< Back to previous page

Publication

An imprecise probabilistic estimator for the transition rate matrix of a continuous-time Markov Chain

Book Contribution - Book Chapter Conference Contribution

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.
Book: UNCERTAINTY MODELLING IN DATA SCIENCE
Pages: 124 - 132
ISBN:9783319975474
Publication year:2019
Accessibility:Open