Statistics 548: Computations in Probabilistic Modeling in Bioinformatics (MATH 548), This will be a computational laboratory course designed in parallel with Math/Stat 547. Meetings will feature lectures by faculty from the University and selected visitors. The seminar will consider statistical questions that arise in the physical sciences. No description, website, or topics provided. Course description. posted to the course web page, and will be due in class approximately It also covers issues related to data collection, study design, and interpretation of findings, including missing data, non-representative samples, causality, and designed experiments. Visiting researchers will provide a brief account of their aims and data before defining the methodological challenge for which they desire discussion. Statistics 818: Seminar in Theoretical Statistics I, Statistics 819: Seminar in Theoretical Statistics II, Statistics 990: Dissertation/Precandidate, Please send permission requests to email@example.com, 2020 Regents of the University of Michigan. Has 18 Credits. 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.
Students are strongly encouraged to take Stats 604 in their second year (Stats 600 is a prerequisite). While there will be some theory, the emphasis will be on applications and data analysis. (3 Credits). (3 Credits), 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. Particular attention is paid to quasi-experimental and observational research design. 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. (3 Credits), Statistics 551: Topics in Bayesian modeling and computation. 265 0 obj <>stream (3 Credits). SurvMeth 600 (Fall term) Fundamentals of Survey Methodology. Concrete examples of homology, gene finding, structure analysis. Course will evaluate the main philosophical interpretations of the probability calculus and resulting paradigms of statistical inference. (3 Credits). (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. 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. Pre-requisites: STATS 520 or equivalent course in measure theory, STATS 620. (1 Credit), 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.
Such phenomena/systems arise extensively in diverse areas of research, ranging from biology, to data networks and production planning. 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. Pre-requisites: MATH 417 and either STATS 611 or BIOSTAT 602. 90 0 obj <> endobj Embedded Master’s in Statistics Checklist For Statistics PhD students . (3 credits).
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. The course will study one or two advanced topics in detail. Problem sets will be include estimation, inference, interpretation of results, diagnostics, lack of fit, robust procedures, weighting and transformations, and model selection. While there will be some theory, the emphasis will be on applications and data analysis. (3 Credits). The response variable could be continuous, binary or counts. Nonresponse weighting adjustments and imputation. This course provides basic concepts and several modern techniques of Bayesian modeling and computation. Pre-requisite: Knowledge of linear algebra; Knowledge of regression and analysis of variance at the level of STATS 500; Knowledge of probability and statistical theory at the level of BIOSTAT 601/602. 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. Statistics 620: Applied Probability and Stochastic Modeling, This course is an introduction to stochastic models that capture the evolution in time of various random phenomena and/or dynamical systems. A capstone project covering the whole Advisory prerequisites: MATH 451, STATS 425, STATS 426. Lectures provide background on case studies, along with reviews of relevant methodology.
Statistics 500: Statistical Learning I: Regression, The course covers concepts and methods for regression analysis and applications. 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. An individual instructor must agree to direct such a reading, and the requirements are specified when approval is granted. STATS 607(B) STATS 608(B) STATS 600 STATS 607(A) STATS 507 STATS 610 STATS 620. (3 Credits).
The course is a self-contained rigorous measure-theoretic introduction to probability theory. Topics vary by instructor.
Topics will be drawn from current research projects, will vary each semester. Pre-requisite: Three or more courses in Statistics and preferably a course in methods of survey sampling. (3 Credits), Pre-requisite: Linear Algebra (at the level of Math 214 or equivalent) AND 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. Problem set 1, due October 1. Topics will be drawn from current research projects, will vary each semester. Emphasis will be placed on new concepts/tools and recent advances. Regression and classification trees. (3 credits), Statistics 509: Statistical Models and Methods for Financial Data, This course will cover statistical models and methods relevant to the analysis of financial data. course is fast-paced, and focuses on the motivation, construction, and Students then conduct independent data analyses for each case study and produce written reports.
This course covers recent developments in statistical modeling and data analysis. Pre-requisite: STATS 626, 725; MATH 725. 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). 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. Topics include: (1) dimension 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.
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