Simulation Study to Identify the Characteristics of Markov Chain Properties

Markov models have a long tradition in modeling and simulation of dynamic systems. In this paper, we look at certain properties of a discrete time Markov chain including entropy, trace and 2nd largest eigenvalue to better understand their role for time series analysis. We simulate a number of possible input signals, fit a discrete time Markov chain and explore properties with the help of Sobol indices. This research is motivated by recent results in the analysis of cell development for Xenopus laevis in cell biology that relied on the considered entropy measure to distinguish development stages from time series data of Calcium levels in cells.