# Baye's Theorem in Networks

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#### anomit

##### In the zone
I COULD NOT MAKE OUT WHERE TO POST THIS. SO I POSTED IT HERE.IF NEEDED MOVE IT.

Notation:
1. P(X) means the probability of occurence of event X.

2. P(X|Y) means the probability of occurence of event X provided event Y has already happened

3. An means A with subscript n.

4. 'sum'is the summation function. *img301.imageshack.us/img301/6494/sigma4nw.jpg

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Introduction to Baye's Theorem
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Suppose for the occurence of an event A, n hypotheses are proposed like A1,A2,......,An. Now for 1<=k<=n,

P(Ak|A)= [P(Ak)*P(A|Ak)] / [sum i=1 to n {P(Ai)*P(A|Ai)} ]

The probabilites P(Ai), i=1,2,.....,n are called a priori probabilities and are known before beginning the experiment. Note these are the probabilities of occurence of the hypotheses.

The probabilities P(A|Ai) are called likelihoods as they show how likely A is to occur given a priori probabilities.

The probabilites P(Ai|A) are called posteriori probabilities as they are obtained after the experiment.

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The Mathematical Model
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*img325.imageshack.us/img325/5561/bayes2kk.th.png

The objective is to send data from A to B through the available nodes on the network.

Now P(Ci|A) implies probability of data being received correctly by Ci provided A sends it and P(A|Ci) implies probability of A sending the data provided Ci acknowledges the transmission. The acknowledgment will depend upon the state of the machine at node Ci. For e.g. if it is engaged in another transmission or is performing a resource hogging task it may not acknowledge the transmission. So P(A|Ci) is to be found out in real time by the network software.

Now applying the Baye's Theorem to the segment of data flow from A to Ci,

P(Ci|A)= [P(Ci)*P(A|Ci)] / [sum i=1 to 4 {P(Ci)*P(A|Ci)} ]

Before the beginning of data flow, the prbability of all Ci receiving data is equal i.e. P(C1)=P(C2)=P(C3)=P(C4)=1/4

From this the probability of Ci receiving the data correctly will be known and the node with P(Ci|A)=1 will recieve the datagrams. If none of them provides with absolute prbability i.e. 1 then the data will not be sent, A will wait for a few minutes or try other nodes in the network.

In the same way data from Ci will be sent to Di and at last to B.

SOMEBODY PLEASE ASK IF YOU HAVE ANY QUERIES RELATED TO THIS. I WOULD BE HAPPY TO ANSWER THEM

[ADDITION] Even handwriting recognition software make use of probability based model, which in this case is known as Hidden Markov Models.

#### abhishekkulkarni

##### Journeyman
Now I know a rip-off when I see one dude..........

#### theraven

##### Technomancer
its his own theory ....
and yes its a complex one at that ..

he might not be able to explain it properly but if u google it u will see researchers have been working on it .. and the many applications of baye's theorem

plz base your allegatiosn on something !

good work anomit .. but u know my views already

OP

#### anomit

##### In the zone
Thanks raven, you are among the saner ppl out here. 8)

Perhaps abhishek needs to understand the meaning of his own sig.. ..

#### abhishekkulkarni

##### Journeyman
Yeah . I am sorry.And don't worry , I understand the meaning of my sig completely which is the reason why I am apologizing ....

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