The Effect of Nonhomogeneous Populations on Markov Steady-State Probabilities

Abstract An important aspect of many Markovian analyses is the steady-state solution. This can give insight into the dynamics or momentum existing in a system. However, when we obtain Markov transition matrices by aggregating across non-homogeneous (with respect to transition probabilities) individuals, this matrix may not bear any resemblance to the transition matrices possessed by the individuals. This article investigates the effect of this heterogeneity on the calculated steady-state solution obtained from the aggregate transition matrix. We find that under various conditions this calculated steady-state solution is quite close to the true steady-state solution. These results have important implications for Markovian forecasting methods.