Consultation is provided by graduate students of the Department with guidance from faculty members. This course covers selected topics in dimension reduction, randomized algorithm, sparsity, convex optimization, and deep learning, with a focus on scientific computing. This course continues the development of Mathematical Statistics, with an emphasis on hypothesis testing. STAT 33910. The course starts with a quick introduction to martingales in discrete time, and then Brownian motion and the Ito integral are defined carefully. Terms Offered: Autumn. Welcome to the Department of Statistics at the University of Chicago. Problems will be motivated by applications in epidemiology, clinical medicine, health services research, and disease natural history studies. This course focuses on the mathematical description of many inverse problems that appear in geophysical and medical imaging: X-ray tomography, ultrasound tomography and seismic imaging, optical and electrical tomography, as well as more recent imaging modalities such as elastography and photo-acoustic tomography. Terms Offered: Not offered in 2019-2020. Graduate education at the University of Michigan is a shared enterprise. 300.00 Units. Computation and application will be emphasized so that students will be able to solve real-world problems with Bayesian techniques. Introduction to Stochastic Processes II. High-Dimensional Statistics I. Instructor(s): Y. Ji Terms Offered: Winter Prerequisite(s): STAT 37601 or STAT 37710 or consent of instructor. Prerequisite(s): Consent of instructor. Statistical Computing A. Note(s): Students with credit for MATH 235 should not enroll in STAT 312. The field of statistics has become a core component of research in the biological, physical, and social sciences, as well as in traditional computer science domains such as artificial intelligence. Prerequisite(s): Multivariate calculus (MATH 15910 or MATH 16300 or MATH 16310 or MATH 19520 or MATH 20000 or MATH 20500 or MATH 20510 or MATH 20900 or PHYS 22100 or equivalent). Please consult with the Office … The primary goal is to expose the students to applications that involve statistical thinking and to have hands on experience on real world data. Prerequisite(s): STAT 24500 or STAT 24510 Observability. Machine Learning and Large-Scale Data Analysis. For linear systems and least squares problems, we will discuss stationary methods (Jacobi, Gauss-Seidel, SOR), semi-iterative methods (Richardson, steepest descent, Chebyshev, conjugate gradient), and Krylov subspace methods (MINRES, SYMMLQ, LSQR, GMRES, QMR, BiCG). Instructor(s): Staff Terms Offered: Spring Sequential parameter Following a brief review of basic concepts in probability, we introduce stochastic processes that are popular in applications in sciences (e.g., discrete time Markov chain, the Poisson process, continuous time Markov process, renewal process and Brownian motion). Downtown Chicago is a short bus or train ride away. This course introduces the theory, methods, and applications of fitting and interpreting multiple regression models. This is an advanced course in statistical genetics. STAT 35700. STAT 31080. Note(s): Students may count either STAT 24500 or STAT 24510, but not both, toward the … Starting in their second year, students should find a topic for a Ph.D. dissertation and establish a relationship with a Ph.D. adviser. on algorithms for such problems, their properties, and computations involving Instructor(s): D. Sanz-Alonso Terms Offered: Autumn This course is about statistical estimation and inference with nuisance parameters. 100 Units. The first part of this course introduces basic properties of PDE's; finite difference discretizations; and stability, consistency, convergence, and Lax's equivalence theorem. 5747 South Ellis Avenue The focus is on methods of bifurcation theory, canonical examples of forced nonlinear oscillators, fast-slow systems, and chaos. This course will cover principles of data structure and algorithms, with emphasis on algorithms that have broad applications in computational biology. STAT 70000. We will first cover some basics of social networks including structure and analysis of such networks and models that abstract their basic properties. Pontryagin Optimality Conditions. This course covers random sampling methods; stratification, cluster sampling, and ratio estimation; and methods for dealing with nonresponse and partial response. STAT 32900. STAT 31100. This is an introductory course on numerical linear algebra, which is quite different from linear algebra. Students enrolled in 200 units are considered half-time. We will concentrate on the metric properties of these random surfaces (including geodesic distances and the electric resistances), as well as their connections to the random motion on these random surfaces. STAT 38510. This is a beginning graduate course on selected numerical methods used in In fact, the median starting salary (according to PayScale. methods in data analysis. The data analytic tools that we will study will go beyond linear and multiple regression and often fall under the heading of "Multivariate Analysis" in Statistics. Terms Offered: To be determined; may not offered in 2020-2021. Equivalent Course(s): STAT 24410. STAT 31440. Genomic Evolution I. Problems associated with multiple time scales will be discussed along with methods to address them (implicit discretizations, multiscale methods and dimensional reduction). Topics may include, but are not limited to, statistical problems in genetic association mapping, population genetics, integration of different types of genetic data, and genetic models for complex traits. The first quarter introduces a range of statistical frameworks for finding low-dimensional structure in high-dimensional data, such as sparsity in regression, sparse graphical models, or low-rank structure. Part of every statistician's job is to evaluate the work of others and to communicate knowledge, experience, and insights. 100 Units. STAT 30600. 100 Units. Prerequisite(s): STAT 24400 or STAT 24410 or STAT 25100 or STAT 25150 Topics will include discussion of matrix factorizations (including diagonalization, the spectral theorem for normal matrices, the singular value decomposition, and the Schur and polar decompositions), and an overview of classical direct and iterative approaches to numerical methods for problems Prerequisite(s): STAT 34700 or permission of instructor. Mathematical Computation III: Numerical Methods for PDE's. 100 Units. 100 Units. We will also discuss approaches that supplement the classical GLM, including quasi-likelihood for over-dispersed data, robust estimation, and penalized GLM. STAT 48100. Suite 222 Not offered in 2020-2021. Instructor(s): Y. Amit Terms Offered: Autumn Topics include storage and accessing of large data; basic working knowledge of relational database and its querying language SQL; introduction to distributed file system and example usage of Hadoop; Python and its applications in text analysis; access and usage of high-performance computer clusters, rudimentary parallel computing, web data access. 100 Units. The second quarter emphasizes foundational aspects of high-dimensional statistics, focusing on principles that are used across a range of problems and are likely to be relevant for methods developed in the future. About. 100 Units. Note(s): Prerequisite notes: Graduate or advanced undergraduate probability theory and undergraduate linear algebra and combinatorics are recommended. Equivalent Course(s): MATH 38511. Homework exercises will give students hands-on experience with the methods on different types of data. Probability and Statistics. The objective is to provide a working knowledge and hands-on experience of the subject suitable for graduate level work in statistics, econometrics, quantum mechanics, and numerical methods in scientific computing. 100 Units. Equivalent Course(s): BUSN 41910. Equivalent Course(s): CHDV 32702, PBHS 33500. Examples include joint projects with Human Genetics, Ecology and Evolution, Neurobiology, Chemistry, Economics, Health Studies, and Astronomy. 300.00 Units. Equivalent Course(s): CMSC 35425. Main topics will include (time permitting) the moment method in RMT and its connection to combinatorics, universality, operator limits, and matrix concentration. An introduction to martingales is given. The class will also cover interacting particle methods and other techniques for the efficient simulation of dynamical rare events. 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