Bayesian semi-parametric approaches to normal/independent and elliptical distributions

Area of Science:

• Statistics
• Bayesian Inference
• Machine Learning

Background:

• Elliptical and normal/independent distributions are common in statistical modeling.
• Existing methods may face challenges with identifiability and model selection.
• There is a need for robust inferential techniques for these distributions.

Purpose of the Study:

• Introduce a novel Bayesian semi-parametric approach for inference in elliptical and normal/independent distributions.
• Address the partial lack of identifiability in these models.
• Develop a new model selection technique for discriminating between distribution types.

Main Methods:

• Parametric modeling of location and scale parameters.
• Dirichlet process mixtures for transformed modular variables.
• Incorporation of restrictions on scale matrix diagonal elements to handle identifiability.
• Markov chain Monte Carlo (MCMC) for posterior computation.
• Approximation of the deviation information criterion for model selection.

Main Results:

• The proposed Bayesian approach effectively handles identifiability issues.
• The novel model selection criterion successfully discriminates between elliptical and normal/independent distributions.
• The methodology is validated through simulation studies and real-world data analysis.

Conclusions:

• The developed Bayesian semi-parametric method offers a robust framework for inference with elliptical and normal/independent distributions.
• The new model selection technique enhances the ability to choose appropriate models.
• The approach demonstrates practical applicability in statistical analysis.