Statistics & Operations Rsrch (STAT-GB)

This is a data-driven applied statistics course focusing on the analysis of data using regression models. It emphasizes applications to the analysis of business and other data and makes extensive use of computer statistical packages. Topics include simple and multiple linear regression, residual analysis and other regression diagnostics, multicollinearity and model selection, auto regression, heteroscedasticity, regression models using categorical predictors, and logistic regression. All topics are illustrated on real data sets obtained from financial markets, market research studies, and other scientific inquiries.

Presented in this course are practical time series forecasting techniques with emphasis on the BoxJenkins ARIMA autoregressive integrated moving average method and conditional volatility ARCH autoregressive conditional heterogeneity and GARCH generalized autoregressive conditional heterogeneity models The course gives a mix of practical data analysis along with an introduction to the relevant theory The ARIMA models are used to forecast series like interest spreads

In this class we study stochastic models for the financial markets mostly in a discrete time setting. We shall discuss the concept of martingales and risk-neutral probability measures, and derive the general pricing formula for contingent claims. We shall study the binomial model and derive the price of a European call option on this model, called the binomial Black-Scholes (BS) formula. We study put options using the put-call parity. We shall compare the binomial BS formula to the continuous time BS formula, and analyze the latter via the "Greeks". We shall also look at exotic options such as the lookback and the knockout option. Additionally, American options, forward and future contracts, and fixed income models will be included as well.

The course discusses mathematical and technical aspects of investments. Topics include measurement of interest and discount rates, accumulated value and present value, annuities, sinking funds, amortization of debt, and determination of yield rates on securities. Applications include bond evaluation, mortgages, capital budgeting, depreciation methods, and insurance.

There are a variety of statistical methods, old and new, that are used nowadays to analyze datasets, which can range in size from the small to the enormous. This course gives an introduction to, an overview of and a comparison between these various methods and the attendant terminology and the different kinds of questions they can help answer. Methods that will be discussed include Regression, the Lasso, Discriminant Analysis, Logistic regression, Regression and Classification Trees, etc. This course is not meant for the people doing the analysis but will be geared more towards helping managers understand the material and aid them in having meaningful conversations with the analytics groups in their firms. However, due to its very nature, there will be a mathematical aspect to the course (i.e. there will be formulae), though the aim is to try to understand the intuition behind them.

This course covers the basic concepts of probability. Topics include the axiomatic definition of probability; combinatorial theorems; conditional probability and independent events; random variables and probability distributions; expectation of functions of random variables; special discrete and continuous distributions, including the chi-square, t, and F distributions; joint distributions with emphasis on the bivariate normal distribution; law of large numbers, central limit theorem; and moment generating functions. The theory of statistical estimation is introduced with a discussion on maximum likelihood estimation.

The course has two distinct components: statistical inference and regression analysis. Topics included in statistical inference are principles of statistical estimation and inference, Neyman-Pearson Lemma, testing of means, variances, tests of independence, and nonparametric methods. Regression analysis focuses on the general linear regression model least squares estimation, departures from standard assumptions, autocorrelation, multicollinearity, analysis of residuals, choice of variables, and nonlinear models.

This course is intended to provide students with a basic understanding of how statistical models can be applied to the areas of business, politics, and public policy as well as common pitfalls, limitations with different approaches, and lessons learned from recent events. The goal is to give students an understanding of what techniques are used in contemporary statistical analyses of these topics and with the tools to carry out their own empirical analyses and to evaluate the work of others. The course covers techniques used to forecast economic, financial, and political events as well as econometric approaches used to identify causal relationships and to evaluate business and government policies. Much of the instruction is motivated by empirical examples that are assigned as readings for each class. Prerequisites: any introductory Statistics course

There are a variety of statistical methods, old and new, that are used nowadays to analyze datasets, which can range in size from the small to the enormous. This course gives an introduction to, an overview of, and a comparison between these various methods and the attendant terminology, and the different kinds of questions they can help answer. Methods that will be discussed include Regression, the Lasso, Discriminant Analysis, Logistic regression, Regression and Classification Trees, etc. This course is not meant for the people doing the analysis but will be geared more towards helping managers understand the material and aid them in having meaningful conversations with the analytics groups in their firms. However, due to its very nature, there will be a mathematical aspect to the course (i.e. there will be formulae), though the aim is to try to understand the intuition behind them.

