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Semiparametric mixed-scale models using shared Bayesian forests.

Antonio R Linero1, Debajyoti Sinha1, Stuart R Lipsitz2

  • 1Department of Statistics, Florida State University, Tallahassee, Florida.

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Summary
This summary is machine-generated.

Sharing information across nonparametric regression model components improves accuracy, especially in complex, high-dimensional datasets. This Bayesian sum-of-tree approach enhances variable selection and analysis of medical expenditure data.

Keywords:
Bayesian additive regression treesheteroskedastic errorshurdle modelsnonparametric Bayesvariable selection

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Area of Science:

  • Statistics
  • Machine Learning
  • Econometrics

Background:

  • Nonparametric regression models often analyze complex data structures independently.
  • Sharing information across related model components can improve estimation and variable selection.
  • Existing methods may not fully leverage shared covariate information in high-dimensional settings.

Purpose of the Study:

  • To present a methodology for nonparametric information sharing across multiple regression model components.
  • To demonstrate the benefits of this information sharing, particularly in sparse, high-dimensional problems.
  • To apply the methodology to analyze medical expenditure data.

Main Methods:

  • Utilizing Bayesian sum-of-tree models to enable nonparametric information sharing.
  • Developing novel Bayesian additive regression trees (BART) models for specific data types.
  • Implementing a heteroskedastic log-normal hurdle model with a novel prior and a gamma hurdle model.

Main Results:

  • Simulation results confirm significant benefits from sharing information across related model components.
  • The proposed methodology proves particularly effective in sparse, high-dimensional scenarios requiring variable selection.
  • The analysis of Medical Expenditure Panel Survey (MEPS) data showcases practical application.

Conclusions:

  • Nonparametric information sharing across model components is advantageous in various regression settings.
  • Bayesian sum-of-tree models provide a flexible framework for implementing such sharing.
  • The developed models offer effective tools for analyzing complex health economics data.