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A general dynamical statistical model with causal interpretation
Author(s) -
Commenges Daniel,
GégoutPetit Anne
Publication year - 2009
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2009.00703.x
Subject(s) - interpretation (philosophy) , representation (politics) , causal model , independence (probability theory) , dynamical systems theory , computer science , econometrics , human immunodeficiency virus (hiv) , mathematics , statistical physics , statistics , physics , medicine , family medicine , quantum mechanics , politics , political science , law , programming language
Summary. We develop a general dynamical model as a framework for causal interpretation. We first state a criterion of local independence in terms of measurability of processes that are involved in the Doob–Meyer decomposition of stochastic processes; then we define direct and indirect influence. We propose a definition of causal influence using the concepts of a ‘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 the 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 human immunodeficiency virus load and CD4 cell counts. We show its inadequacy to capture causal influences whereas in contrast known mechanisms of infection by the human immunodeficiency virus can be expressed directly through a system of differential equations.