AND 500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 Limit theorems, law of the iterated logarithm. Optional topics drawn from: random walks, Markov chains, and/or martingales. The modeling activities include problems arising in the science, engineering and the humanities and will include both quantitative and qualitative features. Students will be expected to complete a course project and present to group. (3 credits). 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. 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. (3 Credits), 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. Statistics 710: Special Topics in Theoretical Statistics I. Pre-requisite: STATS 425 or BIOL 427 or BIOL CHEM 415; basic programming skills desirable. Post-stratification, ratio, regression and difference estimation. (3 Credits). 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. include estimation, inference, interpretation of results, diagnostics, lack of fit, robust procedures, weighting and transformations, and model selection. 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. >> Such phenomena/systems arise extensively in diverse areas of research, ranging from biology, to data networks and production planning. (3 Credits). /LastChar 196 Pre-requisites: MATH 417 and either STATS 611 or BIOSTAT 602. PSYCH 613, ECON 405) and graduate or advanced undergraduate standing, or permission of instructor. 1111.1 1511.1 1111.1 1511.1 1111.1 1511.1 1055.6 944.4 472.2 833.3 833.3 833.3 833.3 /Filter[/FlateDecode] We have a variety of undergraduate and graduate programs that serve a wide spectrum of students interested in statistics and data science. Applications of these models in key scientific and engineering areas, such as genetics, epidemics, computational algorithms, computer and communications networks, inventory systems financial and risk management, are discussed.

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