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Bernoulli stochastics is a new branch of science and deals with human uncertainty of future developments.〔Elart von Collani, State of the Art and Future of Stochastics, in: Ivor Grattan-Guinness and B.S. Yadav (eds): ''History of Mathematical Sciences'', Hindustan Book Agency, New Delhi, pp. 171–190, 2004.〕 It aims at developing quantitative models of the transition from past to future for making reliable and accurate predictions. Bernoulli stochastics should not be confused with stochastics which is a special branch of mathematics covering probability theory, the theory of stochastic processes and mathematical statistics. Bernoulli stochastics is based on Jakob Bernoulli's quantification of randomness and it was mainly developed by Elart von Collani〔Elart von Collani (ed), Defining the Science of Stochastics, Helderman, Lemgo,2004.〕〔Elart von Collani and Xiaomin Zhai, ''Stochastics'', Beijing Publisher Group, Beijing, 2005 (in Chinese).〕 during the last two decades. Since uncertainty of the future constitutes one of the main problems of mankind, Bernoulli stochastics adopts an exceptional position as it provides the means to define and measure uncertainty and thus enables to handle risks adequately for preventing catastrophic developments. ==Scope== Uncertainty of the future constitutes not only the main problem for individuals but also for societies and science. Therefore, Bernoulli stochastics which develops models of uncertainty can be considered as a universal approach for solving problems since it provides the rules how to deal with uncertainty and the indeterminate future. The quantitative models of uncertainty developed according to the rules of Bernoulli stochastics include the two sources of human uncertainty of future development. These are human ignorance about the past or the initial conditions and randomness which affects the future. Ignorance represents the internal source of human uncertainty, while randomness is the external source. Ignorance is characteristic for man, while randomness is characteristic for universe. There are two types of methods in Bernoulli stochastics. The first type of method enables a glance into the future, while the second type enables to look into the past. The first type is called stochastic prediction procedure, the second type stochastic measurement procedure. These stochastic procedures which are based on a model that objectively reflects reality aim at replacing belief and opinion which are still the prevailing means to overcome the problems generated by uncertainty and risks. For understanding and applying Bernoulli stochastics the prevailing causal thinking must be abandoned in favor of stochastic thinking.〔Elart von Collani, ("Response to ‘Desired and Feared—What Do We Do Now and Over the Next 50 Years’ by Xiao-Li Meng" ), ''The American Statistician'', 2010, 64(1): 23–25.〕 Actually, adopting stochastic thinking constitutes a major difficulty in understanding and applying Bernoulli stochastics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bernoulli stochastics」の詳細全文を読む スポンサード リンク
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