# Courses for Statistics

**STAT W 1000x and y Undergraduate Seminar in Statistics**

Prepared with undergraduates majoring in quantitative disciplines in mind,
the presentations in this colloquium focus on the interface between data
analysis, computation, and theory in interdisciplinary research. Meetings are
open to all undergraduates, whether registered for the courses or not.
Presenters are drawn from the faculty of department in Arts and Sciences,
Engineering, Public Health and Medicine. - D. Rabinowitz

*Prerequisites: previous or concurrent enrollment in a course in
statistics.*

*1 point*

**STAT W 3997x and y Independent Research**

This course provides a mechanism for students who undertake research with a
faculty member from the Department of Statistics to receive academic credit.
- Instructor to be announced

*Prerequisites: the project mentor's permission. BC: Fulfillment of
General Education Requirement: Quantitative and Deductive Reasoning
(QUA)..*

*May be repeated for credit.*

## Introductory Courses

The Department of Statistics offers three first introductory courses, STAT W1001, W1111, and W1211. All three may be taken without preparation in statistics. All three cover roughly the same concepts, but differ substantially in the mathematical maturity that is assumed and in the sophistication of the examples.

STAT W1001 is for students who have no more than the most basic algebra, and may be of interest to students in non-mathematical disciplines seeking to satisfy the Quantitative and Deductive Reasoning requirement. STAT W1111 is for students who have mastered basic algebra; practice is emphasized over mathematical theory. STAT W1211 is for students with competence in differential and integral calculus and emphasizes theory over practice.

STAT W1211 or W1111 may be substituted for ECON BC2411 in satisfaction of the major requirements in Economics. STAT W1211 is required for the major in Mathematics-Statistics, Economics-Statistics, and Statistics, and the for the concentration in Statistics. STAT W1001 and W1111 may be applied to the major requirement in Political Science-Statistics. Students that declared their major in Psychology prior to the 2008-2009 academic year may satisfy their major requirements with STAT W1111 or W1211 in lieu of PSYC BC1101.

STAT W2110 follows on the material of the three introductory courses, and is designed for students interested in developing practical skills. Applications of statistics to current issues in the sciences and social sciences are emphasized.

**STAT W 1001x and y Introduction to Statistical
Reasoning**

A friendly introduction to statistical concepts and reasoning with emphasis
on developing statistical intuition rather than on mathematical rigor. Topics
include design of experiments, descriptive statistics, correlation and
regression, probability, chance variability, sampling, chance models, and
tests of significance.

*Prerequisites: some high school algebra. BC: Fulfillment of General
Education Requirement: Quantitative and Deductive Reasoning
(QUA)..*

*3 points*

**STAT W 1111x and y Introduction to Statistics (without
calculus)**

Designed for students in fields that emphasize quantitative methods.
Graphical and numerical summaries, probability, theory of sampling
distributions, linear regression, analysis of variance, confidence intervals
and hypothesis testing. Quantitative reasoning and data analysis. Practical
experience with statistical software. Illustrations are taken from a variety
of fields. Data-collection/analysis project with emphasis on study designs is
part of the coursework requirement.

*Prerequisites: intermediate high school algebra. BC: Fulfillment of
General Education Requirement: Quantitative and Deductive Reasoning
(QUA)..*

*3 points*

**STAT W 1211x and y Introduction to Statistics (with
calculus)**

Designed for students who desire a strong grounding in statistical concepts
with a greater degree of mathematical rigor than in *STAT W1111*. Random variables, probability
distributions, pdf, cdf, mean, variance, correlation, conditional
distribution, conditional mean and conditional variance, law of iterated
expectations, normal, chi-square, F and t distributions, law of large
numbers, central limit theorem, parameter estimation, unbiasedness,
consistency, efficiency, hypothesis testing, p-value, confidence intervals,
maximum likelihood estimation. Serves as the pre-requisite for *ECON W3412*.

*Prerequisites: one semester of calculus. BC: Fulfillment of General
Education Requirement: Quantitative and Deductive Reasoning
(QUA)..*

*3 points*

**STAT W 2024x Applied Linear Regression Analysis**

Develops critical thinking and data analysis skills for regression analysis
in science and policy settings. Simple and multiple linear regression,
non-linear and logistic models, random-effects models, penalized regression
methods. Implementation in a statistical package. Optional computer-lab
sessions. Emphasis on real-world examples and on planning, proposing,
implementing, and reporting.

