Prerequisites: At least one semester of calculus.
A calculus-based introduction to probability theory. 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.
Prerequisites: STAT GR5203 or the equivalent, and two semesters of calculus.
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.
Prerequisites: STAT GR5203 and GR5204 or the equivalent.
Theory and practice of regression analysis, Simple and multiple regression, including testing, estimation, 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 analyse data.
Corequisites: GR5203 or the equivalent.
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.
Prerequisites: STAT GR5205
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.
Prerequisites: STAT GR5205
Statistical inference without parametric model assumption. Hypothesis testing using ranks, permutations, and order statistics. Nonparametric analogs of analysis of variance. Non-parametric regression, smoothing and model selection.
Prerequisites: STAT GR5205.
Multivariate normal distribution, multivariate regression and classification; canonical correlation; graphical models and Bayesian networks; principal components and other models for factor analysis; SVD; discriminant analysis; cluster analysis.
Prerequisites: STAT GR5205
Bayesian vs frequentist, prior and posterior distributions, conjugate priors, informative and non-informative prior subjective and objective bayes, oneand two sample problems, models for normal data, models for binary data, multivariate normal shrinkage, bayesian linear models, bayesian computation (start early), MCMC algorithms, the Gibbs sampler, hierarchical models, empirical bayes, hypothesis testing, bayes factors, model selection, software: R and WinBUGS
Prerequisites: STAT GR5205
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.
Prerequisites: STAT GR5205
Statistical methods for rates and proportions, ordered and nominal categorical responses, contingency tables, odds-ratios, exact inference, logistic regression, Poisson regression, generalized linear models.
Prerequisites: STAT GR5206 or the equivalent.
The course will provide an introduction to Machine Learning and its core models and algorithms. The aim of the course is to provide students of statistics with detailed knowledge of how Machine Learning methods work and how statistical models can be brought to bear in computer systems - not only to analyze large data sets, but to let computers perform tasks that traditional methods of computer science are unable to address. Examples range from speech recognition and text analysis through bioinformatics and medical diagnosis. This course provides a first introduction to the statistical methods and mathematical concepts which make such technologies possible.
Prerequisites: STAT GR5206 or the equivalent.
This course will incorporate knowledge and skills covered in a statistical curriculum with topics and projects in data science. Programming will covered using existing tools in R. Computing best practices will be taught using test-driven development, version control, and collaboration. Students finish the class with a portfolio on GitHub, and deeper understanding of several core statistical/machine-learning algorithms. Bi-weekly project cycles throughout the semester provide students extensive hands-on experience with various data-driven applications.
This course covers features of the C++ programming language which are essential in quantitative/computational finance and its applications. We start by covering basic C++ programming features and then move to some more advance features. We utilize these features for financial engineering and quantitative finance applications primarily for pricing of financial derivatives and computational finance. Those applications include transform techniques, Monte Carlo simulation, calibration and parameter estimation techniques.
Prerequisites: STAT GR5204 or the equivalent. STAT GR5205 is recommended.
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.
Prerequisites: STAT GR5203 or the equivalent.
This course covers theory of stochastic processes applied to finance. It covers concepts of Martingales, Markov chain models, Brownian motion. Stochastic Integration, Ito's formula as a theoretical foundation of processes used in financial modeling. It also introduces basic discrete and continuous time models of asset price evolutions in the context of the following problems in finance: portfolio optimization, option pricing, spot rate interest modeling.
Prerequisites: STAT GR5264
Available to SSP, SMP. Mathematical theory and probabilistic tools for modeling and analyzing security markets are developed. Pricing options in complete and incomplete markets, equivalent martingale measures, utility maximization, term structure of interest rates.
Prerequisites: W4315 and either another statistics course numbered above the 4200 or permission of instructor.
Required for the major in statistics. Data analysis using a computer statistical package and selected exploratory data analysis subroutines. Topics include editing of data for errors, exploratory and standard techniques for one-way analysis of variance, linear regression, and two-way analysis of variance. Material is presented in case-study format.