  We estimate a general mixture of Markov jump processes. The key novel feature
of the proposed mixture is that the transition intensity matrices of the Markov
processes comprising the mixture are entirely unconstrained. The Markov
processes are mixed with distributions that depend on the initial state of the
mixture process. The new mixture is estimated from its continuously observed
realizations using the EM algorithm, which provides the maximum likelihood (ML)
estimates of the mixture's parameters. To obtain the standard errors of the
estimates of the mixture's parameters, we employ Louis' (1982) general formula
for the observed Fisher information matrix. We also derive the asymptotic
properties of the ML estimators. Simulation study verifies the estimates'
accuracy and confirms the consistency and asymptotic normality of the
estimators. The developed methods are applied to a medical dataset, for which
the likelihood ratio test rejects the constrained mixture in favor of the
proposed unconstrained one. This application exemplifies the usefulness of a
new unconstrained mixture for identification and characterization of
homogeneous subpopulations in a heterogeneous population.