*Prerequisites: one of STAT W1001, W1111, or W1211.*

*3 points*

**STAT W 2025y Applied Statistical Methods**

Classical nonparametric methods, permutation tests; contingency tables,
generalized linear models, missing data, causal inference, multiple
comparisons. Implementation in statistical software. Emphasis on on
conducting data analyses and reporting the results. Optional weekly
computer-lab sessions. - E. Whalen

*Prerequisites: STAT W2024.*

*3 points*

**STAT W 2026x Statistical Applications and Case Studies**

A sample of topics and application areas in applied statistics. Topic areas
may include: Markov processes and Queuing theory; Meta-Analysis of clinical
trial research; Receiver-Operator Curves in Medical Diagnosis; Spatial
statistics with applications in geology, astronomy, and epidemiology;
Multiple comparisons in bio-informatics; Causal modeling with missing data;
statistical methods in genetic epidemiology; Stochastic analysis of neural
spike train data; Graphical models for computer and social network
data.

*Prerequisites: STAT W2025.*

*3 points*

**STAT W 3026x Applied Data Mining**

Data Mining is a dynamic and fast growing field at the interface of
Statistics and Computer Science. The emergence of massive datasets containing
millions or even billions of observations provides the primary impetus for
the field. Such datasets arise, for instance, in large-scale retailing,
telecommunications, astronomy, computational and statistical challenges. This
course will provide an overview of current practice in data mining. Specific
topics covered with 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. The use of statistical software will be emphasized. - B.
Emir

*3 points*

## Foundation Courses

The Department offers STAT W3105, W3107, and W4315 as a sequence. W3105 covers probability theory and is a prerequisite for W3107. W3107 covers statistical theory, and is a prerequisite for STAT W4315. STAT W4315 covers linear regression models, and provides an introduction to practical issues in data analysis. Students who have difficulty scheduling STAT W3105 or W3107 may substitute, respectively, STAT W4105 and W4107, or substitute, for the pair, the combined course STAT W4109. The sequences is a pre-requisite for the advanced undergraduate offerings in the Department (except W4604 and W4835, which have only W3105 as a prerequisite, and W4204, which has only STAT W3105 and W3107 as co-requisites). STAT W4150 is an abridged version of W3105 and W3107 designed especially for SEAS students.

**STAT W 3103x Mathematical Methods for Statistics**

A fast-paced coverage of those aspects of the differential and integral
calculus of one and several variables and of the linear algebra required for
the core courses in the Statistics major. The mathematical topics are
integrated with an introduction to computing. Students seeking more
comprehensive background should replace this course with *MATH V1102* and *V2010* and any *COMS* course numbered from
*W1003* to *W1009.*

*Prerequisites: MATH V1101 or the instructor's permission.*

*6 points*

**STAT W 3105x Introduction to Probability**

A calculus-based introduction to probability theory. A quick review of
multivariate calculus is provided. 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: MATH V1101 and V1102 or the equivalent. BC: Fulfillment of General
Education Requirement: Quantitative and Deductive Reasoning
(QUA)..*

*3 points*

**STAT W 3107y Introduction to Statistical Inference**

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 W3105 or W4105, or the equivalent. BC: Fulfillment of General
Education Requirement: Quantitative and Deductive Reasoning
(QUA)..*

*3 points*

**STAT W 3315x Linear Regression Models**

Theory and practice of regression analysis. Simple and multiple regression,
testing, estimation, prediction, 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. Equivalent to *STAT W4315*, except that enrollment is limited to
undergraduate students.

*Prerequisites: STAT W3107(or STAT W4150) and STAT W3103(or MATH V1101, V1102, and V2110).*

*3 points*

**SIEO W 4150x and y Introduction to Probability and
Statistics**

A quick calculus-based tour of the fundamentals of probability theory and
statistical inference. Probability models, random variables, useful
distributions, expectations, law of large numbers, central limit theorem,
point and confidence interval estimation, hypothesis tests, linear
regression. Students seeking a more thorough introduction to probability and
statistics should consider *STAT W3105* and *W3107*. - L. Wright, I. Hueter

*Prerequisites: MATH V1101 and MATH V1102 or the equivalent. BC: Fulfillment of
General Education Requirement: Quantitative and Deductive Reasoning
(QUA)..*

*3 points*

## Advanced Courses

**STAT W 3051x or y Math Finance in Continuous Time**

This follows *MATH V3050*. Basic concepts in probability theory, and
then advanced concepts, including Brownian motion, stochastic calculus,
expectation, Radon-Nikodym theorem, Girsanov's theorem, stochastic
differential equations (inlcuding Black-Merton-Scholes), options and hedging,
stochastic interest rates, forwards and futures. Formal proofs will be
eschewed in favor of understanding concepts.

