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Title:Sampling for conditional inference on contingency tables, multigraphs, and high dimensional tables
Author(s):Eisinger, Robert David
Director of Research:Chen, Yuguo
Doctoral Committee Chair(s):Chen, Yuguo
Doctoral Committee Member(s):Culpepper, Steven A; Marden, John I; Simpson, Douglas G
Department / Program:Statistics
Discipline:Statistics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Monte Carlo method
Sequential importance sampling
Counting problem
Contingency Table
Abstract: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.
Issue Date:2016-07-08
Type:Thesis
URI:http://hdl.handle.net/2142/92928
Rights Information:Copyright 2016 Robert Eisinger
Date Available in IDEALS:2016-11-10
Date Deposited:2016-08


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