Algebraic statistics for random graph models: Markov bases and their uses
author: Alessandro Rinaldo, Carnegie Mellon University
author: Sonja Petrović, University of Illinois at Chicago
published: Dec. 20, 2008, recorded: December 2008, views: 8016
Slides
Related content
Report a problem or upload files
If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Description
We use algebraic geometry to study a statistical model for the analysis of networks represented by graphs with directed edges due to Holland and Leinhardt, known as p1, which allows for differential attraction (popularity) and expansiveness, as well as an additional effect due to reciprocation. In particular, we attempt to derive Markov bases for p1 and to link these to the results on Markov bases for working with log-linear models for contingency tables. Because of the contingency table representation for p1 we expect some form of congruence. Markov bases and related algebraic geometry notions are useful for at least two statistical problems: (i) determining condition for the existence of maximum likelihood estimates, and (ii) using them to traverse conditional (given minimal sufficient statistics) sample spaces, and thus generating ``exact'' distributions useful for assessing goodness of fit. We outline some of these potential uses for the algebraic representation of p1.
Link this page
Would you like to put a link to this lecture on your homepage?Go ahead! Copy the HTML snippet !
Write your own review or comment: