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Stochastic prediction procedure : ウィキペディア英語版
Stochastic prediction procedure

In probability theory and statistics, a stochastic prediction procedure is based on a Bernoulli space and may be used to make predictions under specific conditions. In contrast to a prediction obtained in traditional science, predictions obtained by means of a stochastic predíction procedure〔Elart von Collani (ed.),
''Defining the Science of Stochastics'', Heldermann Verlag, Lemgo, 2004.〕 meet a given reliability requirement and are optimal with respect to accuracy. A prediction procedure refers to a random variable ''X'' and predicts future events for ''X'' depending on the initial conditions or more precisely said on what is known about the initial conditions.
==Mathematical formulation==

A stochastic prediction procedure is a mathematical function〔Elart von Collani, The Need for a Standard for Making Predictions, ''Economic Quality Control'', Vol. 23, 287–299, 2008.〕 denoted A^_X defined on sets representing the possible initial conditions and having images that are the predictions. The function A^_X is derived meeting the following two requirements:
* The stochastic prediction procedure A^_X shall yield predictions which will occur with a probability of at least \beta where \beta is called the reliability level of A^_X.
* The stochastic prediction procedure A^_X shall yield predictions with optimal accuracy, where accuracy is defined by the size of the prediction.
The mathematical task consists of deriving a function A_X^ which meets the above formulated two requirements.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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