**100. Introduction to Statistical Reasoning.
*** No credit granted
to those who have completed or are enrolled in Soc. 210, Stat.
402, 311, 405, or 412, or Econ. 404. (4). (MSA). (BS). (QR/1).
*This course is designed
to provide an overview of the field of statistics. Course topics
include methods of analyzing and summarizing data, statistical
reasoning as a means of learning from observations (experimental
or sample), and techniques for dealing with uncertainties in drawing
conclusions from collected data. Basic fallacies in common statistical
analyses and reasoning are discussed, and proper methods indicated.
Alternative approaches to statistical inference are also discussed.
The course emphasis is on presenting basic underlying concepts
rather than on covering a wide variety of different methodologies.
Course evaluation is based on a combination of a Thursday evening
midterm examination, a final examination, and teaching fellow
input. The course format includes three lectures and a laboratory
(1 hour per week). Cost:2
WL:3 (001: Aliaga;
002: Berube; 003: Gunderson; 004: Hill)

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**170. The Art of Scientific Investigation.
*** (4). (MSA).
(BS). (QR/1).
*The objective of this
course is to introduce students to the learning process in a non-deterministic
environment. An appreciation for measurement, bias, and variation
is essential to formulate questions and learn about things. Underlying this course is the Edwards Deming philosophy. Deming, an American
statistician, was invited to Japan in the early 1950's to help
improve the quality of mass produced items. His success in Japan
is, in part, responsible for our current balance of trade deficit;
and here the Ford Motor Co. has also attained a larger market
share as a result of his ideas. Implementation of the Deming message
requires a critical appreciation of variation and the scientific
method. Specifically, we will discuss: (1) Historical attempts
to learn and the advent of the modern scientific method. (2) The
differences between special or assignable causes and common causes
of variation. Before we can learn how a process operates, the
process must be stable. (3) Differences between observational
and controlled randomized studies and associated ethical issues.
(4) The 'what' and 'how' of measurement and the quantification
of uncertainty-subjective and frequency notions of probability.
(5) Understanding bias and variation. (6) How to use bias to design
efficient studies. (7) Differences between enumerative and analytic
studies. Many of the ideas will be introduced through experimentation

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**311/IOE 365. Engineering Statistics.
*** Engin. 101, Math. 215, and IOE 315 or Stat 310. No credit granted to those
who have completed or are enrolled in Stat. 405 or 412. One credit
granted to those who have completed Stat. 402. (4). (Excl). (BS).
*Collection and analysis
of engineering data associated with stochastic industrial processes.
Topics include: exploratory data analysis, describing relationships, importance of experimentation, applications of sampling distribution theory, test of hypotheses, experiments with one or more factors, and regression analysis. Students are required to use statistical
packages on CAEN for problem solving.

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**402. Introduction to Statistics and Data
Analysis. *** No
credit granted to those who have completed or are enrolled in
Econ. 404 or Stat. 311, 405, or 412. (4). (NS). (BS). (QR/1).
*In this course students
are introduced to the concepts and applications of statistical
methods and data analysis. Statistics 402 has no prerequisite
and has been elected by students whose mathematics background
includes only high school algebra. Examples of applications are
drawn from virtually all academic areas and some attention is
given to statistical process control methods. The course format
includes three lectures and a laboratory (l.5 hours per week).
The laboratory section deals with the computational aspects of the course and provides a forum for review of lecture material.
For this purpose, students are introduced to the use of a micro-computer
package and the Macintosh computer. Course evaluation is based
on a combination of three examinations GIVEN WEDNESDAY EVENINGS, a final examination, and teaching fellow input. Cost:2
WL:3 (002: Gunderson;
003, 004: Kou; 005: Meyer; 006: Muirhead)

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**403. Introduction to Statistics and Data
Analysis II. *** Stat.
402. (4). (Excl). (BS).
*Intermediate topics
in multiple linear regression and the analysis of covariance, stressing applications: least squares estimates, test of hypotheses, prediction analysis, residual analysis, multicollinearity, and the variable selection techniques; fixed and random effects models
in ANOVA; multiple comparisons, randomized blocks, Latin squares, nested and hierarchical designs; and robust procedures, as time
permits. Three hours of lecture supplemented by one and one-half
hours of laboratory. Cost:2
WL:3 (Meyer)

