Bayesian estimation of non-stationary Markov models combining micro and macro data

We develop a Bayesian estimation framework for non-stationary Markov models for situations where both sample data on observed transitions between states (micro data) and population data, where only the proportion of individuals in each state is observed (macro data), are available. Posterior distributions on transition probabilities are derived from a micro-based prior and a macrobased likelihood, thereby providing a new method that combines micro and macro information in a logically consistent manner and merges previously disparate approaches for inferring transition probabilities. Monte Carlo simulations for ordered and unordered states show how observed micro transitions improve the precision of posterior knowledge.