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On Three Conditioning Rules in Evidence Theory
Vejnarová, Jiřina
In evidence theory various rules were proposed to define conditional beliefs and/or plausibilities (or basic assignments). However, there exist no generally accepted criteria along which these rules can be compared. In this paper we concentrate to three of them (Dempster's conditioning rule, focusing and the approach based on lower and upper envelopes of sets of conditional probabilities) to study their mutual relationship. A new conditional rule for variables is presented afterwards and its correctness is proven.
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Approximate Bayesian Recursive Estimation: On Approximation Errors
Kárný, Miroslav ; Dedecius, Kamil
Adaptive systems rely on recursive estimation of a firmly bounded complex- ity. As a rule, they have to use an approximation of the posterior proba- bility density function (pdf), which comprises unreduced information about the estimated parameter. In recursive setting, the latest approximate pdf is updated using the learnt system model and the newest data and then ap- proximated. The fact that approximation errors may accumulate over time course is mostly neglected in the estimator design and, at most, checked ex post. The paper inspects this problem.
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Construction of Mass Migration Process
Fajfrová, Lucie ; Saada, E.
A general model of conservative particle systems on $/Zd$ is treated in this report. We call it the Mass Migration Process. We bring out a construction of an appropriate Markov process, we set conditions on existence, attractiveness and we present many particular examples.
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Separable Utility Functions in Dynamic Economic Models
Sladký, Karel
In this note we study properties of utility functions suitable for performance evaluation of dynamic economic models under uncertainty. At first, we summarize basic properties of utility functions, at second we show how exponential utility functions can be employed in dynamic models where not only expectation but also the risk are considered. Special attention is focused on properties of the expected utility and the corresponding certainty equivalents if the stream of obtained rewards is governed by Markov dependence and evaluated by exponential utility functions.
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Approximate Dynamic Programming based on High Dimensional Model Representation
Pištěk, Miroslav
In this article, an efficient algorithm for an optimal decision strategy approximation is introduced. The proposed approximation of the Bellman equation is based on HDMR technique. This non-parametric function approximation is used not only to reduce memory demands necessary to store Bellman function, but also to allow its fast approximate minimization. On that account, a clear connection between HDMR minimization and discrete optimization is newly established. In each time step of the backward evaluation of the Bellman function, we relax the parameterized discrete minimization subproblem to obtain parameterized trust region problem. We observe that the involved matrix is the same for all parameters owning to the structure of HDMR approximation. We find eigenvalue decomposition of this matrix to solve all trust region problems effectively.
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