Pre-requisite: STATS Master's Standing or stats 500. /FontDescriptor 18 0 R This course covers core topics in statistical theory. This is an advanced introduction to regression modeling and prediction, including traditional and modern computationally-intensive methods. 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. Methods — Stats 600 and 601. Neural networks. The emphasis is not on specific methods, but rather on scientific reasoning, collaboration, communication, and critical evaluation of findings. Modern regression techniques. Course will evaluate the main philosophical interpretations of the probability calculus and resulting paradigms of statistical inference. 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. 600.2 600.2 507.9 569.4 1138.9 569.4 569.4 569.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 277.8 500] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 706.4 938.5 877 781.8 754 843.3 815.5 877 815.5 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. The course is a self-contained rigorous measure-theoretic introduction to probability theory. 493.6 769.8 769.8 892.9 892.9 523.8 523.8 523.8 708.3 892.9 892.9 892.9 892.9 0 0 Computer programming experience is recommended. x��[[o�~��/2���~HѤ�lao�m��-;��X����{9�ɑdǻh_�H�!������H�5w���K��o�Ҧ'�j.o#��M������|�r�g�v��خ���������1��~~�_^/���-o�������q�>���M�5�i'Ҟ@�Y+�nv5�_��ŗ�-��]nΘ�Y��f��-�gLϾ������[�BΛ��!���� /Widths[1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 Random effects and repeated measures. /Type/Font 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. Limit theorems, law of the iterated logarithm. Designed for individual students who have an interest in a specific topic (usually that has stemmed from a previous course). 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. 323 West Hall 1085 South University Ann Arbor, MI 48109-1107 stat-um@umich.edu . A key component of the course would involve data analysis with Bayesian techniques. endobj Prerequisites: STATS 510 and 511 or equivalent,  real analysis (Math 451 or equivalent). (3 Credits). Prerequisites: linear algebra; regression at the level of STATS 413; probability and statistical theory at the level of STATS 425/426. Statistics 610: Statistical Theory I. 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. Regression and classification trees. 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. Topics Statistics 580: Methods and Theory of Sample Design (SOC 717/BIOS 617), Theory underlying sample designs and estimation procedures commonly used in survey practice. Statistics 711: Special Topics in Theoretical Statistics II. Pre-requisite: Graduate level courses in Statistics at the level of STATS 500 and 501 or permission of instructor. 597.2 736.1 736.1 527.8 527.8 583.3 583.3 583.3 583.3 750 750 750 750 1044.4 1044.4 7 0 obj Pre-requisite: 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. Graduate standing. (3 Credits). Advisory Prerequisites: statistics and probability background at the level of STATS 510, which may be taken concurrently. 820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 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. Statistics 701: Special Topics in Applied Statistics II. 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. 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. Sitemap . << 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 Pre-requisite:  STATS 501 and graduate standing. Pre-requisite: STATS 425 or BIOL 427 or BIOL CHEM 415; basic programming skills desirable. 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. /Widths[622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 /Subtype/Type1 The course will study one or two advanced topics in detail. 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 /LastChar 196 (3 Credits). /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 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 0 693.8 954.4 868.9 aC�A�&�L, �m��T�g(�f���0�r��8V 9RBؕ�D�i�LL*��?����i"9����I%̱@�M��#�nU�1; �w�B�]� h,����� k%�@�RН�Ɣ�08S�D{��ވ�#~ ��/�?rR��Ǒ��َ�X�²�A���,����AEގ�>*��nɅŐ;�����J�p�`Ø�\��0���� (3 Credits). Graduate standing. Each student will learn to formulate alternative modeling approaches. Regression and classification trees. Statistics 701: Special Topics in Applied Statistics II. (3 Credits), 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. Course will evaluate the main philosophical interpretations of the probability calculus and resulting paradigms of statistical inference. This course introduces students to the theory of statistical inference. One of the courses must be either Stats 510, 620, or 621 and the other course must be either Stats 511, 610, or 611. 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. (3 Credits). The course reviews basic notions from matrix algebra and real analysis. Pre-requisites: STATS 625. include estimation, inference, interpretation of results, diagnostics, lack of fit, robust procedures, weighting and transformations, and model selection. (3 Credits). 323.4 877 538.7 538.7 877 843.3 798.6 815.5 860.1 767.9 737.1 883.9 843.3 412.7 583.3 1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 666.7 1000 1000 Topics covered include: Markov chains in discrete and continuous time, Poisson and renewal processes, Brownian motion. (3 Credits). The Department of Statistics at U-M has a growing reputation as an international leader in statistical education and research. /FirstChar 33 Graduate standing and permission of instructor. Emphasis will be placed on new concepts/tools and recent advances. 777.8 777.8 1000 1000 777.8 777.8 1000 777.8] /LastChar 196 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. /Subtype/Type1 Advisory prerequisites: MATH 451, STATS 425, STATS 426. Prerequisites: STATS 510 or equivalent, real analysis (Math 451 or equivalent). Particular attention is paid to quasi-experimental and observational research design. endobj endobj (4 Credits), Statistics 504: Practice and Communication in Applied Statistics. Topics 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. 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. (3 Credits), Statistics 503: Statistical Learning II: Multivariate Analysis, The course covers methods for modern multivariate data analysis and statistical 22 0 obj 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. Additional topics may vary with the instructor. Pre-requisites: MATH 597. Prerequisites: STATS 510 or equivalent, real analysis (Math 451 or equivalent). 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. Pre-requisites: STATS 570 or permission of instructor. learning, including both their theoretical foundations and practical applications. (3 Credits). Post-stratification, ratio, regression and difference estimation. (3 Credits). (4 credits). (3 Credits). Other topics of current interest. Pre-requisite: STATS 500 or background in regression. Statistics 505: Econometric Analysis I (ECON 671), Econ 671 and 672 form the basic required sequence in econometrics for all doctoral students.

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