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Stochastic thinking may be looked upon as the opposite of causal thinking, however, the term stochastic thinking is rather ambiguous, because the meaning of ''stochastics'' is not clear. It can be looked upon as a branch of mathematics, or as "a cocktail of statistical ideas and probabilistic ideas",〔Andreas Eichler, Maria Gabriella Ottaviani, Floriane Wozniak and Dave Pratt, Introduction on "Stochastic Thinking", Proceedings of CERME 6, January 28th–February 1st 2009, Lyon France © INRP 2010, ().〕 or in the sense of Bernoulli Stochastics. Here stochastic thinking is explained in the sense of Bernoulli Stochastics.〔Elart von Collani (ed.), Defining the Science Stochastics, Heldermann Verlag, Lemgo, 2004.〕 ==Problem solving by stochastic thinking== Stochastic thinking for problem solving proceeds in three steps: * Stochastic thinking as basis for making decisions starts with observing an effect or problem which needs a decision. The effect is considered not as an isolated event but as an outcome of the whole system, which admitted its occurrence. Thus there are two problems, a minor one which is the actual problem, and a major one which is a problem of the system.〔Elart von Collani, ( "Science – the Great Illusion, Stochastics – the Promising Alternative." )〕 * The second step in stochastic thinking consists of identifying the necessary system changes to avoid the recurrence of the problem or at least to reduce its probability. The identification process starts with identifying "what is not" known and proceeds by modelling the relation between past and future which are to be changed. * The third step of stochastic thinking is to verify that the system changes are effective. The main difference between stochastic thinking and the prevailing causal thinking is the focus: Stochastic thinking focus on improving the whole, while causal thinking focus on improving parts. Stochastic thinking means to think in sets and structures, that is, to link the set representing the past and the sets representing the future by a set of probability distributions.〔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.〕 Improving the system means to reduce the probabilities of the occurrence of problems. 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「Stochastic thinking」の詳細全文を読む スポンサード リンク
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