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

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. 6/222.

Generalized Bayesian Model Selection for Speckle on Remote Sensing Images

“…The recently proposed "trans-space" RJMCMC in [21] lets us to explore different generic model classes instead of focusing on the parameter dimension. Defining transitions over a "common feature" such as moment of different model spaces in the trans-space approach is a mandatory choice for the algorithm not to start the search from the scratch in the jumped model space.…”

“…Defining transitions over a "common feature" such as moment of different model spaces in the trans-space approach is a mandatory choice for the algorithm not to start the search from the scratch in the jumped model space. The approach in [21] utilizes fractional lower ordered moments (FLOMs) as common feature and perform transitions between spaces of different probability distribution families, namely impulsive distributions. In this paper, a trans-space RJMCMC approach with first order negative moment-based transitions which explores spaces of envelope (or amplitude) distribution families, has been used.…”

“…Two different switch moves are defined and utilized for RJMCMC transitions, which are within the same family and between different families. These two different switch moves [21] are named as intra-class-switch and inter-class-switch. Intra-class-switch move is performed within the same family (k = k) whereas the inter-class-switch move performs switching to a different family (k = k).…”

“…In our recent study [21], we have proposed a generalized framework, trans-space RJMCMC, in order to explore different classes of models where moment-based RJMCMC transitions enable the transfer of the information learned in the most recent model class to another and that interpretation donated RJMCMC with the capability of choosing the most suitable model among different (one-dimensional) impulsive distribution families. The methodology proposed in [21] is highly flexible and can be adjusted to various applications by utilizing different types of moments, such as fractional lower orders, negative orders. In this study, we propose utilizing this methodology (trans-space RJMCMC [21]) in generalized model class selection for remote sensing images of SAR and US.…”

“…The methodology proposed in [21] is highly flexible and can be adjusted to various applications by utilizing different types of moments, such as fractional lower orders, negative orders. In this study, we propose utilizing this methodology (trans-space RJMCMC [21]) in generalized model class selection for remote sensing images of SAR and US. This study is dealing with modelling of the amplitudes of the bivariate distributions, i.e.…”