Abstract
In probability theory, as well as in other alternative uncertainty theories, the existence of efficient processes for the multidimensional model construction is a basic assumption making the application of the respective theory to practical problems possible. Most of the approaches are based on the idea that a multidimensional model is set up from a great number of smaller parts representing pieces of local knowledge. Such a process is called knowledge integration. In the probabilistic framework, it means that a multidimensional probability distribution is aggregated from a number of low-dimensional (possibly conditional) ones.
Historically, two different operators of aggregation were designed for this purpose: the operator of combination, and the operator of composition. This paper, using the simplest possible framework of discrete probability theory, answers some natural questions like: What is the difference between these operators? Is there a need for both of them? Are there situations when they can be mutually interchanged?
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Notes
- 1.
An undirected graph containing no loops and no multiple edges.
- 2.
Define \(\frac{0 \cdot 0}{0} = 0\).
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Acknowledgements
This work has been supported in part by funds from grant GAČR 15-00215S to the first author, and from the Ronald G. Harper Distinguished Professorship at the University of Kansas to the second author.
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Jiroušek, R., Shenoy, P.P. (2018). Combination and Composition in Probabilistic Models. In: Anh, L., Dong, L., Kreinovich, V., Thach, N. (eds) Econometrics for Financial Applications. ECONVN 2018. Studies in Computational Intelligence, vol 760. Springer, Cham. https://doi.org/10.1007/978-3-319-73150-6_9
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