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In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement : "If P then Q ", Q is necessary for P , because the truth of Q is guaranteed by the truth of P .
Pages in category "Necessity and sufficiency" The following 5 pages are in this category, out of 5 total. This list may not reflect recent changes. ...
Sufficiency finds a useful application in the Rao–Blackwell theorem, which states that if g(X) is any kind of estimator of θ, then typically the conditional expectation of g(X) given sufficient statistic T(X) is a better (in the sense of having lower variance) estimator of θ, and is never worse.
Possibility theory is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory.It uses measures of possibility and necessity between 0 and 1, ranging from impossible to possible and unnecessary to necessary, respectively.
For this reason, or perhaps for their familiarity and simplicity, necessity and possibility are often casually treated as the subject matter of modal logic. Moreover, it is easier to make sense of relativizing necessity, e.g. to legal, physical, nomological , epistemic , and so on, than it is to make sense of relativizing other notions.
Modal fallacy – confusing necessity with sufficiency. A condition X is necessary for Y if X is required for even the possibility of Y. X does not bring about Y by itself, but if there is no X, there will be no Y. For example, oxygen is necessary for fire.
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