Geometric Sensitivity Measures for Bayesian Nonparametric Density Estimation Models

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.