On the posterior property of the Rician distribution

TL;DR

This paper develops an objective Bayesian inference framework for the Rician distribution, deriving priors, analyzing posterior properties, and demonstrating the effectiveness of Bayesian estimators over classical methods through extensive simulations.

Contribution

It introduces a Bayesian approach with Jeffreys prior for the Rician distribution, analyzing posterior propriety and comparing estimation methods.

Findings

Jeffreys prior yields a proper posterior.

Bayesian estimators are nearly unbiased.

Outperforms classical moment and MLE methods.

Abstract

The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process data. In this paper, we introduce objective Bayesian inference for the Rician distribution parameters, specifically the Jeffreys rule and Jeffreys prior are derived. We proved that the obtained posterior for the first priors led to an improper posterior while the Jeffreys prior led to a proper distribution. To evaluate the effectiveness of our proposed Bayesian estimation method, we perform extensive numerical simulations and compare the results with those obtained from traditional moment-based and maximum likelihood estimators. Our simulations illustrate that the Bayesian estimators derived from the Jeffreys prior provide nearly unbiased estimates, showcasing the advantages of our approach over classical techniques. Additionally, our framework incorporates the S.A.F.E. principles-Sustainable, Accurate, Fair, and Explainable-ensuring robustness, fairness, and transparency in predictive modeling.