Statistics

A time series consists of a set of observations on a random variable taken over time. Time series arise naturally in climatology, economics, environment studies, finance and many other disciplines. The observations in a time series are usually correlated; the course establishes a framework to discuss this. This course distinguishes different type of time series, investigates various representations for the processes and studies the relative merits of different forecasting procedures. Students will analyze real time-series data on the computer. Topics: Stationary and the autocorrelation functions; linear stationary models; linear non-stationary models; model identification; estimation and diagnostic checking; seasonal models and forecasting methods for time series. 

This course examines fundamental concepts in probability and mathematical statistics, including probabilistic modelling, limiting results, estimation and hypothesis testing. Topics include random variables and vectors, distribution and quantile functions, covariance and correlation matri-ces, strong law of large numbers, central limit theorem, estimators and their (asymptotic) properties, parametric estimators (maximum likelihood, method of moments), (asymptotic) conĄdence intervals (mean and variance of a normal, difference of means of two normals, ratio of means of two normals), hypothesis tests (theory, power function, p-value, asymptotic tests, likelihood ratio tests). 

The analysis of variability is mainly concerned with locating the sources of the variability. Many statistical techniques investigate these sources through the use of linear models. This course presents the theory and practice of these models. Topics include: simple linear regression: least squares method, analysis of variance, coefficient of determination, hypothesis tests and confidence intervals for regression parameters, prediction; multiple linear regression: least squares method, analysis of variance, coefficient of determination, reduced versus full models, hypothesis tests and confidence intervals for regression parameters, prediction, polynomial regression; one-way classification models: one-way ANOVA, analysis of treatment effects, contrasts; two-way classification models: interactions, two-way ANOVA for balanced data structures, analysis of treatment effects, contrasts, randomized complete block design; universal approach to linear modeling: dummy variables, multiple linear regression representation of one-way and two-way (unbalanced) models, ANCOVA models, concomitant variables; regression diagnostics: leverage, residual plot, normal probability plot, outlier, studentized residual, influential observation, Cook's distance, multicollinearity, model transformation. 

This course examines major statistical techniques in analyzing categorical data. Topics include measures of association, inference for two-way contingency tables, loglinear models, logit models and models for ordinal variables. The use of related statistical packages will be demonstrated. 

This course examines the fundamentals, basic properties and use of classical and modern nonparametric statistical methods for data analysis. Topics may include: order statistics; goodness-of-fit tests; rank tests for single-sample and two-independent samples; tests for designed experiments; permutation tests; tests for trends and association; jackknife and bootstrapping methods; nonparametric regression; nonparametric estimator and statistical functionals.

This course provides a basic and broad introduction to the representation, analysis, and processing of sampled data. The course introduces statistical analysis, mathematical modeling, machine learning, and visualization for experimental data. Examples are taken from real-world problems, such as analysis of internet traffic, language technology, digital sound, and image processing.

The course is intended to be a (non-exhaustive) survey of regression techniques from both a theoretical and applied perspective. Time permitting, the methods students study include: exploratory data analysis, simple linear regression; multiple linear regression; regression with categorical variables; regression with interaction terms; polynomial regression; model selection for multiple linear models; and regression diagnostics.

This course examines option pricing and hedging. It will concentrate on the theory and idea of derivatives pricing and risk management. Topics include option market; European and American options; conditional expectation and discrete-time martingale, discrete-time option pricing theory; true probabilities vs. risk-neutral probabilities; estimating volatility; the Black-Scholes formula; implied volatility; option Greeks; market-making and hedging; and exotic options.

This is a special studies course involving an internship with a corporate, public, governmental, or private organization, arranged with the Study Center Director or Liaison Officer. Specific internships vary each term and are described on a special study project form for each student. A substantial paper or series of reports is required. Units vary depending on the contact hours and method of assessment. The internship may be taken during one or more terms but the units cannot exceed a total of 12.0 for the year.