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**405/Econ. 405. Introduction to Statistics.
*** Math. 116 or
118. Juniors and seniors may elect this course concurrently with
Econ. 101 or 102. No credit granted to those who have completed
or are enrolled in Stat. 311 or 412. Students with credit for
Econ. 404 can only elect Stat. 405 for 2 credits and must have
permission of instructor. (4). (MSA). (BS). (QR/1).
*Principles of statistical
inference, including: probability, experimental and theoretic
derivation of sampling distributions, hypothesis testing, estimation, and simple regression. Cost:2
WL:3 (Woodroofe)

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**406. Introduction to Statistical Computing.
*** Stat. 425 and 402. (4). (Excl). (BS).
*Acquaints students with
selected topics in statistical computing, including basic numerical
aspects, iterative statistical methods, principles of graphical
analyses, simulation and Monte Carlo methods, generation of random
variables, stochastic modeling, importance sampling, numerical
and Monte Carlo integration. Three hours of lecture and one and one-half hour laboratory session each week. (Y. Wu)

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**412. Introduction to Probability and Statistics. *** Prior
or concurrent enrollment in Math. 215 and CS 183. No credit granted
to those who have completed or are enrolled in Stat. 311 or 405.
One credit granted to those who have completed Stat. 402. (3).
(MSA). (BS).
*The objectives of this
course are to introduce students to the basic ideas of probability
and statistical inference and to acquaint students with some important
data analytic techniques, such as regression and the analysis
of variance. Examples will emphasize applications to the natural
sciences and engineering. There will be regular homework, two
midterms, and a final exam. Cost:2
WL:3 (Muirhead)

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**414. Topics in Applied Statistics. *** Stat 413 or 403; prior or concurrent
enrollment in 426; and permission of instructor. (4). (Excl).
(BS).
*Topics in applied statistics, including random and mixed effects ANOVA models, analysis of covariance
and repeated measure designs, ridge regression, splines, logit-probit
analysis, log-linear models, topics in multivariate analysis (MANOVA, discriminant analysis, profile analysis) topics in time series
analysis, and basics of survival analysis. Cost:2
WL:3 (Berube)

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**425/Math. 425. Introduction to Probability.
*** Math. 215, 255, or 285. (3). (MSA). (BS).
Sections 001 and 002. *
See Mathematics 425.

* Sections 003 and 004. * Sample spaces and axiomatic probability;
elementary combinatorics; conditional probability and independence;
random variables; probability distributions, including binomial, Poisson, Gamma, and normal; expectation, mean, and variance; moment
generating functions; the law of large numbers; central limit theorem. Cost:2
WL:3 (003:Jeganathan;
004:Murphy)

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Times, Location, and Availability

**426. Introduction to Mathematical Statistics.
*** Stat. 425. (3).
(MSA). (BS).
*This course covers the
basic ideas of statistical inference, including sampling distributions, estimation, confidence intervals, hypothesis testing, regression, analysis of variance, nonparametric testing, and Bayesian inference.
The sequence of Statistics 425/426 serves as a prerequisite for
more advanced Statistics courses. Weekly problem sets, two hourly
exams, and one final exam. Cost:2
or 3 WL:3 (Jeganathan)

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**466/IOE 466/Manufacturing 466. Statistical
Quality Control. *** Statistics
311. (3). (Excl). (BS).
*Design and analysis
of procedures for forecasting and control of production processes.
Topics include: attribute and variables sampling plans; sequential
sampling plans; rectifying control procedures; charting, smoothing, forecasting, and prediction of discrete time series. Cost:2
WL:3

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**480. Survey Sampling Techniques. *** Stat. 402. (4). (Excl). (BS).
*Motivating examples, abstraction to: populations, variables, parameters,

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**499. Honors Seminar. *** Permission of departmental Honors advisor.
(2-3). (Excl). (INDEPENDENT).
*Advanced topics, reading
and/or research in applied or theoretical statistics.

