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- W4313184102 abstract "AbstractIn this chapter, we model breast tumor’s growth with the logistic discrete Pielou model. Data of tumor volume is retrieved from the literature. We assign probability density functions (PDF) to the data and their uncertainty using the principle of maximum entropy. Then, we propose a computational technique, probabilistic calibration (PC), to calibrate mathematical models taking into account the data uncertainty. The technique consists of sampling several times in the random data described by PDFs. For each sample and using an optimization algorithm, we seek the logistic model parameters values so that the model output matches as much as possible with the sampled data. Consequently, we obtain a stack of sets of model parameter values whose outputs are around the data and their uncertainty. With all the samples, we are covering most of the possibilities the phenomenon may evolve, and with the calibrations, we get feasible model parameter values that, substituted into the model, may reproduce the data uncertainty. To check the quality of the PC technique, it is compared to a similar one that takes advantage of the fact that the random model utilized has a closed-form solution stochastic process. The differences are not great, and we conclude that PC should be considered in cases where it is not possible to have an explicit solution to the random model. Nevertheless, the PC opens, on the one hand, avenues for improvement by tuning the number of iterations of the calibration algorithm to obtain better calibrations and search for appropriate thresholds, where the calibrated parameters should be rejected because they are not good enough to be considered to quantify the uncertainty. Regarding the latter, this may lead to situations where the models are unable to capture certain areas of data uncertainty.KeywordsBreast tumor growthProbabilistic calibrationProbability density functionPielou’s modelUncertainty quantification" @default.
- W4313184102 created "2023-01-06" @default.
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- W4313184102 date "2022-01-01" @default.
- W4313184102 modified "2023-10-18" @default.
- W4313184102 title "A Computational Probabilistic Calibration of the Pielou’s Model to Study the Growth of Breast Tumors: A Comparative Study" @default.
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- W4313184102 doi "https://doi.org/10.1007/978-3-031-06632-0_4" @default.
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