Szymańska Zuzanna, Skrzeczkowski Jakub, Miasojedow Błażej, Gwiazda Piotr
ICM, University of Warsaw, ul. Tyniecka 15/17, 02-630 Warsaw, Poland.
Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warsaw, Poland.
R Soc Open Sci. 2021 Nov 24;8(11):211279. doi: 10.1098/rsos.211279. eCollection 2021 Nov.
From a systems biology perspective, the majority of cancer models, although interesting and providing a qualitative explanation of some problems, have a major disadvantage in that they usually miss a genuine connection with experimental data. Having this in mind, in this paper, we aim at contributing to the improvement of many cancer models which contain a proliferation term. To this end, we propose a new non-local model of cell proliferation. We select data that are suitable to perform Bayesian inference for unknown parameters and we provide a discussion on the range of applicability of the model. Furthermore, we provide proof of the stability of posterior distributions in total variation norm which exploits the theory of spaces of measures equipped with the weighted flat norm. In a companion paper, we provide detailed proof of the well-posedness of the problem and we investigate the convergence of the escalator boxcar train (EBT) algorithm applied to solve the equation.
从系统生物学的角度来看，大多数癌症模型虽然有趣且能对一些问题给出定性解释，但存在一个主要缺点，即它们通常与实验数据缺乏真正的联系。考虑到这一点，在本文中，我们旨在推动许多包含增殖项的癌症模型的改进。为此，我们提出了一种新的细胞增殖非局部模型。我们选择适合对未知参数进行贝叶斯推断的数据，并对该模型的适用范围进行了讨论。此外，我们利用配备加权平坦范数的测度空间理论，给出了后验分布在全变差范数下稳定性的证明。在一篇配套论文中，我们给出了该问题适定性的详细证明，并研究了用于求解该方程的阶梯箱式列车（EBT）算法的收敛性。
