具有可能因果解释的一般动力学统计模型
A general dynamical statistical model with possible causal interpretation
摘要：
我们开发了一个通用的动力学模型作为可能的因果解释的框架。我们首先陈述了随机过程的Doob-Meyer分解中涉及的过程的可测性的局部独立性准则，如Aalen（1987）;然后我们定义了直接和间接影响。我们提出了一个定义的因果影响使用的概念“物理系统”。这一框架使描述性和解释性统计模型之间的联系成为可能，并涵盖了定量过程和事件。本文的特点之一是明确区分了系统模型和观测模型。我们给出了一个传统的联合模型的HIV载量和CD 4计数的动态表示。我们发现它不足以捕捉因果关系的影响，而相反，已知的艾滋病毒感染的机制，可以直接通过一个系统的微分方程表示。
英文摘要：
We develop a general dynamical model as a framework for possible causal interpretation. We first state a criterion of local independence in terms of measurability of processes involved in the Doob-Meyer decomposition of stochastic processes, as in Aalen (1987); then we define direct and indirect influence. We propose a definition of causal influence using the concepts of ``physical system''. This framework makes it possible to link descriptive and explicative statistical models, and encompasses quantitative processes and events. One of the features of this paper is the clear distinction between the model for the system and the model for the observation. We give a dynamical representation of a conventional joint model for HIV load and CD4 counts. We show its inadequacy to capture causal influences while on the contrary known mechanisms of HIV infection can be expressed directly through a system of differential equations.
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