A Bayesian Approach to Morphological Models Characterization

Bruno Figliuzzi, Antoine Montaux-Lambert, François Willot, Grégoire Naudin, Pierre Dupuis, Bernard Querleux, Etienne Huguet

Abstract

Morphological models are commonly used to describe microstructures observed in heterogeneous materials. Usually, these models depend upon a set of parameters that must be chosen carefully to match experimental observations conducted on the microstructure. A common approach to perform the parameters determination is to try to minimize an objective function, usually taken to be the discrepancy between measurements computed on the simulations and on the experimental observations, respectively. In this article, we present a Bayesian approach for determining the parameters of morphological models, based upon the definition of a posterior distribution for the parameters. A Monte Carlo Markov Chains (MCMC) algorithm is then used to generate samples from the posterior distribution and to identify a set of optimal parameters. We show on several examples that the Bayesian approach allows us to properly identify the optimal parameters of distinct morphological models and to identify potential correlations between the parameters of the models.


Keywords
Bayesian models; Monte Carlo Markov Chains algorithms; Morphological models

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DOI: 10.5566/ias.2641

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)