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GENERALIZED DOUBLE PARETO SHRINKAGE.

Artin Armagan1, David B Dunson2, Jaeyong Lee3

  • 1SAS Institute Inc., Durham, NC 27513, USA, artin.armagan@sas.com.

Statistica Sinica
|January 31, 2014
PubMed
Summary
This summary is machine-generated.

We introduce a flexible double Pareto prior for Bayesian linear model estimation. This new prior offers improved sparse estimation by combining desirable properties of existing priors, validated through simulations and real-world data.

Keywords:
Heavy tailsLASSOhigh-dimensional datamaximum a posteriori estimationrelevance vector machinerobust priorshrinkage estimation

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Area of Science:

  • Statistics
  • Machine Learning
  • Econometrics

Background:

  • Bayesian inference is crucial for statistical modeling.
  • Shrinkage estimation methods are vital for parsimonious models.
  • Existing priors like Laplace and Normal-Jeffreys have limitations.

Purpose of the Study:

  • To propose a generalized double Pareto prior for Bayesian linear models.
  • To offer a flexible prior that bridges Laplace and Normal-Jeffreys priors.
  • To enhance sparse estimation and inference in linear models.

Main Methods:

  • Developed a generalized double Pareto prior using scale mixtures of Laplace or normal distributions.
  • Employed a Gibbs sampling algorithm for straightforward Bayesian computation.
  • Investigated properties of the maximum a posteriori (MAP) estimator.

Main Results:

  • The proposed prior exhibits a spike at zero and Student's t-like tail behavior.
  • Established connections between the new prior and established regularization techniques.
  • Demonstrated asymptotic results for the MAP estimator.

Conclusions:

  • The generalized double Pareto prior provides a robust framework for Bayesian shrinkage estimation.
  • The method is computationally efficient and performs well in simulations and applications.
  • This prior enhances sparse estimation in linear models, offering a valuable tool for researchers.