Imprecise Bayesian networks as causal models

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

Imprecise Bayesian Networks as Causal Models

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

Learning causal relations in multivariate time series data

Applying a probabilistic causal approach, we define a class of time series causal models (TSCM) based on stationary Bayesian networks. A TSCM can be seen as a structural VAR identified by the causal relations among the variables. We classify TSCMs into observationally equivalent classes by providing a necessary and sufficient condition for the observational equivalence. Applying an automated learning algorithm, we are able to consistently identify the data-generating causal structure up to the class of observational equivalence. In this way we can characterize the empirical testable causal orders among variables based on their observed time series data. It is shown that while an unconstrained VAR model does not imply any causal orders in the variables, a TSCM that contains some empirically testable causal orders implies a restricted SVAR model. We also discuss the relation between the probabilistic causal concept presented in TSCMs and the concept of Granger causality. It is demonstrated in an application example that this methodology can be used to construct structural equations with causal interpretation