Dynamic modelling and causality

Abstract

In 1965 Erling Sverdrup published a paper on the use of Markov chains in modelling disability. This paper has been a source of inspiration for further development of statistical theory for Markov processes and the closely related counting processes. The main importance of introducing Markov chains does not lie so much in the Markov property, but more in the fact that a dynamic stochastic process is used as model. For statistical purposes one may dispense with the Markov assumption and may use much more general dynamic models than the Markovian ones. The key concept in this extension is the Doob-Meyer decomposition which is a part of modern martingale theory. With this as a starting point I define a general dynamic statistical model and discuss several examples. Intuitively, a dynamic model will be one where the future development is “explained” in terms of the past. Not surprisingly this is closely related to a causal understanding of the phenomenon. Tore Schweder in 1970 wrote a paper where he related Markov models to causality. I attempt to give a more general formulation of Schweder's important concept of local dependence. I discuss the relationship to other statistical definitions of causality.