Probability and Statistics in Complex Systems, Introduction to

Is the nature of complex systems such that they are in need of a special treatment in terms of statistics andprobability. Yes, they are in the sense that a particular focus suggests itself. This becomes clear if we try to specify what we mean by complexsystems. Although no consensus exists for the definition of what constitutes a complex system, the following summary will probably be accepted by mostpeople.

• Complex Systems consist of a large number of interacting components. The interactions give rise to emergent hierarchical structures. The components of the system and properties at systems level typically change with time. A complex system is inherently open and its boundaries often a matter of convention.

Large numbers of components and interaction between these are central and this has immediate consequences for the nature of therelevant statistics. The interactions between the many components will typically be so strong that correlations cannot be neglected(Correlations in...