The methodology of flowgraph models

Flowgraph models are directed graph models for describing the dynamic changes in a stochastic process. They are one class of multistate models that are applied to analyse time-to-event data. The main motivation of the flowgraph models is to determine the distribution of the total waiting times until an event of interest occurs in a stochastic process that progresses through various states. This thesis applies the methodology of flowgraph models to the study of Markov and SemiMarkov processes. The underlying approach of the thesis is that the access to the moment generating function (MGF) and cumulant generating function (CGF), provided by Mason’s rule enables us to use the Method of Moments (MM) which depends on moments and cumulant. We give a new derivation of the Mason’s rule to compute the total waiting MGF based on the internode transition matrix of a flowgraph. Next, we demonstrate methods to determine and approximate the distribution of total waiting time based on the inversion of the MGF, including an alternative approach using the Pad´e approximation of the MGF, which always yields a closed form density. For parameter estimation, we extend the Expectation-Maximization (EM) algorithm to estimate parameters in the mixture of negative weight exponential density. Our second contribution is to develop a bias correction method in the Method of Moments (BCMM). By investigating methods for tail area approximation, we propose a new way to estimate the total waiting time density function and survival