2009-2010 Bulletin – PDF - SEAS Bulletin - Columbia University

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from many disciplines. Specific topics covered
include databases and data warehousing,
exploratory data analysis and visualization,
descriptive modeling, predictive modeling, pattern
and rule discovery, text mining, Bayesian data
mining, and causal inference.
STAT W4290 y Statistical methods in finance
3 pts. Instructor to be announced.
Prerequisites: STAT W4105 and W4107. This is
a master-level course introducing statistical
methodologies in quantitative finance. Financial
applications and statistical methodologies are
intertwined in all lectures, with several research
topics being introduced through problems in a
term project. Lecture notes by the instructor will
be distributed. The course will cover linear
regression with applications to single and multifactor
pricing models, multivariate analysis and
their applications in Markowitz’s portfolio management,
estimation and modeling of volatilities, calculation
of value-at-risk, nonparametric methods
with applications to option pricing and interest
rate markets.
STAT W4315x and y Linear regression models
3 pts. Instructor to be announced.
Prerequisites: STAT W3107 or the equivalent,
MATH V2110 or the equivalent. Corequisites:
MATH V1101, V1102, and V2110. Simple and
multiple regression, including testing, estimation
and confidence procedures, modeling, regression
diagnostics and plots, polynomial regression,
fixed effects ANOVA and ANCOVA models, nonlinear
regression, multiple comparisons, co-linearity
and confounding, model selection. Emphasis on
geometric approach to the theory and the use of
a statistical package to analyze data.
STAT W4325x Generalized linear models
3 pts. Instructor to be announced.
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 W4335x Sample surveys
3 pts. Instructor to be announced.
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.
Discussions include detail surveys from
areas including public health, social work, opinion
polling, and other topics of interest.
STAT W4413x Nonparametric statistics
3 pts. Instructor to be announced.
Prerequisite: STAT W4107. Statistical inference
without parametric model assumption. Hypothesis
testing using ranks, permutations, and order
statistics. Semi-parametric analysis of censored
survival data. Analysis of discrete outcomes.
Contingency tables. Applications.
STAT W4437x and y Time series analysis
3 pts. Instructor to be announced.
Prerequisite: STAT W4315 or the equivalent. Leastsquares
smoothing and prediction, linear systems,
Fourier analysis and spectral estimation. Impulse
response and transfer function. Fourier series, the
fast Fourier transform algorithm, autocorrelation
function, and spectral density. Univariate Box-
Jenkins modeling and forecasting. Emphasis on
practical applications in examples from the physical
sciences, social sciences, and business. Computing
is an integral part of the course.
STAT W4543y Survival analysis
3 pts. Instructor to be announced.
Prerequisite: STAT W4315 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 covariate data, regression analysis
with lifetime data. Extensive use of the computer
to analyze data. Applications in clinical trials and
acturial science.
STAT W4606x and y Elementary stochastic
processes
3 pts. M. Brown and instructor to be announced.
Prerequisite: STAT W4105 or the equivalent.
Review of elements of probability theory. Poisson
processes. Exponential distribution. Renewal
theory. Wald’s equation. Introduction to discrete
time Markov chains and applications to queueing
theory, inventory models, branching processes.
STAT W4635y. Stochastic processes for
finance
3 pts. Instructor to be announced.
Prerequisites: STAT W3105 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.
STAT W4840x Theory of interest
3 pts. N. Rajah.
No prerequisite. 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 financial
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.
SEAS 2009–2010