Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 23, Issue 7, Pages 1309-1338Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202513500103
Keywords
Bayesian statistics; model validation; diffuse-interface models; model selection; Markov chain Monte Carlo methods
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Funding
- DOE [DE-FC52-08NA28615]
- DOE Multiscale Mathematics Program [DE-FG02-0SER25701]
- NSF [DMS-1115865]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1115865] Funding Source: National Science Foundation
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We address general approaches to the rational selection and validation of mathematical and computational models of tumor growth using methods of Bayesian inference. The model classes are derived from a general diffuse-interface, continuum mixture theory and focus on mass conservation of mixtures with up to four species. Synthetic data are generated using higher-order base models. We discuss general approaches to model calibration, validation, plausibility, and selection based on Bayesian-based methods, information theory, and maximum information entropy. We also address computational issues and provide numerical experiments based on Markov chain Monte Carlo algorithms and high performance computing implementations.
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