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; 003: Gunderson)
Check
Times, Location, and Availability
125. Games, Gambling and Coincidences. (3). (MSA). (QR/1).
This course will emphasize problem solving and modeling. To
achieve this end, students will work together in class attempting
to solve various problems posed by the instructor. Hopefully with
a bit of gentle guidance, the students will be able to create
models and deduce the basic concepts necessary for solution. Students
will be asked to write up solutions and work on a project. Grades
will be determined from this work and class participation. Problems
from the course will be drawn primarily from Markov chains with
a finite state space, dynamic programming, again with a finite
state space, and game theory. Possible examples include: gambler's
ruin; expected run lengths in coin tossing until a specified string
is obtained and chances that one string will occur before another;
optimal strategies in sports and gambling; optimal replacement
strategies; minimax solutions for finite state two-person zero
sum games. Cost:2
WL:3 (Keener)
Check
Times, Location, and Availability
311/IOE 365. Engineering Statistics. Engin. 103, 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. (Majeske)
Check
Times, Location, and Availability
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
(001: Muirhead, 002: Rothman, 003: Meyer, 004: Gunderson)
Check
Times, Location, and Availability
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).
See Economics 405. (Sakata)
Check
Times, Location, and Availability
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 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
(Y. Wu)
Check
Times, Location, and Availability
413. The General Linear Model and Its Applications. Stat. 402 and Math. 217; concurrent enrollment in Stat. 425. Students who have not taken Math. 217 should elect Stat. 403. Two credits granted to those who have completed Stat. 403. (4). (Excl). (BS).
Some motivating real examples – regression, ANOVA, time series
– abstraction into a common model; statement of the model and assumptions; description of the design matrix including dummy
variables; discussion of the error vector and assumptions regarding those errors; geometry of the GLM, including projections, Pythagorus, least squares estimation, residuals, predicted values, Gauss-Markov
result, etc.; normal distribution theory results; confidence
and predictive intervals, F and t tests, the extra sum of squares
principle; multiple and partial correlations with geometry; checking
for violations of the assumptions, normal probability plots, outliers, influence functions, problems of multicollinearity or near collinearity;
cures for violations, transforms, weighting, etc. Multiple
regression applications; choice of independent variables, principal
components, all possible regressions, stepwise procedures, use
of data subsamples (validation); polynomial regression, orthogonal
polynomials. Use of dummy variables and ANOVA applications, fixed
effect completely crossed ANOVA cases, balanced versus unbalanced
designs, contrasts, interactions, multiple inference procedures
including at least Scheffe, studentized range and Bonferroni;
nested designs, etc. Time series applications, use of
polynomial regression, deseasonalization, leads, lags and autoregressive
models, serial correlation, Durbin-Watson test, ARIMA models, etc. Real applications will be stressed. There will be
weekly assignments and a final exam. Class format is three hours
of lecture and 1.5 hours of laboratory per week. Note: This course
is designed primarily for Statistics Undergraduate Concentrators;
other students, without the Mathematics 217 prerequisite, should
elect Statistics 403. Cost:2
WL:3 (Chen)
Check
Times, Location, and Availability
425/Math. 425. Introduction
to Probability. Math. 215, 255, or 285. (3). (MSA).
(BS).
Sections 001 and 002. 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 (Section 001:
Csörgö; Section 002: Muirhead)
Check
Times, Location, and Availability
Sections 003 and 004. See Mathematics
425.
Check
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 (Woodroofe)
Check
Times, Location, and Availability
466/IOE 466/Manufacturing 466. Statistical Quality Control. Statistics 311 or IOE 365. (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 (Shi)
Check
Times, Location, and Availability
470. Experimental Design. Stat. 402. (4). (Excl). (BS).
This course will introduce students to basic principles in
classical experimental design, including randomization, replication, confounding, interaction, covariates, use of the general linear
model. Students will be introduced to the following designs: completely
randomized, randomized blocks, Latin squares, incomplete blocks, factorial, split plot, Taguchi, response surface, optimal. There
will be weekly assignments and a final exam. Class format is 3
hours of lecture and 1.5 hours of laboratory per week. Cost:2
WL:3 (Hamada)
Check
Times, Location, and Availability
499. Honors Seminar. Permission of departmental Honors advisor. (2-3). (Excl). (INDEPENDENT).
Advanced topics, reading and/or research in applied or theoretical
statistics.
Check
Times, Location, and Availability
500. Applied Statistics I. Math. 417, and Stat. 402 or 426. (3). (Excl). (BS).
Review of matrices, multivariate normal and related distributions.
