The use of the relatively new tau-leap algorithm to model the
kinematics of regulatory systems and other chemical processes
inside the cell, is of great interest. We introduce a new method
that enables us to establish the accuracy of the tau-leap method
effectively. Our approach takes advantage of the fact that the
stochastic simulation algorithm (SSA) and the tau-leap method can
be represented as a special type of counting process, that can
essentially "couple," or tie together, a single realization of the
SSA process to one of the tau-leap. Because the SSA is exact we can
evaluate the accuracy of the tau-leap by comparing it to the SSA.
Our approach gives error estimates which are unrivaled by any
method currently available. Moreover, our coupling algorithm allows
us to propose an adaptive parameter selection algorithm which finds
the appropriate parameter values needed to achieve a pre-determined
error threshold in the tau-leap algorithm. This error-controlled
adaptive parameter selection method could not have been proposed
before the introduction of our coupling algorithm, and it is a
novel approach to the use of the tau-leap algorithm.
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