Incorporating postleap checks in tau-leaping

TL;DR

This paper introduces a new adaptive tau-leaping method for simulating discrete chemical systems, ensuring accuracy and avoiding negative populations through postleap checks that do not bias the sample paths.

Contribution

It presents a novel tau-leaping algorithm that guarantees accuracy with postleap checks and maintains unbiased sample paths by separating randomness from system state.

Findings

Guarantees accuracy with postleap checks

Prevents negative population values

Ensures unbiased sample paths

Abstract

By explicitly representing the reaction times of discrete chemical systems as the firing times of independent, unit rate Poisson processes, we develop a new adaptive tau-leaping procedure. The procedure developed is novel in that accuracy is guaranteed by performing postleap checks. Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the postleap checks in such a way that the statistics of the sample paths generated will not be biased by the rejections of leaps. Further, since any leap condition is ensured with a probability of one, the simulation method naturally avoids negative population values