STA 214: Probability and Statistical Models

Applied probability models and uses in statistical analysis. The generation of random variables with specified distributions, and their use in simulation. Elements of applied stochastic processes; random walks, Markov chains, and stationary and ARMA process. Mixture models; linear regression models; queueing models. Additional classes of multivariate distributions and distribution theory. This course covers a range of applied models and methods with illustrative contexts, introducing students to many different application areas as well as more advanced probabilistic. Prerequisites: Math 103 and 104, and STA 213 or equivalent.

Duke University
Spring 1999
TTh, 9:10AM- 10:25
in Old Chemistry,
Room 025

Instructor: Brani Vidakovic

Office: 223 B Old Chemistry Building

Office Hours: By Appointment

Phone: 684-8025

Email: brani@stat.duke.edu

Instructor:	Brani Vidakovic
	Office: 223 B Old Chemistry Building
	Office Hours: By Appointment
	Phone: 684-8025
	Email: brani@stat.duke.edu

Teaching Assistant:

Name Email Phone Office Hours Office Location

Courtney Johnson courtney@stat.duke.edu 684-8840 by appointment 222 Old Chem

Name	Email	Phone	Office Hours	Office Location
Courtney Johnson	courtney@stat.duke.edu	684-8840	by appointment	222 Old Chem

Text: An Introduction to Stochastic Modeling, 3rd Edition. Taylor and Karlin

Groups: Students are encouraged to form small (up to 2-3 people) learning/working groups. Projects will be group assignments.

Class Project: Each group will work on one research project. Details on the format of projects - in class.

Homework: Homeworks will be weekly/biweekly assignments.

Exam: One [late March, early April] midterm exam. The exam will be open book, open notes.

Grading: Course grade is based on midterm (35%), homeworks (30%), in class presentation (15%), research project (20%)

Tentative Outline Syllabus:

Intro.

Review of Probability, Conditional Probability, Conditional Expectation. Simple Simulations. Martingales. Applications.

Markov Chains. Examples. Transition Matrices. First Step Analysis. Random Walks. Branching Processes. Limit Theorems for Markov Chains.

Poisson Precesses. Definition. Spatial Poisson Processes.

Continuous Time Markov Chains. Birth and Death Processes.

Renewal Processes and Queuening Systems.

Brownian Motion. Related Processes.

Statistical Models.

Time Series.

Multiscale Models. Wavelets. Function Estimation, Selfsimilarity and Long-Range Dependence.

Please send comments to brani@stat.duke.edu