2024-11-26
10:48 |
A tribute to Klir’s research on entropy for belief functions
Jiroušek, Radim ; Kratochvíl, Václav
This is a short paper to remind us that although Prof. George Klir passed away eight years ago, his ideas are still alive. He was one of the first to have the idea to extend information theory beyond probability theory and to see the potential of fuzzy sets and belief functions. Some of the problems he raised have not yet been satisfactorily solved. In this paper, we take a fresh look at the problem of what properties entropy should have if it is to be considered a measure of information. Based on these requirements, we consider 24 definitions of entropy for belief functions and study how well they satisfy the proposed conditions.
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2024-11-26
10:48 |
On cardinalities of different degrees of Belief functions conjunctive conflictness
Daniel, Milan ; Kratochvíl, Václav
This paper examines mutual conflict behavior between belief function structures across different discernment frame sizes (\(\Omega\)). Through experiments on \(\Omega_2\) to \(\Omega_6\), we observe that as frame size increases, non-conflicting pairs and higher-order hidden conflicts become exceedingly relatively rare despite the exponential growth of cardinalities of their classes. The super-exponential growth of possible belief structures complicates exhaustive analysis, leading us to employ random sampling. Our findings reveal that the cardinality of a class of first-degree hidden conflicts (HC\(_1\)) grows faster than non-conflicts as frame size increases, highlighting the challenges and implications of applying belief function theory in complex decision-making scenarios.
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2024-11-26
10:48 |
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2024-11-10
00:01 |
On combinatorial descriptions of faces of the cone of supermodular functions
Studený, Milan
This paper is to relate five different ways of combinatorial description of non-empty faces of the cone of supermodular functions on the power set of a finite basic set N. Instead of this cone we consider its subcone of supermodular games; it is also a polyhedral cone and has the same (= isomorphic) lattice of faces. This step allows one to associate supermodular games with certain polytopes in N-dimensional real Euclidean space, known as cores (of these games) in context of cooperative game theory, or generalized permutohedra in context of polyhedral geometry. Non-empty faces of the supermodular cone then correspond to normal fans of those polytopes. This (basically) geometric way of description of faces of the cone then leads to the combinatorial ways of their description.\n\nThe first combinatorial way is to identify the faces with certain partitions of the set of enumerations of N, known as rank tests in context of algebraic statistics. The second combinatorial way is to identify faces with certain collections of posets on N, known as (complete) fans of posets in context of polyhedral geometry. The third combinatorial way is to identify the faces with certain coverings of the power set of N, introduced relatively recently in context of cooperative game theory under name core structures. The fourth combinatorial way is to identify the faces with certain formal conditional independence structures, introduced formerly in context of multivariate statistics under name structural semi-graphoids.\nThe fifth way is to identify the faces with certain subgraphs of the permutohedral graph, whose nodes are enumerations of N. We prove the equivalence of those six ways of description of non-empty faces of the supermodular cone. This result also allows one to describe the faces of the polyhedral cone of (rank functions of) polymatroids over N and the faces of the submodular cone over N: this is because these cones have the same face lattice as the supermodular cone over N. The respective polytopes are known as base polytopes in context of optimization and (poly)matroid theory.
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2024-11-02
00:00 |
Economic Policy Uncertainty in Europe: Spillovers and Common Shocks
Baxa, Jaromír ; Šestořád, T.
This paper proposes a novel approach to decompose the Economic Policy Uncertainty indices of European countries into the common and country-specific components using the time-varying total connectedness. Then, by employing a Bayesian panel VAR model, we assess how common and country-specific uncertainty shocks influence economic activity, prices, and monetary policy, with the shocks identified using zero and sign restrictions. Our results reveal that only common shocks have significant effects on all macroeconomic variables. This result is robust across alternative samples and structural identifications. Therefore, our findings imply that policymakers should focus on uncertainty shocks that are synchronized across countries.
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2024-11-02
00:00 |
Uncertain trends in economic policy uncertainty
Buliskeria, Nino ; Baxa, Jaromír ; Šestořád, T.
