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March, 1989 Advances in Pattern Theory
Ulf Grenander
Ann. Statist. 17(1): 1-30 (March, 1989). DOI: 10.1214/aos/1176347002


Pattern theory offers concepts for modelling images and methods for making inferences from observed images. This will be described briefly and illustrated by examples. We shall present limit theorems for the Markov processes on graphs (that are basic to pattern theory) motivated by computational considerations. They will yield approximations that have been exploited to make the inference algorithms computationally feasible. We shall also consider the problem of estimating parameters in the prior measures encountered in pattern theory. These parameters are high dimensional, not automatically identifiable and notoriously difficult to estimate by standard methods. We therefore present a standardization technique for dealing with them and show how, after standardization, the remaining free parameters can be estimated by different methods. The estimation methods are examined in terms of their asymptotic efficiencies.


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Ulf Grenander. "Advances in Pattern Theory." Ann. Statist. 17 (1) 1 - 30, March, 1989.


Published: March, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0673.62071
MathSciNet: MR981436
Digital Object Identifier: 10.1214/aos/1176347002

Primary: 60B99
Secondary: 62M02

Rights: Copyright © 1989 Institute of Mathematical Statistics


Vol.17 • No. 1 • March, 1989
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