An Imprecise Probabilistic Estimator for the Transition Rate Matrix of a Continuous-Time Markov Chain
This provides a method for robust estimation in stochastic processes, but it is incremental as it builds on existing imprecise probabilistic models.
The paper tackles the problem of estimating the transition rate matrix of a continuous-time Markov chain from finite data by using an imprecise probabilistic framework with sets of prior distributions, resulting in an estimator that is easy to compute and has a simple closed-form expression.
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.