# Statistics

Engineering students interested in advancing their studies in Statistics should consult with a departmental adviser to determine the most appropriate courses for their interests.

**STAT UN2103x Applied linear regression analysis**

*3 pts. Professor Young.*

Prerequisite: An introductory course in statistics (STAT UN1101 is recommended). Student without programming experience in R might find STAT UN2102 very helpful. Develops critical thinking and data analysis skills for regression analysis in science and policy settings. Simple and multiple linear regression, nonlinear and logistic models, random-effects models, penalized regression methods. Implementation in a statistical package. Optional computer-lab sessions. Emphasis on real-world examples and on planning, proposing, implementing, and reporting.

**STAT UN3105y Applied statistical methods**

*3 pts. Professors Landwehr and Whalen.*

Prerequisite: At least one, and preferably both, of STAT UN2103 and UN2104 are strongly recommended. Students without programming experience in R might find STAT UN2102 very helpful. Intended to give students practical experience with statistical methods beyond linear regression and categorical data analysis. The focus will be on understanding the uses and limitations of models, not the mathematical foundations for the methods. Topics that may be covered include random and mixed-effects models, classical non-parametric techniques, the statistical theory causality, sample survey design, multi-level models, generalized linear regression, generalized estimating equations and over-dispersion, survival analysis including the Kaplan-Meier estimator, logrank statistics, and the Cox proportional hazards regression model. Power calculations and proposal and report writing will be discussed.

**STAT UN3106y Applied data mining**

*3 pts. Professor Young.*

Prerequisite: STAT UN2103. Students without programming experience in R might find STAT UN2102 very helpful. Taught as a machine learning class. Covers topics including data-based prediction, classification, specific classification methods (such as logistic regression and random forests), and basics of neural networks. Programming in homeworks will require R.

**STAT GU4001x Introduction to probability and statistics**

*3 pts. Members of the faculty*

Prerequisites: MATH UN1101 and UN1102 or equivalent. A calculus-based tour of the fundamentals of probability theory and statistical inference. Probabilistic models, random variables, useful distributions, conditioning, expectations, laws of large numbers, central limit theorem, point and confidence interval estimation, hypothesis tests, linear regression. This course replaces SIEO W4150.

**STAT GU4203x and y Probability theory**

*3 pts. Professors Lo and Wang.*

Prerequisites: MATH UN1101 and UN1102 or equivalent. An introductory course (STAT UN1201) is strongly recommended. A calculus-based introduction to probability theory. A quick review of multivariate calculus is provided. Topics covered include random variables, conditional probability, expectation, independence, Bayes’ rule, important distributions, joint distributions, moment generating functions, central limit theorem, laws of large numbers and Markov’s inequality.

**STAT GU4204x Statistical inference**

*3 pts. Professors Sobel and Young.*

Prerequisite: STAT GU4203. At least one semester of Calculus is required, two or three semesters are strongly recommended. Calculus-based introduction to the theory of statistics. Useful distributions, law of large numbers and central limit theorem, point estimation, hypothesis testing, confidence intervals maximum likelihood, likelihood ratio tests, nonparametric procedures, theory of least squares, and analysis of variance.

**STAT GU4205x Linear regression models**

*3 pts. Professors Neath, Wu, Liu, and Polak.*

Prerequisites: STAT GU4204 or equivalent, and a course in linear algebra. Theory and practice of regression analysis. Simple and multiple regression, testing, estimation, prediction, and confidence procedures, modeling, regression diagnostics and plots, polynomial regression, colinearity and confounding, model selection, geometry of least squares. Extensive use of the computer to analyze data.

**STAT GU4207x and y Elementary stochastic processes**

*3 pts. Professors Brown and Wang.*

Prerequisite: STAT GU4203 and two, preferably three, semesters of calculus. Review of elements of probability theory. Poisson processes. Renewal theory. Wald’s equation. Introduction to discrete and continuous time Markov chains. Applications to queueing theory, inventory models, branching processes.

**STAT GU4221x and y Time series analysis**

*3 pts. Professors Safikhani, Wu and Wang.*

Prerequisite: STAT GU4205 or equivalent. Least squares smoothing and prediction, linear systems, Fourier analysis, and spectral estimation. Impulse response and transfer function. Fourier series, the fast Fourier transform, autocorrelation function, and spectral density. Univariate Box-Jenkins modeling and forecasting. Emphasis on applications. Examples from the physical sciences, social sciences, and business. Computing is an integral part of the course.

**STAT GU4222y Nonparametric statistics**

*3 pts. Professor Polak*

Prerequisite: STAT UN3204 or the equivalent. Statistical inference without parametric model assumption. Hypothesis testing using ranks, permutations, and order statistics. Nonparametric analogs of analysis of variance. Nonparametric regression, smoothing and model selection.

