JSM 2004 - Toronto

Abstract #300706

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Activity Number: 11
Type: Topic Contributed
Date/Time: Sunday, August 8, 2004 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Computing
Abstract - #300706
Title: Pattern Reproduction Using Likelihood Inference for Cellular Automata
Author(s): Radu V. Craiu*+ and Thomas C.M. Lee
Companies: University of Toronto and Colorado State University
Address: Dept. of Statistics, Toronto, ON, M5S 3G3, Canada
Keywords: stochastic cellular automaton ; binary patterns ; grey-scale patterns ; cellular automaton ; minimum description length principle
Abstract:

Cellular automata are discrete dynamical systems evolving in discrete time over a lattice structure with a multitude of cells. Recent computer experiments have shown that cellular automata dynamics can be used to generate a wide variety of patterns, some highly irregular. Here we report initial findings on likelihood methods for the inverse problem. Specifically, for a given pattern we try to estimate the stochastic cellular automaton that may reproduce it. Issues related to model selection are solved using the minimum description length principle. We will illustrate the approach with a series of patterns some of which are successfully reproduced.


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Revised March 2004