From PBDN

Introduction

When antithetic variates are applied, trajectories are treated in pairs. When one of the pair uses random number x for reaction selection, the other (antithetic) uses 1 − x. Since the random number, x is always between 0 and 1, 1 − x is also between 0 and 1.

Results

Birth-Death Model

Pooled variance plot for birth-death model

For the birth-death model, the result is quite dramatic. The pooled variance is reduced by a factor of between 2.7 and 3.1. This means that, for a given error, it is only necessary to compute a little more than one third as many trajectories when antithetic variates is applied as compared to the baseline, where no variance reduction technique is applied.

Metabolite-Enzyme Model

Pooled variance plot for metabolite A in metabolite-enzyme model

Pooled variance plot for metabolite B in metabolite-enzyme model

For the metabolite-enzyme model, the result is not so good. The pooled variance is reduced a little for the metabolite A species, but increases by about the same amount for the metabolite B species. There is no significant effect on either of the enzyme species.

Variance increase is a known risk with antithetic variates.

Pooled variance plot for enzyme A in metabolite-enzyme model

Pooled variance plot for enzyme B in metabolite-enzyme model

Gains and Losses

Although implementing antithetic variates does require a little extra time per trajectory than the baseline, it is a simple technique to implement, and the additional running time required is negligible. In particular, it doesn't require any special trajectory grouping support (see the baseline discussion in Experiments and Graphs), so the reduction in the pooled variance translates directly into a reduction in the number of trajectories which need to be computed.

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