An information theory based optimality criterion to sample stationary distributions of Markov chains

Biomechanical and molecular systems are complex, high-dimensional systems whose dynamics is described by stochastic laws. Numerical simulations are an invaluable tool to investigate the dynamics and equilibrium properties of these systems. However, the complexity of the calculation often limits severely the sampling, such that many interesting time scales are out of reach. In this thesis, I investigate an information theory inspired algorithm to efficiently invest computational resources to speed-up the sampling of the system’s equilibrium distribution. I introduce a sampling scheme that opportunely reinitialize simulations to obtain a faster convergence of the stationary distributions compared to a brute-force sampling. The methodological framework is based on probability and information theory applied to stochastic Markovian processes. The theory and the results reported in this work are possibly relevant to biological systems and more in general to any stochastic Markovian processes.