11 Simulation Distributions

Performing many stochastic simulations provides an opportunity to obtain many more statistics about a model. One possibility is to obtain the percentage of simulations for which some property is true at or before a given time t. The menu item “Simulation Distributions” opens a wizard which uses stochastic simulation to perform this kind of analysis.

The condition which must be met in our case is that a chosen component reaches a prescribed population count. The Bio-PEPA Eclipse Plug-in allows you to set up a number of simulation runs and, based on the simulation data, plots the Probability Distribution Function (pdf) and the Cumulative Distribution Function (cdf) of any species in the model, with respect to the target population value. The most interesting of the two distributions is the cdf, which is plotted as a red line. The cdf shows the percentage of simulation runs in which the chosen species has reached the target population count, at or before a given time t. In order to take advantage of this feature of the Bio-PEPA Eclipse Plug-in you should set up the simulation by providing values for the following parameters (see Figure 52):

• Dynamic component — The species with varying population size than you wish to monitor

• Target value — The condition which your model must meet, i.e. the population size your chosen component has to reach

• Stop time — The stop time for the simulation (model dependent)

• Number of independent runs — The number of times the simulation is to be run

• Increment in data point size for the graph — the time-difference between consecutive data points in the graph

The pdf and cdf for species of the a-b-c.biopepa model, with a target value of 20, a stop time of 30, 100 independent runs and a 0.1 increment in data point size for the graph, can be seen in Figure 53. The most interesting of the two distributions is the cdf (red line) which shows, at time t, in how many of the simulation runs the condition we have set is true, i.e. the population of has reached the target value, at that time or before. For instance, in 95% of the simulation runs the population of has reached the target value of 20 at or before 10s.

Figure 69: Setting up a simulation distribution analysis

Figure 70: Simulation distributions for species of the a-b-c.biopepa model with a target value of 20