1301 - Introduction to Statistics
Introduction to collecting observations
and measurements, organizing data, variability, and fundamental concepts and
principles of decision-making. Emphasis is placed on statistical
reasoning and the uses and misuses of statistics.
2301 - Statistics for Modern Business Decisions
A
foundation in data analysis and probability models is followed by elementary
applications of confidence intervals, hypothesis
testing, correlation, and regression. Prerequisite: CEE Math
Fundamentals or equivalent.
2331 - Introduction to Statistical Methods
An
introduction to statistics for behavioral, biological, and social scientists.
Topics include descriptive statistics, probability
and inferential statistics including hypothesis testing, analysis of variance,
and contingency tables.
4340 - Statistical Methods for Engineers and
Applied Scientists (Co-listed as CSE 4340)
Basic
concepts of probability and statistics useful in the solution of engineering
and applied science problems. Topics:
probability, probability distributions, data analysis, sampling distributions,
estimation, and simple tests of hypothesis.
Prerequisite: MATH 1337 and 1338.
4370 - Survey Sampling
Simple
random sampling; stratified, systematic, subsampling; means, variances,
confidence limits; finite population correction;
sampling from binomial populations. Principles of planning and conducting
surveys. Prerequisite:
Permission of instructor.
5340 - Probability and Statistics for Scientists
and Engineers (Co-listed as CSE 5370)
Introduction
to fundamentals of probability and distribution theory, statistical techniques
used by engineers and
physical scientists. Examples of tests of significance, operating
characteristic curve, tests of hypothesis about
one and two parameters, estimation, analysis of variance, and the choice
of a particular experimental procedure
and sample size. Prerequisite: Math 1337, 1338 and 2339, or
equivalent.
5344 - Statistical Quality Control (Co-listed
as 5364)
Statistics
and simple probability are introduced in terms of problems that arise in
manufacturing; their application
to control of manufacturing processes. Acceptance sampling in terms
of standard sampling plans.
Prerequisite: STAT (CSE) 4340 or STAT 5340 (CSE 5370).
5371 - Experimental Statistics
A
non-calculus development of the fundamental procedures of applied experimental
statistics, including tests of
hypotheses and interval estimation for the normal, binomial, chi-square
and other distributions, and nonparametric
tests. prerequisite: Junior standing or permission of instructor.
5372 - Experimental Statistics
Analysis
of variance, completely randomized design, randomized complete block designs-nested classifications,
factorials; analysis of covariance, simple and multiple linear regressions,
and correlation.
Prerequisite: STAT 5371.
5377 - Statistical Design and Analysis of Experiments
Introduction
to statistical principles in the design and analysis of industrial experiments.
Completely randomized,
randomized complete and incomplete block, latin square, and Plackett-Burman screening
designs. Complete and fractional factorial experiments. Descriptive
and inferential statistics.
Analysis of variance models. Mean comparisons. Prerequisite:
Senior standing with a
science or engineering major, or permission of instructor.
GRADUATE COURSES
6304. COMPUTATIONAL STATISTICS.
This course
introduces students to the fundamentals of statistical computing used by
both theoretical and applied statisticians
in both academics and industry. Subject matter is divided into two areas,
simulation experiments and statistical
software, and includes generating random deviates from various distributions,
analysis of statistical algorithms,
an introduction to UNIX, an introduction to S-Plus for data analysis and
graphics, interfacing S-Plus to code written
in C and/or FORTRAN, and managing and manipulating very large data sets.
Prerequisite: STAT 6327 or concurrent
enrollment in this course.
6320. QUADRATIC FORMS AND MATRIX COMPUTATIONS.
Statistical
distribution theory of quadratic forms of normal variables. Matrix and
vector operations as they pertain to the distribution
of quadratic forms. Distributions, moments, and independence of quadratic
forms. Computer implementation using
SAS. Prerequisite: Linear Algebra.
6327. MATHEMATICAL STATISTICS.
Theory of probability distributions. Random variables and functions of
random variables. Multivariate and conditional distributions.
Sampling distributions; order statistics. Expected value, transformations,
approximations. Prerequisite: Advanced
Calculus or permission of instructor.
6328. MATHEMATICAL STATISTICS.
Sufficiency and completeness. Unbiased, maximum likelihood and Bayes point
estimators, minimizing risk. Confidence
sets. Most powerful, uniformly MP and likelihood ratio tests. Large-sample
approximations; contingency table
analysis. Prerequisite: STAT 6327.
6336. STATISTICAL ANALYSIS.
Analysis
of data from one and two samples assuming normal distributions and independent
errors. Discussion of paired sample
analyses and of nonparametric location tests.
6337. STATISTICAL ANALYSIS.
Emphasis
on application of statistical principles in the design of experiments.
Complete and fractional factorials, blocking, nesting,
replication, randomization. Analysis of data from classical multifactor
experimental designs with fixed and random effects.
Multiple comparisons and contrasts of main effects and interactions. Introduction
to regression analysis. Prerequisite:
STAT 6336.
