“Bayes' Formula”的概念、定义、习题解题方法及翻译-数学辞典

单词

Bayes' Formula

释义

Bayes' Formula

Let and be Sets. Conditional Probability requires that

(1)

where

denotes Intersection (``and''), and also that

(2)

and

(3)

Since (2) and (3) must be equal,

(4)

From (2) and (3),

(5)

Equating (5) with (2) gives

(6)

(7)

Now, let

(8)

is an event in

and

for

, then

(9)

(10)

From (5), this becomes

(11)

(12)

See also Conditional Probability, Independent Statistics

References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 810, 1992.

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