**STAT GU4231y Survival analysis**

*3 pts. Professor Shnaidman.*

Prerequisite: STAT GU4205 or the equivalent. Survival distributions, types of censored data, estimation for various survival models, nonparametric estimation of survival distributions, the proportional hazard and accelerated lifetime models for regression analysis with failure-time data. Extensive use of the computer.

**STAT GU4232y Generalized linear models**

*3 pts. Professor Sobel.*

Prerequisite: STAT GU4205 of the equivalent. Statistical methods for rates and proportions, ordered and nominal categorical responses, contingency tables, odds-ratios, exact inference, logistic regression, Poisson regression, generalized linear models.

**STAT GU4234x Sample surveys**

*3 pts. Professor Neath.*

Prerequisite: STAT GU4204 of the equivalent. Introductory course on the design and analysis of sample surveys. How sample surveys are conducted, why the designs are used, how to analyze survey results, and how to derive from first principles the standard results and their generalizations. Examples from public health, social work, opinion polling, and other topics of interest.

**STAT GU4261y Statistical methods in finance**

*3 pts. Professors ElBarmi, Wang, and Ying.*

Prerequisite: STAT GU4204 or the equivalent. A fast-paced introduction to statistical methods used in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. Topics include regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, smoothing techniques and estimation of yield curves statistical methods for financial time series, value at risk, term structure models and fixed income research, and estimation and modeling of volatilities. Hands-on experience with financial data.

**STAT GU4262y Stochastic processes for finance**

*3 pts. Professor Rios.*

Prerequisite: STAT GU4203. STAT GU4207 is recommended. A careful review of the concept of stochastic process as a model of random phenomena evolving through time and of conditional expectation, basic markov process theory, and the exponential distribution. Marked point processes and their compensators, beginning with Poisson processes, and proceeding through general marked point processes. The use of compensators will be justified by the Doob- Meyer decomposition theorem, and as such it will connect the theory to martingales. Markov processes will enter to provide a description of sufficient conditions for the compensators to have absolutely continuous paths (and as such, have "hazard rates"). Applications to survival analysis and, especially, to mathematical finance, including default and bankruptcy models. Cox process construction.

**STAT GU4281x Theory of interest**

*3 pts. Professor Zhang.*

Prerequisite: MATH UN1101 or equivalent. Introduction to the mathematical theory of interest as well as the elements of economic and financial theory of interest. Topics include rates of interest and discount; simple, compound, real, nominal, effective, dollar (time)-weighted; present, current, future value; discount function; annuities; stocks and other instruments; definitions of key terms of modern financial analysis; yield curves; spot (forward) rates; duration; immunization; and short sales. The course will cover determining equivalent measures of interest, discounting, accumulating, determining yield rates, and amortization.

**STAT GU4291x and y Advanced data analysis**

*3 pts. Professors Alemayehu and Liu.*

Prerequisite: STAT GU4205. At least one Statistic course between GU4221 and GU4261. This is a course on getting the most out of data. The emphasis will be on hands-on experience, involving case studies with real data and using common statistical packages. The course covers, at a very high level, exploratory data analysis, model formulation, goodness of fit testing, and other standard and nonstandard statistical procedures, including linear regression, analysis of variance, nonlinear regression, generalized linear models, survival analysis, time series analysis, and modern regression methods. Students will be expected to propose a data set of their choice for use as case study material.

**STAT GR5242x and y Advanced Machine Learning**

*3 pts. Professors Cunningham and Orbanz.*

Prerequisite: STAT GR5241. Course covers some advanced topics in machine learning and has emphasis on applications to real world data. Major part of the course is course project which consists of in-class presentation and written project report.

**STAT GR5703x Statistical inference and modeling**

*3 pts. Professor Zheng.*

Prerequisites: Working knowledge of calculus and linear algebra (vectors and matrics), and STAT GR5701 or equivalent. Familiarity with a programming language (e.g., R, Python) or statistical data analysis. Course covers fundamentals of statistical inference and testing, and gives an introduction to statistical modeling. First half focused on inference and testing, covering topics such as maximum likelihood estimates, hypothesis testing, likelihood ratio test, Bayesian inference, etc. Second half will provide introduction to statistical modeling via introductory lectures on linear regression models, generalized linear regression models, nonparametric regression, and statistical computing. Throughout the course, real-data examples will be used in lecture discussion and homework problems. Course lays foundation, preparing MS in Data Science students, for other courses ni machine learning,data mining, and visualization.

**2018-2019 Academic Year: the system of course numbering and designated level is in transition; please consult an adviser.*