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Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

A complete procedure for testing a claim about a population proportion is provided here.
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A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
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A Bayesian Discovery Procedure.

Michele Guindani1, Peter Müller, Song Zhang

  • 1University of New Mexico, Alberquerque, NM 87111, U.S.A.

Journal of the Royal Statistical Society. Series B, Statistical Methodology
|August 10, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a Bayesian discovery procedure (BDP) for multiple comparisons, approximating the optimal discovery procedure (ODP). The BDP enhances discovery by exploiting clustered data structures, showing improved performance in simulations and gene expression analysis.

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Area of Science:

  • Statistics
  • Bioinformatics
  • Computational Biology

Background:

  • Multiple comparison problems are prevalent in statistical analysis, requiring robust methods for accurate inference.
  • Existing procedures like the optimal discovery procedure (ODP) offer a framework for controlling false discoveries.
  • Bayesian decision theory provides a coherent approach to statistical inference and decision-making.

Purpose of the Study:

  • To develop a Bayesian discovery procedure (BDP) for multiple comparison problems.
  • To approximate and improve upon the optimal discovery procedure (ODP) using a Bayesian framework.
  • To investigate the performance of the BDP in simulation studies and real-world applications, such as differential gene expression analysis.

Main Methods:

  • Formulated a Bayesian discovery procedure based on a decision theoretic framework with a specific loss function.
  • Utilized a semi-parametric model to approximate the Bayes rule with the optimal discovery procedure (ODP).
  • Developed an improved Bayesian discovery procedure (BDP) by incorporating multiple shrinkage in clusters from a nonparametric model.
  • Applied the BDP and ODP to simulated data and microarray data for differential gene expression analysis.
  • Extended the ODP framework by modifying the loss function to yield different thresholding statistics.
  • Applied the methods to dependent (spatial) data.

Main Results:

  • The Bayes rule under the specified loss function is based on a posterior probability threshold.
  • The optimal discovery procedure (ODP) serves as an approximation to the Bayes rule under a semi-parametric model.
  • The proposed Bayesian discovery procedure (BDP) improves upon the ODP by exploiting clustered data structures.
  • Comparative analysis showed comparable or improved performance of BDP over ODP in simulations and gene expression data.
  • Modifications to the loss function allow for flexible thresholding statistics.
  • The framework is applicable to dependent spatial data.

Conclusions:

  • The Bayesian discovery procedure (BDP) offers a principled and effective approach to multiple comparison problems.
  • The BDP provides an improvement over the ODP, particularly in the presence of clustered data structures.
  • The developed methods are versatile and applicable to various data types, including spatial data.