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A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types

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Marginally specified priors for non-parametric Bayesian estimation.

David C Kessler¹, Peter D Hoff², David B Dunson³

¹University of North Carolina, Chapel Hill, USA.

Journal of the Royal Statistical Society. Series B, Statistical Methodology

|February 10, 2015

Summary

This summary is machine-generated.

This study introduces a new Bayesian inference framework for complex parameters. It simplifies prior specification by separating information about parameter functions from the parameter itself, improving model usability.

Keywords:

Contingency tables Density estimation Dirichlet process mixture model Multivariate unordered categorical data Non-informative prior Prior elicitation Sparse data

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Area of Science:

Statistics
Computational Statistics
Bayesian Inference

Background:

Specifying priors for high-dimensional parameters in non-parametric Bayesian inference is challenging.
Statisticians often have more information about parameter functionals (e.g., mean, variance) than the entire parameter.
Existing methods may lack flexibility or be computationally intensive.

Purpose of the Study:

To propose a novel framework for non-parametric Bayesian inference with improved prior specification.
To develop priors that are easily constructed and leverage existing non-parametric distributions.
To facilitate posterior approximation using established computational techniques.

Main Methods:

Decomposing the prior distribution into an informative part on parameter functionals and a conditional non-parametric part.
Constructing these priors from standard non-parametric distributions.
Adapting existing Markov chain approximation algorithms for posterior inference.

Main Results:

The proposed priors are easily constructed and retain the broad support of standard non-parametric priors.
Posterior approximations can be achieved with minor modifications to existing algorithms.
The framework is demonstrated effective in multivariate density estimation and high-dimensional sparse contingency table modeling.

Conclusions:

The new framework simplifies prior specification in non-parametric Bayesian inference for high-dimensional parameters.
It offers a practical approach for incorporating prior knowledge through parameter functionals.
The method is computationally feasible and broadly applicable in statistical modeling.