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Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
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Bayes multiple decision functions.

Wensong Wu1, Edsel A Peña2

  • 1Division of Statistics, Department of Mathematics and Statistics, Florida International University, Miami, Florida 33199.

Electronic Journal of Statistics
|November 22, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces a Bayesian approach for making multiple binary decisions from complex data, optimizing gene selection and other applications using a novel dependent data structure. It ensures accurate decision-making by controlling false discovery rates.

Keywords:
Archimedean copulaBayesian frameworkdecision theoretic frameworkfalse discovery ratefrailtymultiple testingsequential Monte Carlo

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Area of Science:

  • Decision Theory
  • Statistical Inference
  • Bioinformatics

Background:

  • Simultaneously making numerous binary decisions from large datasets is a common challenge in fields like genomics and reliability.
  • Existing methods often assume data independence, which may not reflect real-world complexities.

Purpose of the Study:

  • To develop a Bayesian decision-theoretic framework for multiple binary decisions.
  • To incorporate dependent data structures using frailty-induced Archimedean copulas.
  • To derive an efficient algorithm for optimal Bayes action and assess decision quality using false discovery rates.

Main Methods:

  • Bayesian decision theory with a cost-weighted loss function.
  • Frailty-induced Archimedean copulas for modeling dependent data structures.
  • Sequential Monte Carlo techniques for numerical implementation.

Main Results:

  • Derivation of the Bayes multiple decision function (BMDF).
  • Development of an efficient algorithm for optimal Bayes action.
  • Demonstrated applicability to simple and composite hypotheses, and a colon cancer microarray dataset.

Conclusions:

  • The proposed Bayesian approach effectively handles multiple binary decisions with dependent data.
  • The method offers flexibility in loss function specification, including false discovery rates.
  • The framework is extendable to multiple hypotheses testing, classification, and variable selection.