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Towards a Supra-Bayesian Approach to Merging of Information
Sečkárová, Vladimíra
Merging of information given by different decision makers (DMs) has become a much discussed topic in recent years and many procedures were developed towards it. The main and the most discussed problem is the incompleteness of given information. Little attention is paid to the possible forms in which the DMs provide them; in most of cases arising procedures are working only for a particular type of information. Recently introduced Supra-Bayesian approach to merging of information brings a solution to two previously mentioned problems. All is based on a simple idea of unifying all given information into one form and treating the possible incompleteness. In this article, beside a brief repetition of the method, we show, that the constructed merger of information reduces to the Bayesian solution if information calls for this.
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Towards Distributed Bayesian Estimation A Short Note on Selected Aspects
Dedecius, Kamil ; Sečkárová, Vladimíra
The rapid development of ad-hoc wireless networks, sensor networks and similar calls for efficient estimation of common parameters of a linear or nonlinear model used to describe the operating environment. Therefore, the theory of collaborative distributed estimation has attained a very considerable focus in the past decade, however, mostly in the classical deterministic realm. We conjecture, that the consistent and versatile Bayesian decision making framework, whose applications range from the basic probability counting up to the nonlinear estimation theory, can significantly contribute to the distributed estimation theory. The limited extent of the paper allows to address the considered problem only very superficially and shortly. Therefore, we are forced to leave the rigorous approach in favor of a short survey indicating the arising possibilities appealing to the non- Bayesian literature.
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Variational Bayes in Distributed Fully Probabilistic Decision Making
Šmídl, Václav ; Tichý, Ondřej
We are concerned with design of decentralized control strategy for stochastic systems with global performance measure. It is possible to design optimal centralized control strategy, which often cannot be used in distributed way. The distributed strategy then has to be suboptimal (imperfect) in some sense. In this paper, we propose to optimize the centralized control strategy under the restriction of conditional independence of control inputs of distinct decision makers. Under this optimization, the main theorem for the Fully Probabilistic Design is closely related to that of the well known Variational Bayes estimation method. The resulting algorithm then requires communication between individual decision makers in the form of functions expressing moments of conditional probability densities. This contrasts to the classical Variational Bayes method where the moments are typically numerical.
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Ideal and non-ideal predictors in estimation of Bellman function
Zeman, Jan
The paper considers estimation of Bellman function using revision of the past decisions. The original approach is further extended by employing predictions coming from an imperfect predictor. The resulting algorithm speeds up the convergence of Bellman function estimation and improves the results quality. The potential of the approach is demonstrated on a futures market data.
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Automated Preferences Elicitation
Kárný, Miroslav ; Guy, Tatiana Valentine
Systems supporting decision making became almost inevitable in the modern complex world. Their efficiency depends on the sophisticated interfaces enabling a user take advantage of the support while respecting the increasing on-line information and incomplete, dynamically changing user’s preferences. The best decision making support is useless without the proper preference elicitation. The paper proposes a methodology supporting automatic learning of quantitative description of preferences. The proposed elicitation serves to fully probabilistic design, which is an extension of Bayesian decision making.
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