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Spectral Estimation using Reversible Jump Markov Chain Monte Carlo

Published in in preparation, 2022

The present work serves as a stepping stone to the task of rational spectral approximation given signal observations. Rational approximations can be preferred over the common Laurent polynomial approximation since they often can achieve great accuracy with much fewer parameters. The task of Rational approximation is essentially that of ARMA fitting. And the hope of this work is to provide guidance for solving that problem by first considering AR fitting by reversible jump Markov chain Monte Carlo over the space of poles and error variance, which things determine the centered AR process. In a sense this is a proof of concept or trial run to understand the problem well enough to better determine whether the full ARMA problem is worthwhile.