Abstract
When applying probabilistic models to support decision making processes, the users have to strictly distinguish whether the impact of their decision changes the considered situation or not. In the former case it means that they are planing to make an intervention, and its respective impact cannot be estimated from a usual stochastic model but one has to use a causal model. The present paper thoroughly explains the difference between conditioning, which can be computed from both usual stochastic model and a causal model, and computing the effect of intervention, which can only be computed from a causal model. In the paper a new type of causal models, so called compositional causal models are introduced. Its great advantage is that both conditioning and the result of intervention are computed in very similar ways in these models. On an example, the paper illustrates that like in Pearl’s causal networks, also in the described compositional models one can consider models with hidden variables.
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Notes
- 1.
Instead of probability distributions we could speak, equivalently, about probability measures on \({\mathbb {X}}_N\). From the computational point of view it is important to realize that such a distribution/measure as a set function can be, thanks to the additivity of probability, represented by a point function \({\mathbb {X}}_N \rightarrow [0,1]\).
- 2.
Define \(\frac{0 \cdot 0}{0} = 0\).
- 3.
In [8] this degenerated distribution was denoted by \(\pi _{|u;\mathbf {a}}\), which appeared to be slightly misleading.
- 4.
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This work was supported in part by the National Science Foundation of the Czech Republic by grant no. GACR 15-00215S.
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Jiroušek, R. (2016). Brief Introduction to Causal Compositional Models. In: Huynh, VN., Kreinovich, V., Sriboonchitta, S. (eds) Causal Inference in Econometrics. Studies in Computational Intelligence, vol 622. Springer, Cham. https://doi.org/10.1007/978-3-319-27284-9_12
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