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Marginal problem, statistical estimation, and Möbius formula

Martin Janžura — 2007


A solution to the marginal problem is obtained in a form of parametric exponential (Gibbs–Markov) distribution, where the unknown parameters are obtained by an optimization procedure that agrees with the maximum likelihood (ML) estimate. With respect to a difficult performance of the method we propose also an alternative approach, providing the original basis of marginals can be appropriately extended. Then the (numerically feasible) solution can be obtained either by the maximum pseudo-likelihood...

An efficient estimator for Gibbs random fields

Martin Janžura — 2014


An efficient estimator for the expectation f P ̣ is constructed, where P is a Gibbs random field, and f is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer [6], and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.

A method for knowledge integration

Martin JanžuraPavel Boček — 1998


With the aid of Markov Chain Monte Carlo methods we can sample even from complex multi-dimensional distributions which cannot be exactly calculated. Thus, an application to the problem of knowledge integration (e. g. in expert systems) is straightforward.

Prognosis and optimization of homogeneous Markov message handling networks

Pavel BočekTomáš FeglarMartin JanžuraIgor Vajda — 2001


Message handling systems with finitely many servers are mathematically described as homogeneous Markov networks. For hierarchic networks is found a recursive algorithm evaluating after finitely many steps all steady state parameters. Applications to optimization of the system design and management are discussed, as well as a program product 5P (Program for Prognosis of Performance Parameters and Problems) based on the presented theoretical conclusions. The theoretic achievements as well as the practical...

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