Stochasticity

Stochasticity refers to the inclusion of randomness or uncertainty in the model. Randomness can be introduced through probabilistic processes, random events, or noisy behaviors of agents. Stochasticity acknowledges that real-world systems often exhibit inherent variability and unpredictability, which can be essential to capture the dynamics and outcomes of the model.

Introduction

What processes are modeled by assuming they are random or partly random?

Explanation

Here, describe where and how stochastic processes—those driven by pseudorandom numbers— are used in the model. While some ABMs base most of their processes on random events, others can produce highly variable results with no stochasticity at all. In general, stochastic processes are used when we want some part of a model to have variation (among entities, over time, etc.) but we do not want to model the mechanisms that cause the variability. It may be critical for a model to include how weather affects some system such as the electric power grid, but we certainly do not want to add the enormous complexity of predicting weather to the model; instead, we simply model the timing and duration of weather events as stochastic processes. One common use of stochasticity in ABMs is to insert variability in initial conditions: when we create our agents (and other entities) at the start of a simulation (Element 5, below) we do not want them to be identical, so we use pseudorandom number distributions to set the initial values of some state variables. A second common use is to simplify submodels by assuming they are partly stochastic. Assuming that an agent dies if a random number between 0.0 and 1.0 is greater than its survival probability is a very common example: we do not want to represent all the detail of when agents die. A third use of stochasticity is modeling agent behaviors in a way that causes the model agents to use different alternatives with the same frequency as real agents have been observed to. For example, a sociological model could use a stochastic process to model the age at which people marry, comparing random numbers to the marriage rates observed in real people. This approach would impose the observed marriage rates on the simulated population. Describe: • Which processes are modeled as stochastic, using pseudorandom number distributions to determine the outcome. • Why stochasticity was used in each such process. Often, the reason is simply to make the process variable without having to model the causes of variability; or the reason could be to make model events or behaviors occur with a specified frequency.

Examples

In ITC evaluation model:

  • At initialization (setup) new agents are created at random locations
  • Agents are assigned a pre-evacuation time (this contains randomness)
  • Agents have a certain preference for an exit (random element)
  • Stochasticity is used in two ways. First, the model is initialized stochastically in such a way that (a) the total number of households, (b) whether each location is occupied initially, (c) the color of each household, and (d) the number of households of each color, are all stochastic (Initialization, below). These initialization methods are stochastic so that the model can be assumed unsegregated at the start of a simulation, and so that each model run produces different results. Second, when a household decides to move, its choice of new location (the “move” submodel) is stochastic (but not completely random). The new location of households when they move is stochastic because modeling the details of movement is unnecessary for this model.
  • Stochasticity is used in initializing the model (Initialization, below) to create irregular clumps of each habitat type; this stochastic process allows creation of multiple landscapes that have the same over-all habitat characteristics (e.g., area of each habitat type, number and mean size of habitat clumps), which are used as replicates in analysis of model responses to habitat availability scenarios. Stochasticity is also used in initialization to assign each bird a home cell, and to impose variability among cells in coffee pest infestation rates (see the “pest infestation rate” submodel, below). During a simulation, the main uses of stochasticity are to (1) avoid a feeding hierarchy by randomizing the order in which birds execute their foraging trait each foraging time step, and (2) decide whether birds die if they did not make their daily intake requirement (see the “mortality” submodel, below). In bird foraging, several cells may offer exactly the same, highest, food intake rate; in such cases, the bird chooses one of these cells randomly

Outgoing relations