Approaches to Geo-mathematical Modelling

Chapter 13A Simple Approach for the Prediction of Extinction Events in Multi-agent Models

Thomas P. Oléron Evans, Steven R. Bishop and Frank T. Smith

13.1 Introduction

The prediction of rare and extreme events in complicated real-world systems is a mathematical challenge for which the stakes are extremely high. Analysing seismological data to predict large earthquakes or meteorological data to predict hurricanes is of vital importance to preserving human life and taking measures to protect infrastructure. Predicting extreme events in complex systems of interacting agents, such as damaging crashes in financial markets or the extinction a certain species in an ecosystem, is an equally important goal and potentially an even more difficult one.

A common method of prediction, applied to a wide variety of such problems, is to model the system of interest with an agent-based model (ABM) or a cellular automaton (CA). The model can be calibrated with data observed from the real system and run multiple times to produce a range of possible outcomes. The probability of a given real-world event can then be inferred from the proportion of runs of the model in which it is observed. This variability of outcomes in such models may arise from in-built stochasticity or from the use of an ensemble forecast, in which differing initial conditions are applied to each run, reflecting uncertainty about the true state of the world (Smith, 2001).

However, comparatively little attention has been paid ...