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Modeling and Inverse Problems in the Presence of Uncertainty
book

Modeling and Inverse Problems in the Presence of Uncertainty

by H. T. Banks, Shuhua Hu, W. Clayton Thompson
April 2014
Intermediate to advanced content levelIntermediate to advanced
405 pages
13h
English
Chapman and Hall/CRC
Content preview from Modeling and Inverse Problems in the Presence of Uncertainty
8 Modeling and Inverse Problems in the Presence of Uncertainty
and
Prob{A
k
|B} =
Prob{A
k
, B}
Prob{B}
=
Prob{B|A
k
}Prob{A
k
}
P
l
j=1
Prob{B|A
j
}Prob{A
j
}
. (2.9)
Equation (2.8) is often called the law of total probability. Equation (2.9) is
known as Bayes’ formula or Bayes’ Theorem. Here Prob{A
k
} is called a prior
probability of event A
k
, Prob{B|A
k
} is called the likelihood of B given A
k
, and
Prob{A
k
|B} is called a posterior probability of event A
k
obtained by using
the information g ained from B.
2.2 Random Variables and Their Associated Distribu-
tion Functions
In most applications of probability theory, we are not interested in the
details associated with each sample ...
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Publisher Resources

ISBN: 9781482206432