PROBABILITY AND BAYES THEOREM
Probability : We can say , it is
description of the likelihood of some event occurring (ranging from 0 to
1).
2)Probabilities are the
numeric values between 0 and 1that represent ideal uncertainties.
3) Bayesian : The fundamental notion
of Bayesian statistics is that of conditional probability.
4) Bayes theorem is also know as
Bayes rules or Bayes law.
5) Bayes theorem describes the
probability of event based on the prior knowledge of the situation
or a condition that might be related with event .
6) Thomas Bayes , who first provided
an equation that allowed new evident to update belief in 1763.
7) An important goal for many
problem solving system is to collect evidence as the system goes along
and to modify its behavior on the basis of the evidence.
8) The fundamental notation of
Bayesian statistic is that of conditional probability.
9) It is a result that allowed new
information is used to update the conditional probability of the event.
10) The probability of an event A
conditional on another event B i.e P(A|B) is different from probability of B
conditional pm another event A i.e P(B|A)
Bayes theorem stated mathematically as the following equation
Bayes theorem stated mathematically as the following equation
 | |||||
| Fig : Bayes theorem equation |
Where A and Bare event and P(B) <> 0
P(A|B) conditional probability :
event A occurring given that B is true.
P(B|A) Conditional probability event
B occurring given that A is true.
P(A) and P(B) are the probabilities
of observing A and B independently of each other.
11)Next equation for the Bayes Theorem
11)Next equation for the Bayes Theorem
 | |
| Fig: Bayes theorem equation |
P(Hi\E) = Probability that
hypothesis Hi is true given evidence
P(E\Hi) = Probability that we will
observe evidence E given that hypothesis i is true.
P(Hi)= a prior probability that
hypothesis i is true in the absence of any specific evidence.
k= Number of possible
hypotheses
This expression as the probability of
hypothesis H of evidence E.To solve this we need to take into account the prior
probability of Hand the ex tented to W provides evidence of H.
Consider the one of the example
Suppose we are interested to
examining the geological evidence at a particular location to determine
that it is a good place to dig to find a coal. So we check the prior
probabilities of finding coal or certain physical characteristic will be
observed.. Then we use Bayes' formula to compute, from the evidence we collect how
likely that the various minerals are present.
The key to using Bayes' theorem as a
basis for uncertain reasoning is to recognize exactly what it says.
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