Sampling for conditional inference on contingency tables, multigraphs, and high dimensional tables

We propose new sequential importance sampling methods for sampling contingency tables with fixed margins, loopless, undirected multigraphs, and high-dimensional tables. In each case, the proposals for the method are constructed by leveraging approximations to the total number of structures (tables, multigraphs, or high-dimensional tables), based on results in the literature. The methods generate structures that are very close to the target uniform distribution. Along with their importance weights, the data structures are used to approximate the null distribution of test statistics. In the case of contingency tables, we apply the methods to a number of applications and demonstrate an improvement over competing methods. For loopless, undirected multigraphs, we apply the method to ecological and security problems, and demonstrate excellent performance. In the case of high-dimensional tables, we apply the sequential importance sampling method to the analysis of multimarker linkage disequilibrium data and also demonstrate excellent performance.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2016

Author dc:creator

• Eisinger, Robert David

Contributors dc:contributor

• Chen, Yuguo
• Culpepper, Steven A.
• Marden, John I.
• Simpson, Douglas G.

• Monte Carlo method
• Sequential importance sampling
• Counting problem
• Contingency Table

Statement dc:rights

• Copyright 2016 Robert Eisinger

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/92928

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/92928