The news-based Economic Policy Uncertainty indices (EPU) of Germany, France, and the United Kingdom display discernible trends that can be found neither in other European countries nor in other uncertainty indicators. Therefore, we replicate the EPU index of European countries and show that these trends are sensitive to the rather arbitrary choice of normalizing the raw counts of news related to economic policy uncertainty by the count of all newspaper articles. We show that an alternative normalization by news on economic policy leads to different long-term dynamics\nwith less pronounced trends and markedly lower uncertainty during recent periods of uncertainty such as Brexit or the COVID-19 pandemic. Consequently, our results suggest that the effects of uncertainty related to these events on economic activity may have been overestimated.
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2024-09-14
00:04 |
Applicable Adaptive Discounted Fully Probabilistic Design of Decision Strategy
Molnárová, Soňa
The work addresses the issue of decreased utility of future rewards, referred to as discounting, while utilizing fully probabilistic design (FPD) of decision strategies. FPD obtains the optimal strategy for decision tasks using only probability distributions, which is its main asset. The standard way of solving decision tasks is provided by Markov decision processes (MDP), which FPD covers as a special case. Methods of solving discounted MDPs have already been introduced. However, the use of FPD might be advantageous when solving tasks with an unknown system model. Due to its probabilistic nature, FPD is able to obtain a more precise estimation of this model. After previously introducing discounting and system model estimation to FPD, the current work examines the effect of discounting on decision processes and its possible advantages when dealing with an unknown system model.
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2024-03-24
00:07 |
Central Moments and Risk-Sensitive Optimality in Markov Reward Processes
Sladký, Karel
In this note we consider discrete- and continuous-time Markov decision processes with finite state space. There is no doubt that usual optimality criteria examined in the literature on optimization of Markov reward processes, e.g. total discounted or mean reward, may be quite insufficient to select more sophisticated criteria that reflect also the variability-risk features of the problem. In this note we focus on models where the stream of rewards generated by the Markov process is evaluated by an exponential utility function with a given risk sensitivity coefficient (so-called risk-sensitive models).For the risk sensitive case, i.e. if the considered risk-sensitivity coefficient is non-zero, we establish explicit formulas for growth rate of expectation of the exponential utility function. Recall that in this case along with the total reward also it higher moments are taken into account. Using Taylor expansion of the utility function we present explicit formulas for calculating variance a higher central moments of the total reward generated by the |Markov reward process along with its asymptotic behaviour.
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2024-03-10
03:13 |
Statistical Method Selection Matters: Vanilla Methods in Regression May Yield Misleading Results
Kalina, Jan
The primary aim of this work is to illustrate the importance of the choice of the appropriate methods for the statistical analysis of economic data. Typically, there exist several alternative versions of common statistical methods for every statistical modeling task\nand the most habitually used (“vanilla”) versions may yield rather misleading results in nonstandard situations. Linear regression is considered here as the most fundamental econometric model. First, the analysis of a world tourism dataset is presented, where the number of international arrivals is modeled for 140 countries of the world as a response of 14 pillars (indicators) of the Travel and Tourism Competitiveness Index. Heteroscedasticity is clearly recognized in the dataset. However, the Aitken estimator, which would be the standard remedy in such a situation, is revealed here to be very inappropriate. Regression quantiles represent a much more suitable solution here. The second illustration with artificial data reveals standard regression quantiles to be unsuitable for data contaminated by outlying values. Their recently proposed robust version turns out to be much more appropriate. Both\nillustrations reveal that choosing suitable methods represent an important (and often difficult) part of the analysis of economic data.
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2024-03-10
03:13 |
Ambiguity in Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure via Wasserstein Metric
Kaňková, Vlasta
Many economic and financial applications lead to deterministic optimization problems depending on a probability measure. It happens very often (in applications) that these problems have to be solved on the data base. Point estimates of an optimal value and estimates of an optimal solutionset can be obtained by this approach. A consistency, a rate of convergence and normal properties, of these estimates, have been discussed (many times) not only under assumptions of independent data corresponding to the distributions with light tails, but also for weak dependent data and the distributions with heavy tails. However, it is also possible to estimate (on the data base) a confidence intervals and bounds for the optimal value and the optimal solutions. To analyze this approach we focus on a special case of static problems depending nonlineary on the probability measure. Stability results based on the Wasserstein metric and the Valander approach will be employed for the above mentioned analysis.
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