6342. ADVANCED STATISTICAL QUALITY CONTROL.
Investigate
statistical methods and management principles useful for understanding
and improving measurable performance
in human endeavors. Develop a “statistical thinking” foundation through
the evaluation of case studies and class
labs. Prerequisite: STAT 4340/CSE 4340, or STAT 5340/CSE 5370, or
STAT 5371; or Corequisite: STAT 6327
or 6336.
6345. LINEAR REGRESSION.
The
classical tools of linear regression based upon least squares estimation
and inference through the assumption of normally
distributed errors. Topics in model formulation, data transformations,
variable selection, and regression diagnostics
for influential observations. Collinear predictors and biased estimation.
Survey of alternatives to least squares. Prerequisite:
STAT 6320 and 6337.
6346. ADVANCED REGRESSION ANALYSIS.
Nonlinear
least-squares estimation. Theory and applications of generalized linear
models. Estimation, asymptotic distribution
theory, and tests for model parameters. Topics in spatial statistical modeling,
including variogram estimation and
kriging. Prerequisites: STAT 6345 or permission of instructor.
6355. APPLIED MULTIVARIATE ANALYSIS.
Statistical
methods of analysis of multivariate data, tests and estimation of multivariate
normal parameters; Hotelling’s T2, discriminant
analysis, canonical correlation, principal components, and factor analysis.
Applications are emphasized. Prerequisites:
STAT 6337 and 6320.
6358. TOPICS IN BIOSTATISTICS.
Introduction
to various statistical methods that are widely used in the biosciences,
especially biomedical research. Subject matter
includes survival analysis, contingency tables, logistic regression, analysis
of longitudinal data, design of clinical experiments,
epidemiology, and statistical genetics; topics may vary with instructor.
Prerequisite: STAT 6328 or permission
of instructor.
6363. TIME SERIES ANALYSIS.
Statistical methods of analyzing time series. Autocorrelation function
and spectrum. Autoregressive and moving average
processes. More general models, forecasting, stochastic model building.
Prerequisite: Permission of instructor.
6366. STATISTICAL CONSULTING.
Apprenticeship under an experienced consultant, with exposure to real problems
handled by the Center for Statistical Consulting
and Research. Between four to six hours per week will be spent in consultation
sessions and seminars. In addition
to a variety of technical statistical issues the class will study the existing
literature on the nonstatistical aspects of the
consulting endeavor.
6370 (CSE 6370). STOCHASTIC MODELS.
Model
building with stochastic processes in applied sciences. Phenomena with
uncertain outcomes are formulated as stochastic
models and their properties are analyzed. Some specific problems discussed
come from areas such as population
growth, queueing, reliability, time series, and social and behavioral processes.
Statistical properties of the models
are emphasized. Prerequisites: STAT 5340/CSE 5370 and graduate standing.
6371. PROBABILITY THEORY.
An
introduction to measure theoretic probability. Random variables, expectation,
conditional expectation, characteristic
functions. Prerequisite: STAT 6327 or permission of instructor.
6372 (CSE 6372). QUEUEING THEORY.
Queueing
theory provides the theoretical basis for the analysis of stochastic service
systems. The underlying stochastic processes
are point processes of which Markov and renewal processes are two major
examples. The emphasis of the course
is in the formulation of queueing models and their behavioral and statistical
analyses using Markov and renewal techniques.
Prerequisite: An introductory course in Stochastic Processes (e.g.
STAT 6370/CSE 6370, STAT 6376, 6379,
EE 5306).
6378. MULTIVARIATE ANALYSIS.
Theory and
inference in the multivariate normal distribution. Regression, correlation,
Wishart distribution, Hotelling's
T2 , MANOVA and discriminant analysis. Prerequisite:
STAT 6320, and 6328 or 6381.
6381. THEORY OF LINEAR MODELS.
Theory
of the general linear model; estimability and testability. Theory
of analysis of fixed, random and
mixed models. Prerequisite: STAT 6328, 6337, and 6320.
6385. SURVEY OF NONPARAMETRIC STATISTICS.
Topics
include robust and distribution-free techniques; order statistics, EDF
statistics, quantiles, asymptotic distributions
and tolerance intervals; linear rank statistics for one, two, and several
sample problems involving location
and scale; runs; multiple comparison; rank correlation; and asymptotic
relative efficiency. Prerequisite:
STAT 6328.
6388. LARGE SAMPLE THEORY.
Limit theorems
useful in mathematical statistics. The foundation of asymptotic theory
in statistics including modes
of convergence, laws of large numbers and the central limit theorem.
Systematic coverage of useful representations
of certain basic statistics and large sample optimality of maximum likelihood procedures. Prerequisites:
STAT 6328 and 6371.
7327. ADVANCED STATISTICAL INFERENCE.
Topics
in statistical inference; estimation (point and interval estimates, Bayesian
and likelihood); tests
of hypotheses (invariant, unbiased, most powerful, conditional, Bayesian);
large-sample theory for
multiparameter problems. Prerequisite: STAT 6371.
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