Biyolojik ağlardaki yaklaşık stokastik simülasyon algoritmalarında sıçrama koşulunun genişletilmesi

The approximate stochastic simulation (ASS) algorithms are the alternative approaches to generate the complex biological systems with a loss in accuracy by gaining from computational demand. There are a number of approximate methods which can successfully simulate the systems, such as poisson tau-leap and approximate Gillespie algorithms. The common property of these approaches is that they are based on the leap conditon which controls the change in hazard functions under a time interval. By means of this interval we can find an interval for the number of simultaneous reactions k in the time interval generated from the leap condition. In this study, we propose alternative intervals for k that are dependent on the sufficient statistics and also, we derive confidence intervals for k whose parameters are obtained via maximum likelihood estimator, moment estimators and bayesian estimators. Furthermore, we extend the leap condition by using higher order Taylor expansion whose original estimators are found under the first order. In our derivations, we use the poisson tau-leap approach since it is the fundamental approximate stochastic simulation method. Moreover, we apply the approximate Gillespie algorithm since it is one of the recent approaches that is derived from the idea of the poisson tau-leap method. We consider that although the proposal approaches to these two algortihms, they can be also adapted to other algorithms whose derivation are based on the parametric assumption.