# A general dynamical statistical model with causal interpretation

4 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : 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.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00194281
Contributor : Anne Gégout-Petit <>
Submitted on : Thursday, December 6, 2007 - 11:26:29 AM
Last modification on : Thursday, October 18, 2018 - 11:24:06 AM

### Identifiers

• HAL Id : hal-00194281, version 1
• ARXIV : 0710.4396

### Citation

Daniel Commenges, Anne Gegout-Petit. A general dynamical statistical model with causal interpretation. J. Roy. Statist. Soc., 2009, 71, pp.1-18. 〈hal-00194281〉

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