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**501. Applied Statistics II. *** Stat. 500. (3). (Excl). (BS).
*A variety of topics
in applied statistics will be covered in the course. The main
topics are survey sampling methods including: simple random sampling, stratification, cluster sampling, systematic sampling and multistage
sampling methods. Survival analysis including: hazard and survival
functions, censoring, Kaplan-Meier estimation, graphical methods
and proportional hazards models. Bootstrap and jackknife methods
and their uses. Topics in time series analysis including: autocorrelation
functions, stationarity, identification, estimation and forecasting
with ARIMA models and spectra. Non-parametric density estimation
including: kernels, cross validation, splines, and the penalized
maximum likelihood estimators. Discriminant analysis including:
linear and quadratic discriminators, relation to regression and non-parametric approaches. Cost:3
WL:3 (Faraway)

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**503. Applied Multivariate Analysis. *** Stat. 500. (3). (Excl). (BS).
*Topics in applied multivariate
analysis including Hotelling's T

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**511. Mathematical Statistics II. *** Stat. 510. (3). (Excl). (BS).
*Topics covered will
include: hypothesis testing and related topics such as size, power, similarity and optimality properties. Likelihood ratio tests, generalized likelihood ratio tests, decision theory, and Bayes
approaches. Sequential procedures, large sample theory, and various
other topics. Cost:3
WL:3 (Keener)

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**525/Math. 525. Probability Theory. *** Math. 450 or 451. Students with credit
for Math. 425/Stat. 425 can elect Math. 525/Stat. 525 for only
1 credit. (3). (Excl). (BS).
*See Mathematics
525.

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**526/Math. 526. Discrete State Stochastic
Processes. *** Math.
525, or Stat. 525, or EECS 501. (3). (Excl). (BS).
*This is a course on the theory and applications of stochastic processes, mostly on
discrete state spaces. It is a second course in probability which
should be of interest to students of mathematics and statistics
as well as students from other disciplines in which stochastic
processes have found significant applications. The material is
divided between discrete and continuous time processes. In both, a general theory is developed, and detailed study is made of some
special classes of processes and their applications. Some specific
topics include generating functions; recurrent events and the
renewal theorem; random walks; Markov chains; branching processes;
limit theorems; Markov chains in continuous time with emphasis
on birth and death processes and queuing theory; an introduction
to Brownian motion; stationary processes and martingales. This
course is similar to EECS 502 and IOE 515, although the latter
course tends to be somewhat more oriented to applications. The
next courses in probability are Math 625 and 626, which presuppose
substantial additional background (Math 597). WL:2 (Woodroofe)

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**550/SMS 576 (Business Administration)/IOE
560. Bayesian Decision Analysis. *** Stat.
425. (3). (Excl). (BS).
*Axiomatic foundations
for personal probability and utility; interpretation and assessment
of personal probability and utility; formulation of Bayesian decision
problems; risk functions, admissibility likelihood principle and properties of likelihood functions; natural conjugate prior distributions;
improper and finitely additive prior distributions; examples of
posterior distributions, including the general regression model
and contingency tables; Bayesian credible intervals and hypothesis
tests; application to a variety of decision-making situations.
There will be assigned homework exercises, a midterm, and a final
exam. Cost:3
WL:3 (Hill)

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**560/Biostat. 685 (Public Health). Introduction
to Nonparametric Statistics. *** Stat.
426. (3). (Excl). (BS).
*Order statistics and confidence intervals for quantiles; rank tests for the 1, 2, and k-sample problems; asymptotic distributions of rank statistics;
asymptotic efficiency; randomization as a basis for inference;
permutation tests; the sample distribution function and goodness
of fit tests. Cost:4
WL:3

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**576/Econ. 776. Econometric Theory II.
*** Stat. 575. (3).
(Excl). (BS).
*This course is the second
course of the econometric theory sequence. It rigorously examines
(a) the properties of the quasi-maximum likelihood and generalized
method-of-moment estimators and (b) statistical inference based
on them. Economics 673, 674, and Statistics 575, or their equivalents
are prerequisites for this course. Cost:3
WL:4 (Sakata)

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