Modelling logistic growth by a new diffusion process: Application to biological systems
Modelling logistic growth by a new diffusion process: Application to biological systems
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DOI：
10.1016/j.biosystems.2012.06.004
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发表时间：
2012-10-01
期刊：
影响因子：
1.6
通讯作者：
Torres-Ruiz, Francisco
中科院分区：
文献类型：
--
作者：
Roman-Roman, Patricia;Torres-Ruiz, Francisco
本文介绍了一种新的扩散过程，用于建模物流类型的行为模式。与相同背景下的其他过程不同，这个过程验证其平均函数是逻辑斯蒂曲线。此外，它的跃迁密度可以明确地找到，这允许分析从轨迹的离散采样推断。该过程的主要特征将被分析，参数的最大似然估计将通过离散抽样进行。对于求解似然方程的数值问题，本文提出了几种求得通常数值过程初始解的策略。通过仿真算例对这两种策略进行了比较。此外，为了将该过程中的估计与Giovanis和Skiadas（1999）考虑的logistic扩散模型中通过连续抽样进行的估计进行比较，还进行了另一项模拟研究。最后给出了一个微生物培养物生长的例子。这个例子说明了新过程的预测可能性，以及它研究时间变量的能力，这些时间变量表示为首次通过时间。2012爱思唯尔爱尔兰有限公司版权所有。
The present paper introduces a new diffusion process for the purpose of modelling logistic-type behaviour patterns. Unlike other processes in the same context, this one verifies that its mean function is a logistic curve. In addition, its transition density can be found explicitly, which allows to analyse inference from the discrete sampling of trajectories. The main features of the process will be analysed and the maximum likelihood estimation of parameters will be carried out through discrete sampling. Regarding the numerical problems found to solve the likelihood equations, several strategies are developed for obtaining initial solutions for the usual numerical procedures. Such strategies are compared by means of a simulation example. Also, another simulation study is carried out in order to compare the estimation in this process to that developed by means of continuous sampling in the logistic diffusion model considered by Giovanis and Skiadas (1999). Finally an example is given for the growth of a microorganism culture. This example illustrates the predictive possibilities of the new process, as well as its ability to study time variables formulated as first-passage-times. (C) 2012 Elsevier Ireland Ltd. All rights reserved.