Notes from Dr. Borkosky

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). GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together.

endstream endobj 86 0 obj <. It is intended for graduate students with modest prior background in statistics. (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. endstream endobj 91 0 obj <.

Pre-requisite:  STATS 501 and graduate standing. Simple random sampling, stratification systematic sampling, cluster sampling, multistage sampling, sampling with probability proportional to size, replicated sampling, multiphase sampling. Other topics of current interest. (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. Lectures  provide background on case studies, along with reviews of relevant methodology.

Pre-requisite:  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.

Least squares; Decomposing variance; Model specification and confounding; Model diagnostics (3 Credits), Pre-requisite: STATS 425 and 426 (or IOE 316 and 366), 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.

(3 Credits).

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. Particular attention is paid to quasi-experimental and observational research design.

It introduces a set of principles of survey design that are the basis of standard practices in the field. Several modern inferential techniques arising in machine learning and applied statistics will be reviewed. %PDF-1.6 %���� 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. 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.

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Theoretical Statistics (at the level of Stats 426 or equivalent), Generalized linear models including logistics regression, Poisson regression, contingency tables. %%EOF 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.

Regular attendance at the lecture and lab is expected. Knowledge of probability at the level of BIOSTAT 601 or MATH 525. (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. (3 credits).

Pre-requisites: MATH 597. 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). Nonresponse weighting adjustments and imputation. It then introduces students to measure theory and integration. 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. dimension reduction regression, and smoothing-based methods; (5) Concrete examples of homology, gene finding, structure analysis. Statistics 631: Advanced Time Series Analysis. Post-stratification, ratio, regression and difference estimation. Computer programming experience is recommended. 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. 210 0 obj <>stream (3 Credits).

Variance estimation with complex sample designs: Taylor series method, repeated replications, jackknife repeated replications. The bulk of this course focuses on stochastic models that capture the evolution in time of various random phenomena and/or dynamical systems.

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. alternative approaches to regression, including quantile regression, Statistics 701: Special Topics in Applied Statistics II.

Statistics 601: Analysis of Multivariate and Categorical Data, This is an advanced introduction to the analysis of multivariate and categorical data. Statistics 625: Probability and Random Processes I (MATH 625), Axiomatics; measures and integration in abstract spaces. 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). 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 vary by instructor. The response variable could be continuous, binary or counts.

Designed for individual students who have an interest in a specific topic (usually that has stemmed from a previous course). A capstone project covering the whole Course will evaluate the main philosophical interpretations of the probability calculus and resulting paradigms of statistical inference.

Emphasis will be placed on new concepts/tools and recent advances. Special topics in the second semester.

Topics vary by instructor.

learning, including both their theoretical foundations and practical applications. 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.

Statistics 710: Special Topics in Theoretical Statistics I.

Pre-requisites: Permission of instructor.

Additional topics in modern probability theory chosen by the instructor are covered in the last few weeks of the course. experiments. A seminar will allow students and instructor to learn the process of question formulation, and alternative strategies for analysis.

(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. (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). (4 credits). Graduate standing. While there will be some theory, the emphasis will be on applications and data analysis. (3 Credits).

Topics PSYCH 613, ECON 405) and graduate or advanced undergraduate standing, or permission of instructor.

endstream endobj startxref 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. The course covers algorithms for large-scale matrix computations, majorization-minimization methods, Newton-type methods, and stochastic approximation.

The class includes a lab that meets each week. (3 Credits). Topics Statistics 816: Interdisciplinary Seminar in the Physical Sciences. 0

; 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. Advisory Prerequisites: statistics and probability background at the level of STATS 510, which may be taken concurrently. Contribute to kshedden/UMStats600 development by creating an account on GitHub. (3 Credits), Pre-requisite: Linear Algebra (at the level of Math 214 or equivalent) AND (3 credits). Pre-requisites: MATH 417 and either STATS 611 or BIOSTAT 602.

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. Pre-requisite: STATS 425 or BIOL 427 or BIOL CHEM 415; basic programming skills desirable.

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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