**1241**

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**Second Order Optimality in Markov and Semi-Markov Decision Processes**

Sladký, Karel

2019 - English
Semi-Markov decision processes can be considered as an extension of discrete- and continuous-time Markov reward models. Unfortunately, traditional optimality criteria as long-run average reward per time may be quite insufficient to characterize the problem from the point of a decision maker. To this end it may be preferable if not necessary to select more sophisticated criteria that also reflect variability-risk features of the problem. Perhaps the best known approaches stem from the classical work of Markowitz on mean-variance selection rules, i.e. we optimize the weighted sum of average or total reward and its variance. Such approach has been already studied for very special classes of semi-Markov decision processes, in particular, for Markov decision processes in discrete - and continuous-time setting. In this note these approaches are summarized and possible extensions to the wider class of semi-Markov decision processes is discussed. Attention is mostly restricted to uncontrolled models in which the chain is aperiodic and contains a single class of recurrent states. Considering finite time horizons, explicit formulas for the first and second moments of total reward as well as for the corresponding variance are produced.
Keywords:
*semi-Markov processes with rewards; discrete and continuous-time Markov reward chains; risk-sensitive optimality; average reward and variance over time*
Fulltext is available at external website.
Second Order Optimality in Markov and Semi-Markov Decision Processes

Semi-Markov decision processes can be considered as an extension of discrete- and continuous-time Markov reward models. Unfortunately, traditional optimality criteria as long-run average reward per ...

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**Mean-Risk Optimization Problem via Scalarization, Stochastic Dominance, Empirical Estimates**

Kaňková, Vlasta

2019 - English
Many economic and financial situations depend simultaneously on a random element and on a decision parameter. Mostly it is possible to influence the above mentioned situation by an optimization model depending on a probability measure. We focus on a special case of one-stage two objective stochastic “Mean-Risk problem”. Of course to determine optimal solution simultaneously with respect to the both criteria is mostly impossible. Consequently, it is necessary to employ some approaches. A few of them are known (from the literature), however two of them are very important: first of them is based on a scalarizing technique and the second one is based on the stochastic dominance. First approach has been suggested (in special case) by Markowitz, the second approach is based on the second order stochastic dominance. The last approach corresponds (under some assumptions) to partial order in the set of the utility functions.\nThe aim of the contribution is to deal with the both main above mentioned approaches. First, we repeat their properties and further we try to suggest possibility to improve the both values simultaneously with respect to the both criteria. However, we focus mainly on the case when probability characteristics has to be estimated on the data base.
Keywords:
*Two-objective stochastic optimization problems; scalarization; stochastic dominance; empirical estimates*
Fulltext is available at external website.
Mean-Risk Optimization Problem via Scalarization, Stochastic Dominance, Empirical Estimates

Many economic and financial situations depend simultaneously on a random element and on a decision parameter. Mostly it is possible to influence the above mentioned situation by an optimization model ...

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**Proceedings of the 22nd Czech-Japan Seminar on Data Analysis and Decision Making**

Inuiguchi, M.; Jiroušek, Radim; Kratochvíl, Václav

2019 - English
The history of the series of the Czech-Japan seminars started in 1999. Thus, it is now more than 20 years ago when the first Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty was held in JAIST, Hokuriku. Since that time, these seminars were held in eleven splendid places in Japan, offering the Czech participants possibility to discover different parts of the Japanese islands. In reciprocity, it was the goal of the Czech partners organizing the past ten seminars to show the beauty of Czechia to Japanese colleagues, who, during the long Japan–Czech cooperation, became our close friends. This is also why the seminar has never visited one place two times.
Keywords:
*Decision Making; Data Analysis; Uncertainty*
Fulltext is available at external website.
Proceedings of the 22nd Czech-Japan Seminar on Data Analysis and Decision Making

The history of the series of the Czech-Japan seminars started in 1999. Thus, it is now more than 20 years ago when the first Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty ...

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**A Step towards Upper-bound of Conflict of Belief Functions based on Non-conflicting Parts**

Daniel, M.; Kratochvíl, Václav

2019 - English
This study compares the size of conflict based on non-conflicting parts of belief functions $Conf$ with the sum of all multiples of bbms of disjoint focal elements of belief functions in question. In general, we make an effort to reach a simple upper bound function for $Conf$. (Nevertheless, the maximal value of conflict is, of course, equal to 1 for fully conflicting belief functions). We apply both theoretical research using the recent results on belief functions and also experimental computational approach here.
Keywords:
*Belief functions; Dempster-Shafer theory; Uncertainty; Conflict-ing belief masses; Conflict between belief functions; Hidden conflict*
Fulltext is available at external website.
A Step towards Upper-bound of Conflict of Belief Functions based on Non-conflicting Parts

This study compares the size of conflict based on non-conflicting parts of belief functions $Conf$ with the sum of all multiples of bbms of disjoint focal elements of belief functions in question. In ...

