  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.
