Courses
AMS 507 Introduction to Probability
The topics include sample spaces, axioms of probability, conditional probability and
independence, discrete and continuous random variables, jointly distributed random
variables, characteristics of random variables, law of large numbers and central limit
theorem, Markov chains. Note: Crosslisted with HPH 696.
Fall, 3 credits, ABCF grading
AMS 507 webpage
AMS 569 Probability Theory I
Probability spaces and sigma-algebras. Random variables as measurable mappings. Borel-Cantelli
lemmas. Expectation using simple functions. Monotone and dominated convergence theorems.
Inequalities. Stochastic convergence. Characteristic functions. Laws of large numbers
and the central limit theorem. This course is offered as both AMS 569 and MBA 569.
Prerequisite: AMS 504 or equivalent
AMS 569 webpage
3 credits, ABCF grading
AMS 570 Introduction to Mathematical Statistics
Probability and distributions; multivariate distributions; distributions of functions
of random variables; sampling distributions; limiting distributions; point estimation;
confidence intervals; sufficient statistics; Bayesian estimation; maximum likelihood
estimation; statistical tests.
Prerequisite: AMS 507
Spring, 3 credits, ABCF grading
AMS 570 webpage
AMS 571 Mathematical Statistics
Sampling distribution; convergence concepts; classes of statistical models; sufficient
statistics; likelihood principle; point estimation; Bayes estimators; consistency;
Neyman-Pearson Lemma; UMP tests; UMPU tests; Likelihood ratio tests; large sample
theory.
Prerequisite: AMS 570 is preferred but not required
Fall, 3 credits, ABCF grading
AMS 571 webpage
AMS 572 Data Analysis I
Introduction to basic statistical procedures. Survey of elementary statistical procedures
such as the t-test and chi-square test. Procedures to verify that assumptions are
satisfied. Extensions of simple procedures to more complex situations and introduction
to one-way analysis of variance. Basic exploratory data analysis procedures (stem
and leaf plots, straightening regression lines, and techniques to establish equal
variance). Coscheduled as AMS 572 or HPH 698.
Fall, 3 credits, ABCF grading
AMS 572 webpage
AMS 573 Design and Analysis of Categorical Data
Measuring the strength of association between pairs of categorical variables. Methods
for evaluating classification procedures and inter-rater agreement. Analysis of the
associations among three or more categorical variables using log linear models. Logistic
regression.
Spring, 3 credits, ABCF grading
AMS 573 webpage
AMS 575 Internship in Statistical Consulting
Directed quantitative research problem in conjunction with currently existing research
programs outside the department. Students specializing in a particular area work on
a problem from that area; others work on problems related to their interests, if possible.
Efficient and effective use of computers. Each student gives at least one informal
lecture to his or her colleagues on a research problem and its statistical aspects.
Prerequisite: Permission of instructor
Fall and Spring, 3-4 credits, ABCF grading
AMS 575 webpage
AMS 577 Multivariate Analysis
The multivariate distribution. Estimation of the mean vector and covariance matrix
of the multivariate normal. Discriminant analysis. Canonical correlation. Principal
components. Factor analysis. Cluster analysis.
Prerequisites: AMS 572 and AMS 578
3 credits, ABCF grading
AMS 577 webpage
AMS 580 Statistical Learning
This course teaches the following fundamental topics: (1) General and Generalized
Linear Models; (2) Basics of Multivariate Statistical Analysis including dimension
reduction methods, and multivariate regression analysis; (3) Supervised and unsupervised
statistical learning.
Spring, 3 credits, ABCF grading
AMS 580 Webpage
AMS 582 Design of Experiments
Discussion of the accuracy of experiments, partitioning sums of squares, randomized
designs, factorial experiments, Latin squares, confounding and fractional replication,
response surface experiments, and incomplete block designs. Coscheduled as AMS 582
or HPH 699. Prerequisite: AMS 572 or equivalent
Fall, 3 credits, ABCF grading
AMS 582 webpage
AMS 585 Internship in Data Science
Directed data science problem in conjunction with currently existing research programs
outside the department. Students specializing in a particular area work on a problem
from that area; others work on problems related to their interests, if possible. Efficient
and effective use of computers. Each student gives at least one informal lecture to
his or her colleagues on a research problem and its statistical aspects.
3 credits, ABCF grading
AMS 585 Webpage
AMS 586 Time Series
Analysis in the frequency domain. Periodograms, approximate tests, relation to regression
theory. Pre-whitening and digital fibers. Common data windows. Fast Fourier transforms.
Complex demodulation, GibbsÕ phenomenon issues. Time-domain analysis.
Prerequisites: AMS 507 and AMS 570
Fall, 3 credits, ABCF grading
AMS 586 webpage
AMS 587 Nonparametric Statistics
This course covers the applied nonparametric statistical procedures: one-sample Wilcoxon
tests, two-sample Wilcoxon tests, runs test, Kruskal-Wallis test, KendallÕs tau, SpearmanÕs
rho, Hodges-Lehman estimation, Friedman analysis of variance on ranks. The course
gives the theoretical underpinnings to these procedures, showing how existing techniques
may be extended and new techniques developed. An excursion into the new problems of
multivariate nonparametric inference is made.
3 credits, ABCF grading
AMS 587 webpage
AMS 588 Failure and Survival Data Analysis
Statistical techniques for planning and analyzing medical studies. Planning and conducting
clinical trials and retrospective and prospective epidemiological studies. Analysis
of survival times including singly censored and doubly censored data. Quantitative
and quantal bioassays, two-stage assays, routine bioassays. Quality control for medical
studies.
3 credits, ABCF grading
AMS 588 Webpage
AMS 598 Big Data Analysis
Introduction to the application of the supercomputing for statistical data analyses,
particularly on big data.
Prerequisites: AMS 572, AMS 573 and AMS 578
Fall, 3 credits, ABCF grading
AMS 598 Webpage