Assessment of the transition-rates importance of Markovian systems at steady state using the unscented transformation

Abstract

The Unscented Transformation (UT) is a technique to understand and compute how the uncertainty of a set of random variables, with known mean and variance is propagated on the outputs of a model, through a reduced set of model evaluations as compared with other approaches (e.g., Monte Carlo). This computational effort reduction along with the definition of a proper UT model allows proposing an alternative approach to quantify the transition rates (TR) having the highest contribution to the variance of the steady-state probability, for each possible state of a system represented by a Markov model. The so called “main effects” of each transition rate, as well as high order component interactions are efficiently derived from the solution of only (2n+1) linear system of simultaneous equations, being n the number of transition rates in the model.