Chapter 10: Processes of Perception and Analysis

Section 9: Statistical Analysis

Probabilistic models

A probabilistic model must associate with every sequence a probability that is a number between 0 and 1. This can be done either by giving an explicit procedure for taking sequences and finding probabilities, or by defining a process in which sequences are generated with appropriate probabilities. A typical example of the first approach is the Ising model for spin systems in which relative probabilities of sequences are found by multiplying together the results of applying a simple function to blocks of nearby elements in the sequence. Monte Carlo methods and probabilistic cellular automata provide examples of the second approach.

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From Stephen Wolfram: A New Kind of Science [citation]