Prediction

TL;DR

This paper explores predictability in complex systems, highlighting the role of heterogeneity and interactions, and draws parallels between earthquakes, financial crashes, and epileptic seizures using stochastic point processes like Hawkes models.

Contribution

It offers a unified phase diagram framework for understanding diverse systems and introduces the application of Hawkes point processes to epileptology based on earthquake phenomenology.

Findings

Heterogeneity and coupling strength are key to system behavior.

Hawkes processes effectively model event cascades in earthquakes and seizures.

A phase diagram links system disorder with emergent phenomena.

Abstract

This chapter first presents a rather personal view of some different aspects of predictability, going in crescendo from simple linear systems to high-dimensional nonlinear systems with stochastic forcing, which exhibit emergent properties such as phase transitions and regime shifts. Then, a detailed correspondence between the phenomenology of earthquakes, financial crashes and epileptic seizures is offered. The presented statistical evidence provides the substance of a general phase diagram for understanding the many facets of the spatio-temporal organization of these systems. A key insight is to organize the evidence and mechanisms in terms of two summarizing measures: (i) amplitude of disorder or heterogeneity in the system and (ii) level of coupling or interaction strength among the system's components. On the basis of the recently identified remarkable correspondence between earthquakes and seizures, we present detailed information on a class of stochastic point processes that has been found to be particularly powerful in describing earthquake phenomenology and which, we think, has a promising future in epileptology. The so-called self-exciting Hawkes point processes capture parsimoniously the idea that events can trigger other events, and their cascades of interactions and mutual influence are essential to understand the behavior of these systems.