Modelling mechanisms with causal cycles

Abstract

Mechanistic philosophy of science views a large part of scientific activity as engaged in modelling mechanisms. While science textbooks tend to offer qualitative models of mechanisms, there is increasing demand for models from which one can draw quantitative predictions and explanations. Casini et al. (Theoria 26(1):5-33, 2011) put forward the Recursive Bayesian Networks (RBN) formalism as well suited to this end. The RBN formalism is an extension of the standard Bayesian net formalism, an extension that allows for modelling the hierarchical nature of mechanisms. Like the standard Bayesian net formalism, it models causal relationships using directed acyclic graphs. Given this appeal to acyclicity, causal cycles pose a prima facie problem for the RBN approach. This paper argues that the problem is a significant one given the ubiquity of causal cycles in mechanisms, but that the problem can be solved by combining two sorts of solution strategy in a judicious way

Another problem with RBN models of mechanisms

“…Casini et al's (2011) RBN approach for modeling mechanisms, which is also endorsed by Clarke et al (2014), should provide predictions about the effects of manipulations on a mechanism's parts across levels. Such manipulations are typically represented in causal models either by intervention variables or by deleting arrows and fixing the values of the manipulated variables.…”

“…Casini, Illari, Russo, and Williamson (2011) argue that recursive Bayesian networks (RBNs), which were originally developed by Williamson and Gabbay (2005) to model nested causal relationships, can also be used to model mechanisms and that RBN models of mechanisms provide quantitative answers to questions concerning explanation, prediction, and control. In a follow-up paper Clarke, Leuridan, and Williamson (2014) extend the RBN approach in such a way that it can also be applied to mechanisms featuring causal feedback. One of the main selling points of the RBN approach should be that RBN models of mechanisms can be used to calculate post-intervention distributions, i.e., to predict the effects of interventions on a mechanism's parts even across levels.…”

“…

ABSTRACT: Casini, Illari, Russo, and Williamson (2011) suggest to model mechanisms by means of recursive Bayesian networks (RBNs) and Clarke, Leuridan, and Williamson (2014) extend their modeling approach to mechanisms featuring causal feedback. One of the main selling points of the RBN approach should be that it provides answers to questions concerning the effects of manipulation and control across the levels of a mechanism.

In this paper I demonstrate that the method to compute the effects of interventions the authors mentioned endorse leads to absurd results under the additional assumption of faithfulness, which can be expected to hold for many RBN models of mechanisms.

Keywords: recursive Bayesian networks, mechanism, modeling, intervention, manipulation, control.

RESUMEN: Casini, Illari, Russo y Williamson (2011) proponen modelar los mecanismos mediante redes bayesianas recursivas (RBNs) y Clarke, Leuridan y Williamson (2014) extienden su enfoque sobre la modelización a mecanismos que presentan retroalimentación causal.

…”

“…ABSTRACT: Casini, Illari, Russo, and Williamson (2011) suggest to model mechanisms by means of recursive Bayesian networks (RBNs) and Clarke, Leuridan, and Williamson (2014) extend their modeling approach to mechanisms featuring causal feedback. One of the main selling points of the RBN approach should be that it provides answers to questions concerning the effects of manipulation and control across the levels of a mechanism.…”

Mechanisms and Difference-Making

“…(Illari and Williamson 2012, p. 125). Casini, et al (2011) and Clarke et al (2014b) have put forward a scheme for modelling mechanisms using recursive or dynamic Bayes nets, which is quite consistent with the difference making view of mechanisms, given that causal modelling looks of course for probabilistic dependencies between variables. The authors do not draw the consequences as to the nature of mechanisms though; Clarke et al (2014b) note that Woodward's counterfactual approach and the epistemic account is consistent with Bayes nets, but choose to remain agnostic on this side (pp.…”