Развој на протокол за адаптивна динамичка баесова инференција

Abstract

Several methods exist that allow the study of interactions between dynamical systems, including the method of dynamical Bayesian inference, which allows for the reconstruction of a model that describes the interactions between different dynamic systems, based on measured time series originating from those systems. In this method, the time series measurements are considered as sequences of blocks of information and in each block an inference is made of the parameters and the coupling functions of the model, which describe the dynamics of the system and the mechanisms of interactions. The aim of this doctoral thesis is to improve this method, by establishing a new protocol for adaptive dynamical Bayesian interference, which determines the time window of the inference, as well as the propagation parameter, which determines how much of the infered information in the current block is used for the inference in the next block. The new protocol was introduced through numerical analysis of a system of two coupled phase oscillators and then tested on a second system of limit cycle oscillators, i.e. Poincaré oscillators. The new protocol was then applied to the study of cardiorespiratory interactions in a single subject breathing under three different patterns of respiration. The obtained coupling functions that describe the cardiorespiratory interaction were analyzed in order to determine the mechanisms of influence of the respiration on the heart and it was found that some of the obtained results confirm previously known results, while some led to new, previously unknown conclusions.