University of Illinois Urbana-Champaign

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

Eisinger, Robert David

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

Description

Title
Sampling for conditional inference on contingency tables, multigraphs, and high dimensional tables
Author(s)
Eisinger, Robert David
Issue Date
2016-07-08
Director of Research (if dissertation) or Advisor (if thesis)
Chen, Yuguo
Doctoral Committee Chair(s)
Chen, Yuguo
Committee Member(s)
  • Culpepper, Steven A.
  • Marden, John I.
  • Simpson, Douglas G.
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
Graduation Semester
2016-08
Type of Resource
text
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http://hdl.handle.net/2142/92928
Copyright and License Information
Copyright 2016 Robert Eisinger

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