# Courses

The courses taught by members of the Statlab are offered in the Department of Operations Research. They consist of both undergraduate courses and graduate courses. For more information on a course, visit the Registrar's website.

### Undergraduate courses

#### ORF 245: Fundamentals of Engineering Statistics

A first introduction to probability and statistics. This course will provide background to understand and produce rigorous statistical analysis including estimation, confidence intervals, hypothesis testing and regression. Applicability and limitations of these methods will be illustrated in the light of modern data sets and manipulation of the statistical software R. Precepts are based on real data analysis.

#### ORF 350: Analysis of Big Data

The amount of data in our world has been exploding, and analyzing large data sets is becoming a central problem in our society. This course introduces the statistical principles and computational tools for analyzing big data: the process of exploring and predicting large datasets to find hidden patterns and gain deeper understanding, and of communicating the obtained results for maximal impact. Topics include massively parallel data management and data processing, model selection and regularization, statistical modeling and inference, scalable computational algorithms, descriptive and predictive analysis, and exploratory analysis.

#### ORF 405: Regression and applied time series

Statistical Analysis of financial data: Density estimation, heavy tail distributions and dependence. Regression: linear, nonlinear, nonparametric. Time series analysis: classical models (AR, MA, ARMA, ..), state space systems and filtering, and stochastic volatility models (ARCH, GARCH, ....).

### Graduate courses

#### ORF 504: Financial econometrics

Econometric and statistical methods as applied to finance. Topics include: Overview of Statistical Methods; Predictability of asset returns; Discrete time volatility models; Efficient Portfolio and CAPM; Multifactor Pricing Models; Intertemporal Equilibrium and Stochastic Discount Models; Expectation and present value relation; Simulation methods for financial derivatives; Econometrics of financial derivatives; Forecast and Management of Market Risks; Multivariate time series in finance; Nonparametric methods in financial econometrics

#### ORF 505: Modern regression and time series

Heavy tailed distributions and copulas. Simple and multiple linear regressions. Nonlinear regression. Nonparametric regression and classification. Time series analysis: stationarity and classical linear models (AR, MA, ARMA, ..). Nonlinear and nonstationary time series models. State space systems, hidden Markov models and filtering.

#### ORF 524: Statistical theory and methods

A graduate-level introduction to statistical theory and methods and some of the most important and commonly-used principles of statistical inference. Covers the statistical theory and methods for point estimation, confidence intervals, and hypothesis testing, and the applications of the fundamental theory to generalized linear models.

#### ORF 525: Statistical learning and nonparametric estimation

A theoretical introduction to statistical learning problems related to regression and classification. Topics covered include: Principle Component Analysis, nonparametric estimation, sparse regression, and Classification and Statistical learning.

#### ORF 565: Empirical processes and asymptotic statistics

Empirical Process theory mainly extends the law of large numbers (LLN), central limit theorem (CLT) and exponential inequalities to uniform LLN's and CLT's and concentration inequalities. This uniformality is useful to statisticians and computer scientists in that they often model data as a sample from some unknown distribution and desire to estimate certain aspects of the population. The applications to the theory and methods of high-dimensional statistical learning will be emphasized.

#### ORF 566: High dimensional statistics

This course is on statistical theory and methods for high-dimensional statistical learning and inferences, arising from processing massive data from various scientific disciplines. The emphasis will be given to penalized likelihood methods, independence screening, large covariance modeling, and large-scale hypothesis testing. The important theoretical results will be proved.

#### ORF 570: Special topics in statistics and operations research - Prediction games

This course presents an alternative approach to (sequential) forecasting problems. The core idea is to design strategies that work without any probabilistic assumption on the data-generating mechanism. These new methods can be applied in a great variety of settings, including sequential investment in the stock market, sequential pattern analysis, dynamic pricing and online linear optimization. Moreover, on the mathematical level, this new theory gives the opportunity to study important notions that can be useful in completely different topics than forecasting, in particular: simple concentration inequalities etc.

#### ORF 570: Special topics in statistics and operations research - Probability in High Dimension

An introduction to nonasymptotic methods for the study of random structures in high dimension that arise in probability, statistics, computer science, and mathematics. Emphasis is on developing a common set of tools that has proved to be useful in different areas. Topics may include: suprema of random processes; Gaussian and Rademacher inequalities; generic chaining; entropy and combinatorial dimensions; concentration of measure; functional, transportation cost, martingale inequalities; isoperimetry; Markov semigroups, mixing times, random fields; hypercontractivity; thresholds and influences; Stein's method; selected applications