Regression and general least squares theory, Gauss-Markov Theorem, estimation of regression coefficients, polynomial regression, step-wise regression, residuals. ANOVA models, multiple comparisons, analysis of covariance, Latin squares, 2p factorial
designs, random and mixed-effects models. Applications and real
data analysis will be stressed, with students using a computer
to perform statistical analyses. Cost:2
WL:3 (Faraway)
Check
Times, Location, and Availability
505/Econ. 673. Econometric Analysis. Permission of instructor. (3). (Excl). (BS).
This course is designed for first-year graduate students in
economics, business, and related subjects. It involves a fairly
rigorous development of statistical reasoning and methods relating
to hypothesis testing, estimation, and regression analysis. Students
are supposed to have had a course in calculus and in introductory
statistics. Knowledge of matrix algebra is required. Evaluation
of students is based on midterm and final examinations and weekly
assignments. Students taking this course are expected to take
Economics 674 – Econometric Analysis II in the following term.
Cost:2 WL:3
(Killian)
Check
Times, Location, and Availability
506. Statistical Computing. Stat. 426 or 500, and CS 380 or 283. (3). (Excl). (BS).
Selected topics in statistical computing, including: Monte
Carlo procedures, generation of random numbers, computation of
estimators, linear and non-linear problems, resampling algorithms, splines, other special topics. Cost:2
or 3 WL:3 (Y. Wu)
Check
Times, Location, and Availability
510. Mathematical Statistics I. Math. 450 or 451, and a course in probability or statistics. (3). (Excl). (BS).
Review of probability theory including: probability, conditioning, independence, random variables, standard distributions, exponential
families, inequalities, and the central limit theorem. Introduction
to decision theory including: models, parameter spaces, decision
rules, risk functions, Bayes versus classical approaches, admissibility, minimax rules, likelihood functions and sufficiency. Estimation theory including unbiasedness, complete sufficient statistics, Lehmann-Scheffe and Rao-Blackwell theorems, and various types
of estimators. Cost:3
WL:3 (Keener)
Check
Times, Location, and Availability
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.
Check
Times, Location, and Availability
526/Math. 526. Discrete State Stochastic Processes. Math. 525, or Stat. 525, or EECS 501. (3). (Excl). (BS).
See Mathematics 526.
Check
Times, Location, and Availability
531/Econ. 677. Analysis of Time Series. Stat. 426. (3). (Excl). (BS).
Decomposition of series; trend and regression as a special
case of time series; cyclic components; smoothing techniques; the variate difference method; representations including spectogram, periodogram, etc., stochastic difference equations, autoregressive
schemes, moving averages; large sample inference and predictions;
covariance structure and spectral densities; hypothesis testing
and estimation; applications and other topics. Cost:3
WL:3 (Howrey)
Check
Times, Location, and Availability
535. Reliability. Statistics 425 and 426. (3). (Excl).
This course will cover the important reliability concepts and methodology that arise in modeling, assessing, and improving product
reliability and in analyzing field and warranty data. Topics will
be selected from the following: Basic reliability concepts; Common
parametric models for component reliability; Censoring schemes;
Analysis of time-to-failure data; Accelerated testing for reliability
assessment; Modeling and analyzing repairable systems reliability;
Analysis of warranty and field-failure data; Maintenance policies
and availability; Reliability improvement through experimentation.
Cost:2 or 3 WL:3 (Nair)
Check
Times, Location, and Availability
570. Experimental Design. Stat. 426 and a basic knowledge of matrix algebra. (3). (Excl). (BS).
Basic topics and ideas in the design of experiments: randomization
and randomization tests; the validity and analysis of randomized
experiments; randomized blocks; Latin and Graeco-Latin squares;
plot techniques; factorial experiments; the use of confounding
and response surface methodology; weighing designs, lattice and incomplete block and partially balanced incomplete block designs.
Cost:3 or 4 WL:3 (J. Wu, Hamada)
Check
Times, Location, and Availability
575/Econ. 775. Econometric Theory I. Math. 417 and 425 or Econ. 653, 654, 673, and 674. (3). (Excl). (BS).
The purpose of this course is to develop the results of asymptotic
distribution theory needed for statistical inference in econometrics
and to use these results to derive the properties of various estimators
and test procedures used in econometrics. The course is a prerequisite
for Statistics 576 (Econometric Theory II). Cost:2
or 3 WL:3 (Howrey)
Check
Times, Location, and Availability
University of Michigan | College of LS&A | Student Academic Affairs | LS&A Bulletin Index
This page maintained by LS&A Academic Information and Publications, 1228 Angell Hall
The Regents
of the University of Michigan,
Ann Arbor, MI 48109 USA +1 734 764-1817
Trademarks of the University of Michigan may not be electronically or otherwise altered or separated from this document or used for any non-University purpose.