2008-2009 Bulletin – PDF - SEAS Bulletin - Columbia University

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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. General
Education Requirement: Quantitative and
Deductive Reasoning (QUA).
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. Nonparametric analogs of analysis of
variance. Tolerance limits. Robust estimation.
Introduction to sequential statistical procedures.
Applications to quality control and clinical trials.
STAT W4437x and y Time series analysis
3 pts. Instructor to be announced.
Prerequisite: STAT W4315 or the equivalent.
Least-squares 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 lectures.
STAT W4543y Survival analysis
3 pts. Instructor to be announced.
Prerequisite: STAT W3659/W4107 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 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.
STAT W6501x Stochastic processes and
application, I
3 pts. J. Vecer.
Prerequisite: STAT W4105 or the equivalent.
Discrete and continuous-time Markov chains; elements
of renewal theory; Martingales and their
basic properties. Brownian motion: construction,
basic properties, sample paths. Stochastic integration,
Ito’s rule, applications. Introduction to stochastic
differential equations and diffusion
processes.
SEAS 2008–2009