Uncertainty importance measures of dependent transition rates for transient and steady state probabilities

Markov models are widely used for describing the behavior of multi-state systems, whose transition rates can be approximated through Bayesian inference based on data from field collections and experiments. The estimates of transition rates departing from the same state can be dependent. In this paper, we investigate the influence of uncertainties associated with the transition rates due to the finiteness of the available data, upon the transient and steady state probabilities. Variance-based methods are employed to understand how the uncertainty in the model output can be apportioned to the model inputs. To deal with dependencies among the transition rates, the dependent transition rates are represented by a group of independent random variables. Uncertainty importance measures (UIMs) are derived based on the total sensitivity indices to rank the transition rates based on their contributions to the output variance. Therefore, actions to improve the accuracy of their estimation can be appropriately guided to reduce the output variance. The extended Fourier amplitude sensitivity test is used for the quantification of the UIMs. A numerical example is provided to illustrate the approaches.