  We consider the problem of estimating the transition rate matrix of a
continuous-time Markov chain from a finite-duration realisation of this
process. We approach this problem in an imprecise probabilistic framework,
using a set of prior distributions on the unknown transition rate matrix. The
resulting estimator is a set of transition rate matrices that, for reasons of
conjugacy, is easy to find. To determine the hyperparameters for our set of
priors, we reconsider the problem in discrete time, where we can use the
well-known Imprecise Dirichlet Model. In particular, we show how the limit of
the resulting discrete-time estimators is a continuous-time estimator. It
corresponds to a specific choice of hyperparameters and has an exceptionally
simple closed-form expression.
