## 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 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 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 Biostatistics **

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