Abstract
This article considers the extent to which Bayesian networks with imprecise probabilities, which are used in statistics and computer science for predictive purposes, can be used to represent causal structure. It is argued that the adequacy conditions for causal representation in the precise context—the Causal Markov Condition and Minimality—do not readily translate into the imprecise context. Crucial to this argument is the fact that the independence relation between random variables can be understood in several different ways when the joint probability distribution over those variables is imprecise, none of which provides a compelling basis for the causal interpretation of imprecise Bayes nets. I conclude that there are serious limits to the use of imprecise Bayesian networks to represent causal structure.
Highlights
Probabilistic models in many scientific contexts are often characterized by ambiguity
For one set of inputs, Antonucci et al.’s model determines that the probability of a low-severity flow is in the interval [0.08, 0.30], that the probability of a medium-severity flow is in the interval [0.23, 0.32], and that the probability of a high severity flow is in the interval [0.46, 0.69] ([1], p. 7). (In the example cited, these probability intervals are calculated using the imprecise Bayes nets techniques discussed in this paper.)
I have shown that the adequacy conditions used in the causal interpretation of precise
Summary
Probabilistic models in many scientific contexts are often characterized by ambiguity. I argue that neither strong nor epistemic independence can be neatly “plugged in” to CMC and Minimality to yield a compelling set of adequacy conditions for the causal interpretation of IBNs without troubling implications These implications can be avoided by positing further restrictions on the probabilistic features of IBNs, but such restrictions demonstrate the extent to which many otherwise innocuous imprecise probabilistic models cannot be interpreted causally. I present the basic formalism for IBNs. In Section 4, I illustrate the distinction between strong and epistemic independence between random variables in an imprecise probabilistic context.
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