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1
Content available Philosophical foundations of statistical research
100%
Pociecha J.
Przegląd Statystyczny
|
2020
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tom 67
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nr 3
195-211
EN
Every researcher desires to uncover the truth about the object of the undertaken study. When conducting statistical research, however, scientists frequently give no deeper thought as to their motivation underlying the choice of the particular purpose and scope of the study, or the choice of analytical tools. The aim of this paper is to provide a reflection on the philosophical foundations of statistical research. The three basic understandings of the term ‘statistics’ are outlined, followed by a synthetic overview of the understanding of the concept of truth in the key branches of philosophy, with particular attention devoted to the understanding of truth in probabilistic terms. Subsequently, a short discussion is presented on the philosophical bases of statistics, touching upon such topics as determinism and indeterminism, chance and chaos, deductive and inductive reasoning, randomness and uncertainty, and the impact of the information revolution on the development of statistical methods, especially in the context of socio-economic research. The article concludes with the formulation of key questions regarding the future development of statistics.
2
Content available Nieprzemienne rachunki prawdopodobieństwa
86%
Heller M.
Zagadnienia Filozoficzne w Nauce
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2010
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nr 47
38-53
PL
The paper can be regarded as a short and informal introduction to noncommutative calculi of probability. The standard theory of probability is reformulated in the algebraic language. In this form it is readily generalized to that its version which is virtually present in quantum mechanics, and then generalized to the so-called free theory of probability. Noncommutative theory of probability is a pair (M, φ) where M is a von Neumann algebra, and φ a normal state on M which plays the role of a noncommutative probability measure. In the standard (commutative) theory of probability, there is, in principle, one mathematically interesting probability measure, namely the Lebesgue measure, whereas in the noncommutative theories there are many nonequivalent probability measures. Philosophical implications of this fact are briefly discussed.
3
Content available remote Applying the idea of fusionism in the probability theory
86%
Major M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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tom Vol. 12
69-76
EN
The solutions presented in this paper may serve as an illustration of the principle of internal integration, know as the idea of fusionism. In the paper we consider some problem. From an urn containing b white balls and c black ones are selected simultaneously some balls. If the balls are of the same colours one of the players wins, otherwise the other player is the winner. For which values of b and c is the game fair?
4
Content available Generalization of probability density of random variables
72%
Ziółkowski M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2009
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tom Vol. 14
163-172
EN
In this paper we present generalization of probability density of random variables. It is obvious that probability density is definite only for absolute continuous variables. However, in many practical applications we need to define the analogous concept also for variables of other types. It can be easily shown that we are able to generalize the concept of density using distributions, especially Dirac’s delta function.
5
Content available remote The granular computing in uncertain identification problems
72%
Orantek P. , Burczyński T.
Computer Assisted Mechanics and Engineering Sciences
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2007
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tom Vol. 14, No. 4
695-704
EN
The paper is devoted to applications of evolutionary algorithms in identification of structures being under the uncertain conditions. Uncertainties can occur in boundary conditions, in material parameters or in geometrical parameters of structures and are modelled by three kinds of granularity: interval mathematics, fuzzy sets and theory of probability. In order to formulate the optimization problem for such a class of problems by means of evolutionary algorithms the chromosomes are considered as interval, fuzzy and random vectors whose genes are represented by: (i) interval numbers, (ii) fuzzy numbers and (iii) random variables, respectively. Description of evolutionary algorithms with granular representation of data is presented in this paper. Various concepts of evolutionary operator such as a crossover and a mutation and methods of selections are described. In order to evaluate the fitness functions the interval, fuzzy and stochastic finite element methods are applied. Several numerical tests and examples of identification of uncertain parameters are presented.
6
Content available W obronie tak zwanych „pragmatycznych” uzasadnień probabilizmu
51%
Dziurosz-Serafinowicz P.
Studia Philosophiae Christianae
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2013
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tom 49
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nr 2
49-78
PL
Celem artykułu jest obrona tak zwanych „pragmatycznych” uzasadnień probabilizmu, tj. tezy mówiącej, iż stopnie przekonania racjonalnego podmiotu powinny być zgodne z aksjomatami teorii prawdopodobieństwa. Analizowane uzasadnienia to: Argument z Zakładu Holenderskiego (AZH) oraz Argument z Twierdzenia o Reprezentacji (ATR). Oba te argumenty natrafiają na szereg problemów istotnie podważających ich wartość, a tym samym probabilizm (operacjonizm, wymuszony zakład, itd.). W niniejszym artykule wykazane zostało, iż odpowiednia reinterpretacja tych argumentów prowadzi do wyeliminowania najistotniejszych problemów.
EN
The aim of this article is to defend the so-called “pragmatic” arguments for probabilism, i.e., a thesis which holds that a rational agent’s degrees of belief should be modeled by the theory of probability. Two such arguments are analyzed: Dutch-Book Argument (DBA) and Representation Theorem Argument (RTA). Both of these arguments encounter a number of problems that seriously undermine their value, and thus probabilism (operationalism, a forced bet, etc.) The article shows that amongst the various interpretations of DBA and RTA we can find those that are able to resolve the main difficulties that beset those arguments.
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