The Bayesian Inference of Pareto Models Based on Information Geometry

Area of Science:

• Statistics
• Probability Theory
• Data Analysis

Background:

• Bayesian methods are crucial for understanding causality in practical applications.
• Pareto models are frequently used for analyzing phenomena like sea clutter.
• Geometric approaches offer novel perspectives in statistical inference.

Purpose of the Study:

• To develop geometric Bayesian inference methods for two-parameter Pareto models.
• To apply these methods to the analysis of sea clutter data.
• To introduce new Bayesian estimation techniques using geodesic and Al-Bayyati's loss functions.

Main Methods:

• Geometric inference applied to Pareto distribution.
• Utilizing Jeffreys prior due to the non-existence of alpha-parallel priors.
• Employing geodesic distance and Al-Bayyati's loss functions for estimation.
• Simulation studies for parameter estimation and posterior prediction.

Main Results:

• Demonstrated the non-existence of alpha-parallel priors for Pareto models.
• Obtained Bayesian estimations based on minimal mean geodesic distance.
• Introduced a new class of Bayesian estimations using Al-Bayyati's loss function.
• Showcased the effectiveness of proposed Bayesian estimations and posterior predictions for sea clutter.

Conclusions:

• Geometric Bayesian inference provides effective tools for Pareto model analysis.
• The proposed methods offer advantages in parameter estimation and prediction for sea clutter.
• This work extends Bayesian inference techniques with novel loss functions and geometric approaches.