Parameter identification in nonstationary Markov chains with external impact and its application to computational sociology

A numerical framework for analysis and online prediction of nonstationary discrete ensemble probability distribution dynamics is presented. This framework is based on a databased estimation of time-dependent Markov chain models under influence of external factors. A numerical algorithm for the solution of the resulting mixed discrete-continuous optimization problem is described, existence and uniqueness of the partial optimizers is investigated. The resulting numerical algorithm is applied to analyze a historical time series of political preferences in Germany from the monthly anonymized opinion polls. The obtained Markovian voter models with external influence are analyzed and the resulting online predictions are compared to the ones obtained by standard methods of time series analysis.