The Order of Degeneracy of Markov Chain Monte Carlo Method

Sometimes Markov chain Monte Carlo (MCMC) procedures work poorly. The identification of this inefficiency is important, but appropriate theoretical tools have not been investigated adequately. For this purpose, we propose the order of degeneracy, which measures the mixing property of an MCMC procedure. As an application, we consider major three sources of inefficiency, one being the fragility of the identification of parameters. We present a numerical simulation to show the effect of each source of inefficiency.