Every reversible Markov chain defines an operator whose spectrum encodes the
convergence properties of the chain. When the state space is finite, the
spectrum is just the set of eigenvalues of the corresponding Markov transition
matrix. However, when the state space is infinite, the spectrum may be
uncountable, and is nearly always impossible to calculate. In most applications
of the data augmentation (DA) algorithm, the state space of the DA Markov chain
is infinite.