Stratified sampling
From PBDN
Contents |
Introduction
When stratified sampling is applied, trajectories are treated in groups. The interval (0 to 1) from which random numbers are drawn for reaction selection is divided into as many strata as there are trajectories in a group: if there are 5 trajectories in a group, the interval is divided into 5: 0.0-0.2, 0.2-0.4, 0.4-0.6, 0.6-0.8, and 0.8 to 1.0. Each trajectory in the group gets a random number from a different stratum at each timestep.
Results
Birth-Death Model
For the birth-death model, the result is significant. The pooled variance is reduced by a factor of approximately 2.4 in going from 1 stratum to 2 strata. As the number of strata is increased, small additional gains are seen up to about 10 strata but, thereafter, increasing the number of strata doesn't make much difference.
Metabolite-Enzyme Model
For the metabolite-enzyme model, we again see that the pooled variance decreases with increasing number of strata, with little additional gain for more than 10 strata, where the variance is reduced by a factor of about 1.3.
In contrast to the application of antithetic variates, we see a gain for both metabolite species, not a gain in one at the expense of a loss in the other.
Gains and Losses
Unfortunately, implementing stratified sampling is more complex than a simpler implementation with no variance reduction: with 10 strata, it takes about three times as long per trajectory. This means that the time saved by reducing the number of trajectories which it is necessary to calculate is more than canceled out by the longer time taken to compute each trajectory and stratified sampling is actually slower by about 25% for the birth-death model and by about 130% for the metabolite-enzyme model (where the variance reduction is considerably lower).
However, there is some chance that a lower-cost implementation could make stratified sampling an attractive alternative.
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