Beyond trans-dimensional RJMCMC with a case study in impulsive data modeling

TL;DR

This paper introduces trans-space RJMCMC, a novel extension of RJMCMC that explores different model classes, demonstrated through impulsive data modeling to select appropriate noise distribution families in complex real-world signals.

Contribution

It proposes trans-space RJMCMC, expanding the original method to explore diverse model spaces, with a case study on impulsive noise modeling in real and synthetic data.

Findings

Effective in selecting suitable impulsive distribution models

Successfully applied to real-world PLC impulsive noise data

Demonstrates flexibility in modeling non-Gaussian noise processes

Abstract

Reversible jump Markov chain Monte Carlo (RJMCMC) is a Bayesian model estimation method which has been used for trans-dimensional sampling. In this study, we propose utilization of RJMCMC beyond trans-dimensional sampling. This new interpretation, which we call trans-space RJMCMC, reveals the undiscovered potential of RJMCMC by exploiting the original formulation to explore spaces of different classes or structures. This provides flexibility in using different types of candidate classes in the combined model space such as spaces of linear and nonlinear models or of various distribution families. As an application for the proposed method, we have performed a special case of trans-space sampling, namely trans-distributional RJMCMC in impulsive data modeling. In many areas such as seismology, radar, image, using Gaussian models is a common practice due to analytical ease. However, many noise processes do not follow a Gaussian character and generally exhibit events too impulsive to be successfully described by the Gaussian model. We test the proposed method to choose between various impulsive distribution families to model both synthetically generated noise processes and real-life measurements on power line communications (PLC) impulsive noises and 2-D discrete wavelet transform (2-D DWT) coefficients.