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**Theory of SSB Representation of Preferences Revised**

Pištěk, Miroslav

2019 - English
A continuous skew-symmetric bilinear (SSB) representation of preferences has recently been proposed in a topological vector space, assuming a weaker notion of convexity of preferences than in the classical (algebraic) case. Equipping a linear vector space with the so-called inductive linear topology, we derive the algebraic SSB representation on a topological basis, thus weakening\nthe convexity assumption. Such a unifying approach to SSB representation permits also to fully discuss the relationship of topological and algebraic axioms of continuity, and leads to a stronger existence result for a maximal element. By applying this theory to probability measures we show the existence of a maximal preferred measure for an infinite set of pure outcomes, thus generalizing all available existence theorems in this context.
Keywords:
*probability measures; inductive linear topology; topological vector space*
Fulltext is available at external website.
Theory of SSB Representation of Preferences Revised

A continuous skew-symmetric bilinear (SSB) representation of preferences has recently been proposed in a topological vector space, assuming a weaker notion of convexity of preferences than in the ...

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**Preliminary Results from Experiments on the Behavior under Ambiguity**

Jiroušek, Radim; Kratochvíl, Václav

2019 - English
In the literature, some experiments proving that human decision-makers manifest an ambiguity aversion are described. In our knowledge, no one has studied a possibility to measure the strength of this aversion and its stability in time. The research, we have recently started to realize should find out answers to these and similar questions. The goal of this paper is to present some preliminary results to initiate a discussion that should help us to modify either the process of data collection and/or the analysis of the collected data.
Keywords:
*decision making; data analysis; measure*
Fulltext is available at external website.
Preliminary Results from Experiments on the Behavior under Ambiguity

In the literature, some experiments proving that human decision-makers manifest an ambiguity aversion are described. In our knowledge, no one has studied a possibility to measure the strength of this ...

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**Approximate Bayesian state estimation and output prediction using state-space model with uniform noise**

Lainová, Eva; Kuklišová Pavelková, Lenka; Jirsa, Ladislav

2019 - English
This paper contributes to the problem of approximate Bayesian state estimation and output prediction using state space model with uniformly distributed noise. Algorithms for Bayesian filtering and output prediction for states uniformly distributed on an orthotopic support and Bayesian filtering and output prediction for states uniformly distributed on a parallelotopic support are presented and compared.
Keywords:
*Bayesian filtering; state estimation; output prediction; uniform noise; parallelotopic support; orthotopic support*
Fulltext is available at external website.
Approximate Bayesian state estimation and output prediction using state-space model with uniform noise

This paper contributes to the problem of approximate Bayesian state estimation and output prediction using state space model with uniformly distributed noise. Algorithms for Bayesian filtering and ...

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**On Experimental Part of Behavior under Ambiguity**

Kratochvíl, Václav; Jiroušek, Radim

2019 - English
People are risk-takers, risk-averse, or neutral. In the literature, one can find experiments illustrating the ambiguity aversion of human decision-makers. Recently, a personal coefficient of ambiguity aversion has been introduced. We have decided to measure the coefficient and its stability during the time. In this paper, we describe performed experiments and their structure to launch a discussion of possible design weaknesses or to suggest other methods of measuring it.
Keywords:
*decision making; uncertainty; personal coefficient*
Fulltext is available at external website.
On Experimental Part of Behavior under Ambiguity

People are risk-takers, risk-averse, or neutral. In the literature, one can find experiments illustrating the ambiguity aversion of human decision-makers. Recently, a personal coefficient of ...

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**Bayesian Networks for the Analysis of Subjective Well-Being**

Švorc, Jan; Vomlel, Jiří

2019 - English
We use Bayesian Networks to model the influence of diverse socio-economic factors on subjective well-being and their interrelations. The classical statistical analysis aims at finding significant explanatory variables, while Bayesian Networks can also help sociologists to explain and visualize the problem in its complexity. Using Bayesian Networks the sociologists may get a deeper insight into the interplay of all measured factors and their influence on the variable of a special interest. In the paper we present several Bayesian Network models -- each being optimal from a different perspective. We show how important it is to pay a special attention to a local structure of conditional probability tables. Finally, we present results of an experimental evaluation of the suggested approaches based on real data from a large international survey. We believe that the suggested approach is well applicable to other sociological problems and that Bayesian Networks represent a new valuable tool for sociological research.
Keywords:
*Bayesian networks; Subjective well-being*
Fulltext is available at external website.
Bayesian Networks for the Analysis of Subjective Well-Being

We use Bayesian Networks to model the influence of diverse socio-economic factors on subjective well-being and their interrelations. The classical statistical analysis aims at finding significant ...

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**Application of the Cox regression model with time dependent parameters to unemployment data**

Volf, Petr

2019 - English
The contribution deals with the application of statistical survival analysis with the intensity described by a generalized version of Cox regression model with time dependent parameters. A\nmethod of model components non-parametric estimation is recalled, the flexibility of result is assessed with a goodness-of-fit test based on martingale residuals. The application\nconcerns to the real data representing the job opportunities development and reduction, during a given period. The risk of leaving the company is changing in time and depends also on the age of employees and their time with company. Both these covariates are considered and their impact to the risk analyzed.
Keywords:
*mathematical statistics; survival analysis; unemployment data*
Fulltext is available at external website.
Application of the Cox regression model with time dependent parameters to unemployment data

The contribution deals with the application of statistical survival analysis with the intensity described by a generalized version of Cox regression model with time dependent parameters. A\nmethod of ...

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