In probability theory, tau-leaping, or τ-leaping, is an approximate method for the simulation of a stochastic system.
[1] It is based on the Gillespie algorithm, performing all reactions for an interval of length tau before updating the propensity functions.
[2] By updating the rates less often this sometimes allows for more efficient simulation and thus the consideration of larger systems.
Many variants of the basic algorithm have been considered.
[3][4][5][6][7] The algorithm is analogous to the Euler method for deterministic systems, but instead of making a fixed change
is a Poisson distributed random variable with mean
occurring at rate
and with state change vectors
indexes the state variables, and
indexes the events), the method is as follows: This algorithm is described by Cao et al.[4] The idea is to bound the relative change in each event rate
(Cao et al. recommend
, although it may depend on model specifics).
This is achieved by bounding the relative change in each state variable
depends on the rate that changes the most for a given change in
is equal the highest order event rate, but this may be more complex in different situations (especially epidemiological models with non-linear event rates).
This algorithm typically requires computing
auxiliary values (where
is the number of state variables
), and should only require reusing previously calculated values
An important factor in this is that since
is an integer value, there is a minimum value by which it can change, preventing the relative change in
being bounded by 0, which would result in
leaping algorithm.