Estimating the granularity coefficient of a Potts-Markov random field within a Markov chain Monte Carlo algorithm

Area of Science:

• Computational Statistics
• Image Analysis
• Bayesian Inference

Background:

• Estimating the Potts parameter β jointly with other Bayesian model parameters is challenging.
• Standard Markov chain Monte Carlo (MCMC) methods are unsuitable due to the intractable normalizing constant of the Potts model.
• Accurate estimation of β is crucial for reliable Bayesian model performance.

Purpose of the Study:

• To develop a novel MCMC algorithm for joint estimation of the Potts parameter β and other Bayesian model parameters.
• To address the computational intractability of the Potts model's normalizing constant.
• To validate the proposed method's performance using synthetic and real-world image data.

Main Methods:

• A likelihood-free Metropolis-Hastings algorithm is employed for estimating the Potts parameter β.
• The proposed MCMC method integrates β estimation within the broader Bayesian inference framework.
• The algorithm's efficacy is tested on synthetic datasets for parameter estimation accuracy.

Main Results:

• Joint estimation of β with other parameters yields results comparable to using the true β value.
• Incorrect β values significantly degrade estimation performance, highlighting the method's sensitivity.
• The algorithm is successfully applied to bidimensional Synthetic Aperture Radar (SAR) and tridimensional ultrasound images.

Conclusions:

• The proposed likelihood-free MCMC method effectively estimates the Potts parameter β jointly with other model parameters.
• Accurate estimation of β is vital for optimal performance of Bayesian models in image analysis.
• The method demonstrates practical applicability in analyzing complex biomedical and remote sensing imagery.