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Geometric Sensitivity Measures for Bayesian Nonparametric Density Estimation Models.

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  • 1Department of Statistics, The Ohio State University.

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Summary
This summary is machine-generated.

This study introduces a novel geometric framework for analyzing global sensitivity in Bayesian nonparametric density estimation models. The approach quantifies how parameter changes affect model outputs using Riemannian geometry, enhancing model reliability.

Keywords:
Bayesian nonparametric density estimationDirichlet processDirichlet process Gaussian mixture modelFisher–Rao metricGlobal sensitivity analysisSquare-root density

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Area of Science:

  • Statistics
  • Computational Statistics
  • Bayesian Inference

Background:

  • Bayesian nonparametric models are powerful for density estimation.
  • Assessing model sensitivity to parameter choices is crucial for reliable inference.
  • Existing sensitivity analysis methods may not fully capture complex model behaviors.

Purpose of the Study:

  • To develop a geometric framework for global sensitivity analysis in Bayesian nonparametric density estimation.
  • To quantify the impact of parameter and hyperparameter perturbations on posterior distributions.
  • To provide robust tools for evaluating the stability of Bayesian density estimation models.

Main Methods:

  • Proposing a geometric framework utilizing the Fisher-Rao Riemannian metric on the space of densities.
  • Defining three sensitivity measures based on geodesic distances and variances of posterior samples.
  • Applying the framework to Dirichlet-type priors in Bayesian density estimation.

Main Results:

  • The proposed geometric framework effectively quantifies global sensitivity in Bayesian nonparametric density estimation.
  • The three defined sensitivity measures provide distinct insights into parameter and hyperparameter influences.
  • The methodology demonstrates robustness across simulation studies and real-world datasets.

Conclusions:

  • The geometric approach offers a principled way to assess global sensitivity in complex Bayesian models.
  • This framework enhances the understanding and trustworthiness of Bayesian density estimation.
  • The methods are validated and applicable to practical data analysis scenarios.