Bayes, Theorem
المؤلف:
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T.
المصدر:
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press
الجزء والصفحة:
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6-3-2021
2021
Bayes' Theorem
Let 
and 
be sets. Conditional probability requires that
 |
(1)
|
where 
denotes intersection ("and"), and also that
 |
(2)
|
Therefore,
 |
(3)
|
Now, let
 |
(4)
|
so 
is an event in 
and 
for 
, then
 |
(5)
|
 |
(6)
|
But this can be written
 |
(7)
|
so
 |
(8)
|
(Papoulis 1984, pp. 38-39).
REFERENCES:
Papoulis, A. "Bayes' Theorem in Statistics" and "Bayes' Theorem in Statistics (Reexamined)." §3-5 and 4-4 in Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 38-39, 78-81, and 112-114, 1984.
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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