Error analysis of tau-leap simulation methods

TL;DR

This paper provides an error analysis of tau-leap methods for continuous time Markov chains, showing that midpoint tau-leaping outperforms Euler tau-leaping under a new, more appropriate scaling.

Contribution

It introduces a novel scaling approach for error analysis and demonstrates that midpoint tau-leaping achieves higher accuracy than Euler tau-leaping.

Findings

Midpoint tau-leaping has higher order accuracy than Euler tau-leaping.

The new scaling is more appropriate for error analysis of these methods.

Examples confirm the theoretical results.

Abstract

We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of different approximation methods and, specifically, Euler tau-leaping and midpoint tau-leaping. We perform our analysis under a scaling in which the size of the time discretization is inversely proportional to some (bounded) power of the norm of the state of the system. We argue that this is a more appropriate scaling than that found in previous error analyses in which the size of the time discretization goes to zero independent of the rest of the model. Under the present scaling, we show that midpoint tau-leaping achieves a higher order of accuracy, in both a weak and a strong sense, than Euler tau-leaping; a result that is in contrast to previous analyses. We present examples that demonstrate our findings.