Reconstructing a Noisy Markov Chain
Jay L. Devore · Journal of the American Statistical Association · 1973
We attempt to observe a realization of a stationary two-state Markov chain, but conditions are such that there may be misidentification of states. The objective is therefore to use the observed sequence to reconstruct the underlying Markov sequence. For a symmetric transition matrix it is shown that the best reconstruction in a certain sense is that which minimizes a particular linear combination of the number of state transitions in the reconstructed sequence and the number of mismatches between the reconstructed and observed sequences. For this case an algorithm for reconstruction is presented. Reconstruction in the nonsymmetric case is also briefly discussed.