*Prerequisites: MATH V3050.*

*3 points*

**STAT W 4201x and y Advanced Data Analysis**

This is a course on getting the most out of data. The emphasis will be on
hands-on experience, involving case studies with real data and using common
statistical packages. The course covers, at a very high level, exploratory
data analysis, model formulation, goodness of fit testing, and other standard
and non-standard statistical procedures, including linear regression,
analysis of variance, nonlinear regression, generalized linear models,
survival analysis, time series analysis, and modern regression methods.
Students will be expected to propose a data set of their choice for use as
case study material. - Demissie Alemayehu

*Prerequisites: STAT W4315. At least one of W4290, W4325, W4330, W4437, W4413, W4543 is recommended. BC: Fulfillment of General
Education Requirement: Quantitative and Deductive Reasoning
(QUA)..*

*3 points*

**STAT W 4240x Data Mining**

Data Mining is a dynamic and fast growing field at the intersection of
statistics and computer science, driven by the growing prevalence of large
data sets. This course covers the elementary theory of bias-variance
trade-offs and cross-validation in supervised learning, and surveys methods
for regression, classification, and clustering. Students implement the
methods on large and small data sets using a statistical package.

*Prerequisites: Linear Algebra, Calculus, and an introductory class in
statistics. Corequisites: either STAT W3105 or W4105, and either STAT W3107 or W4107.*

*3 points*

**STAT W 4290y Statistical Methods in Finance**

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 W3107 or W4107. BC: Fulfillment of General Education
Requirement: Quantitative and Deductive Reasoning (QUA)..*

*3 points*

**STAT W 4325y Generalized Linear Models**

Statistical methods for rates and proportions, ordered and nominal
categorical responses, contingency tables, odds-ratios, exact inference,
logistic regression, Poisson regression, generalized linear models. - M.
Sobel

*Prerequisites: STAT W4315. BC: Fulfillment of General Education
Requirement: Quantitative and Deductive Reasoning (QUA)..*

*3 points*

**STAT W 4330x Multilevel Models**

Theory and practice, including model-checking, for random and mixed-effects
models (also called hierarchical, multi-level models). Extensive use of the
computer to analyse data. - TBA

*Prerequisites: STAT W4315. BC: Fulfillment of General Education
Requirement: Quantitative and Deductive Reasoning (QUA)..*

**STAT W 4335x Sample Surveys**

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. Examples from public health, social work, opinion
polling, and other topics of interest. - M. Sobel

*Prerequisites: STAT W3107 or W4107. BC: Fulfillment of General Education
Requirement: Quantitative and Deductive Reasoning (QUA)..*

*3 points*

**STAT W 4400y Statistical Machine Learning**

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. -
Peter Orbanz

*Prerequisites: Calculus I and Linear Algebra.*

**STAT W 4413y Nonparametric Statistics**

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. - B. Sen

*Prerequisites: STAT W3107 or W4107. BC: Fulfillment of General Education
Requirement: Quantitative and Deductive Reasoning (QUA)..*

*3 points*

**STAT W 4437x and y Time Series Analysis**

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 W4315 or the equivalent. BC: Fulfillment of
General Education Requirement: Quantitative and Deductive Reasoning
(QUA)..*

*3 points*

**STAT W 4543y Survival Analysis**

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. - M. Shnaidman

*Prerequisites: STAT W4315. BC: Fulfillment of General Education
Requirement: Quantitative and Deductive Reasoning (QUA)..*

**STAT W 4606x and y Elementary Stochastic Processes**

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. - M.
Brown

*Prerequisites: STAT W3105, W4105, or the equivalent. BC: Fulfillment of General
Education Requirement: Quantitative and Deductive Reasoning
(QUA)..*

*3 points*

**STAT W 4635y Stochastic Processes for Finance**

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 W3105, W4105, or equivalent.*

*3 points*

## Actuarial Science Courses

**ACTU K 4821x and y Actuarial Methods**

This course covers the non-stochastic process portions of the MLC/3L exam,
and is about pricing and reserving of life insurance. Topics include
actuarial present value, the equivalence principle, premiums, three methods
of calculating reserves, joint life and multiple hazard.

*Prerequisites: STAT W4105, STAT W4840.*

*3 points*

**ACTU K 4823x and y Actuarial Models**

This course covers portions of the C/4 exam not covered elsewhere in the
curriculum. Topics may include Bayesian statistics, credibility, and risk
measures.

*Prerequisites: STAT W4840, STAT W4107.*

*3 points*