The naive rule for reconstructing a noisy Markov chain
Jay L. Devore · Biometrika · 1973
An observer desires to record a realization of a stationary two-state Markov chain X, but experimental conditions are such that he instead sees a realization of a sequence Y subject to error. The objective is to reconstruct X. The naive reconstruction rule is that rule which assumes that X is a sequence of independent random variables and selects X^i, the reconstructed Xi, using only Yi. A necessary and sufficient condition is given for the naive rule to be the optimal reconstruction rule.