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 post-leap checks. Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the post-leap checks in such a way that the statistics of the sample paths generated will not be skewed 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 .
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 
A
,
R
post-leap
postleap
R
post-leap
postleap
R
skewed
biased
D
.