Bayesian inference for differential equations
Bayesian inference for differential equations
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DOI：
10.1016/j.tcs.2008.07.005
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发表时间：
2008-11-17
影响因子：
1.1
通讯作者：
Girolami, Mark
中科院分区：
文献类型：
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作者：
Girolami, Mark
非线性动力学系统，如生化途径，可以表示在抽象形式，使用一些建模形式主义。特别是微分方程提供了一个高度表达的数学框架，用它来模拟动态系统，和一个非常自然的方式来模拟一个生化途径的动态确定性的方式是通过使用非线性普通或时间延迟微分方程。然而，例如，如果我们考虑一个生化途径的组成化学物种，因此途径结构很少被充分表征。此外，通常不可能获得形成数学模型的自由参数的激活或衰减速率的值。因此，在许多情况下，系统模型在结构或参数取值方面都没有完全表征。当模型用于模拟或预测模式时，必须以系统的方式考虑这种不确定性，以防止得出关于系统特性的不必要的结论，或者在给定模型的不确定性的情况下做出不可否认的乐观预测。贝叶斯推理方法提供了一个连贯的框架，它来解释和传播这种机械模型中的不确定性，本文介绍了贝叶斯方法，适用于微分方程表示的系统模型。(c)2008 Elsevier B.V.保留所有权利。
Nonlinear dynamic systems such as biochemical pathways can be represented in abstract form using a number of modelling formalisms. In particular differential equations provide a highly expressive mathematical framework with which to model dynamic systems, and a very natural way to model the dynamics of a biochemical pathway in a deterministic manner is through the use of nonlinear ordinary or time delay differential equations. However if, for example, we consider a biochemical pathway the constituent chemical species and hence the pathway structure are seldom fully characterised. In addition it is often impossible to obtain values of the rates of activation or decay which form the free parameters of the mathematical model. The system model in many cases is therefore not fully characterised either in terms of structure or the values which parameters take. This uncertainty must be accounted for in a systematic manner when the model is used in simulation or predictive mode to safeguard against reaching conclusions about system characteristics that are unwarranted, or in making predictions that are unjustifiably optimistic given the uncertainty about the model. The Bayesian inferential methodology provides a coherent framework with which to characterise and propagate uncertainty in such mechanistic models and this paper provides an introduction to Bayesian methodology as applied to system models represented as differential equations. (c) 2008 Elsevier B.V. All rights reserved.