Mathematical models in decision making under uncertainty usually contain a large number of variables. The relations of independence and conditional independence enable the efficient construction of multidimensional models such as Bayesian networks or graphical Markov models. Real applications of these models require fast algorithms. A promising alternative to the graphical models are compositional models, which emphasize the computational aspects. Incomplete data or presence of various sources of uncertainty lead to the introduction of multidimensional models within non-additive approaches such as Dempster-Shafer theory or possibility theory. Applicability of such models depends on (conditional) independence that is not sufficiently studied in this context. The structural properties of non-additive models can also be determined by purely geometrical properties of a compact convex set of probability measures. The essence of the project is the research of the computational facets of multidimensional models from the viewpoint of their structural and geometrical properties. (en)
Cílem projektu je návrh metod pro efektivní výpočty v pravděpodobnostních multidimenzionálních modelech a získání nových poznatků umožňujících návrh výpočetních metod v rámci neaditivních multidimenzionálních modelů. Navržené výpočetní procedury budou ověřeny na reálných datech.