Before revision:  We first deal with the estimation of a continuous time Markov chain using discrete (missing) data and derive a simpler expression for the Fisher information matrix, reducing the computation time of Wald confidence intervals to less than half of the current standard .
After revision:  We first deal with the estimation of a continuous time Markov chain using discrete (missing) data and derive a simpler expression for the Fisher information matrix, reducing the computational time needed for the Wald confidence interval by a factor of a half .