This is an introductory course in stochastic processes. Its purpose is to introduce students to the classes of stochastic processes, which are widely used as modeling tools in business fields such as finance, marketing and actuarial science as well as in physical and social sciences. The course covers basic theory of discrete and continuous time Markov chains, of Brownian motion and its generalizations, and of martingales. The discussion of Markov chains and Brownian motion includes statistical aspects of these processes. If time permits, the idea of stochastic integration is introduced and the rules of stochastic calculus are developed.

Independent Study

This course contains two parts: (1) In the first part, we will cover the basics of supervised (regression and classification) and unsupervised learning (clustering and dimension reduction). We will also discuss modern topics such as deep neural networks, semi-supervised learning, multi-armed bandit learning, and stochastic optimization for training web-scale data. (2) In the second part, we will cover applications relevant to information and operations, including crowdsourcing, dynamic pricing, and choice-model based recommendation. The Ph.D. students should also prepare the course project and present in class how to use machine learning techniques to address challenges in their own domains.

RESEARCH PRACTICUM-STAT

RESEARCH PRACTICUM

RESEARCH PRACTICUM

RESEARCH PRACT IV - STAT

RESEARCH PRACTICUM - 5

TEACHING PRACT-STAT/OR

This course surveys theory and methods addressing important statistical aspects of data science with a focus on high-dimensional data, statistical learning, and causal inference. We will begin with advances in hypothesis testing such as control of the false discovery rate for multiple comparisons. Then we will discuss statistical theory for popular learning and model selection methods such as the lasso, including recent advances in post-selection inference. Finally, after reviewing frameworks for causal inference the course will conclude by reading literature on the application of statistical learning methods to causal inference. Throughout the course we will combine theory, through mathematical understanding, with practice, through empirical understanding and competency with applications such as simulation studies. We assume a working knowledge of probability and linear algebra, familiarity with statistics, and willingness to code in the R statistical programming language, but otherwise the course is self-contained.

Presents a mathematical background for the stochastic processes that are widely employed as modeling tools in finance. The emphasis is on an intuitive approach and examples rather than on proofs and mathematical rigor. Topics include random walks, martingales, Markov chains, Poisson process and other continuous time Markov chains, Brownian motion, geometric Brownian motion, and other diffusion processes. The relevance of the considered processes to financial modeling is stressed throughout. In particular, applications to pricing of derivative securities and to modeling of the term structure of interest rates are discussed.

Covers the basic concepts of probability. Topics include the axiomatic definition of probability; combinatorial theorems; conditional probability and independent events; random variables and probability distributions; expectation of functions of random variables; special discrete and continuous distributions, including the chi-square, t, F, and bivariate normal distributions; law of large numbers; central limit theorem; and moment generating functions. The theory of statistical estimation is introduced with a discussion on maximum likelihood estimation.

Consists of two distinct components: statistical inference and regression analysis. Statistical inference topics include the principles of statistical estimation and inference, Neyman Pearson Lemma, testing of means, variances, tests of independence, and nonparametric methods. Regression analysis discusses the general linear regression model, least squares estimation, departures from standard assumptions, autocorrelation, multicollinearity, analysis of residuals, choice of variables, and nonlinear models.

This is a data-driven, applied statistics course focusing on the analysis of data using regression models. It emphasizes applications to the analysis of business and other data and makes extensive use of computer statistical packages. Topics include simple and multiple linear regression, residual analysis and other regression diagnostics, multicollinearity and model selection, autoregression, heteroscedasticity, regression models using categorical predictors, and logistic regression. All topics are illustrated on real data sets obtained from financial markets, market research studies, and other scientific inquiries.

A model-based approach to forecasting time series data, with emphasis on model building, foundations, and applications. Students will use the methodology of the course to analyze data sets of their choice in two projects. Weekly homework assignments on data analysis and theory. Topics of the course include the following: Autocorrelation vs. trend; Mean Squared Error for measuring forecast performance; Conditional distribution of future given present and past; Mean reversion (stationarity) and differencing; ARIMA models, their properties, and the corresponding forecasts; Box-Jenkins approach to statistical modeling: estimation, identification, diagnostic checking; Model Selection using information criteria; Exponential Smoothing; Linear vs. Nonlinear models; Chaos; Best possible forecast vs. best linear forecast; ARCH/GARCH models for forecasting volatility; Fractional ARIMA and long-memory models; Seasonal ARIMA models; Unit root tests and cointegration.

Discusses the mathematical and technical aspects of investments. Topics include measurement of interest and discount rates, accumulated value and present value, annuities, sinking funds, amortization of debt, and determination of yield rates on securities. Applications include bond evaluation, mortgages, capital budgeting, and depreciation methods.