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Tools for Decision Making under Uncertainty
Sečkárová, Vladimíra
In this paper we focus on two often considered distinct aims, namely maximizing of an utility function (e.g. an investment profit) and getting a more reliable global description of considered situation based on observed data (e.g. the final outcome of databases merging). In both cases we face the problem, that the data are unreliable, since they contain uncertainty caused by their source (i.e. human being). If we are looking for the optimum of the former aim, a game theory reformulation of the decision making task brings a smoother way to reach it. If the latter aim is considered, a merging procedure (also called fusion) processing the data should help us. This paper describes four recently developed methods dealing with decision making under uncertainty in two considered directions and one tool used for comparison of the fusion algorithms.
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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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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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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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A Note on Factorization of Belief Functions
Jiroušek, Radim ; Shenoy, P. P.
The paper compares two main types of factorization of belief functions (one based on the Dempster´s rule of combination, the other based on the operator of composition) and shows that both the approaches are equivalent to each other in case of unconditional factorization and shows what are the differences when overlapping factorization is studied.
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Conditioning and Flexibility in Compositional Models
Kratochvíl, Václav
Reasoning by cases or assumptions is a common form of human reasoning. In case of probability reasoning, this is modeled by conditioning of a multidimensional probability distribution. Compositional models are defined as a multidimensional distributions assembled from a (so called generating) sequence of lowdimensional probability distributions, with the help of operators of composition. In this case, the conditioning process can be viewed as a transformation of one generating sequence into another one. It appears that the conditioning process is simple when conditioning variable appears in the argument of the first distribution of the corresponding generating sequence. That is why we introduce the so called flexible sequences. Flexible sequences are those, which can be reordered in many ways that each variable can appears among arguments of the first distribution. In this paper, we study the problem of flexibility in light of the very recent solution of the equivalence problem.
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Hmotnostní korekce aplikované aktivity 18F-FDG při PET vyšetření
Bělohlávek, Otakar ; Skopalová, Magdaléna ; Boldyš, Jiří ; Dvořák, Jiří
Pozitronová emisní tomografie (PET) je medicínská zobrazovací technika umožňující zaznamenat prostorovou distribuci podaného radiofarmaka a zkoumat tak některé funkční procesy v těle pacienta. Cílem této práce je ukázat, že předpis v současnosti používaný k určení množství podané aktivity (potřebného množství radiofarmaka) vede k nekonstantní kvalitě PET snímků mezi pacienty s různými tělesnými parametry. Práce je retrospektivní studií využívající dat získaných v minulosti při běžných PET vyšetřeních.
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