Bringing consistency to simulation of population models - Poisson simulation as a bridge between micro and macro simulation
Bringing consistency to simulation of population models - Poisson simulation as a bridge between micro and macro simulation
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DOI：
10.1016/j.mbs.2007.02.004
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发表时间：
2007-10-01
影响因子：
4.3
通讯作者：
Sternad, Mikael
中科院分区：
文献类型：
--
作者：
Gustafsson, Leif;Sternad, Mikael
种群模型关注诸如原子、细胞、人类、动物等离散实体的集合，其重点是种群中实体的数量。由于这些模型的复杂性，通常需要模拟来重现它们完整的动态和随机行为。两种主要类型的模拟模型用于不同的目的，即微观模拟模型，其中每个个体都用其特定的属性和行为来描述，以及基于随机微分方程的宏观模拟模型，其中总体由不同状态下的个体数量以汇总术语来描述。微观和宏观模型之间的一致性是一个至关重要但经常被忽视的方面。本文演示了如何使用泊松模拟技术来产生与相应的微观模型相一致的种群宏观模型。这是通过用严格的数学术语将泊松模拟定义为一系列泊松过程来实现的，这些泊松过程产生具有动态变化参数的泊松分布序列。该方法适用于任何种群模型。它提供了与正确的微观模型相一致的独特的随机动态宏观模型。本文还提出了随机动态种群模型的一般宏观形式。在附录中，将泊松模拟与马尔可夫模拟进行了比较，显示出许多优点。特别是状态变量的聚合和每时间步多事件的聚合使得泊松模拟比马尔可夫模拟快几个数量级。此外，与使用马尔可夫方法相比，您可以使用泊松模拟构建和执行更大、更复杂的模型。(C) 2007爱思唯尔公司版权所有。
Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro- and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach. (C) 2007 Elsevier Inc. All rights reserved.