Calculating Conditional Probability for a given Event (a=1)

In summary, the conversation discusses Bayes' Law and the calculation of p(a=1|b) given the data for p(a=1 and b) and p(b). The person is trying to find the probability of event a=1 occurring at a certain b, independent of the frequency of occurrences of different b's. They then go on to explain how they normalize their data to find the desired probability and inquire about whether this formula has a name.
  • #1
hughwf
1
0
Hello,

This question relates to Bayes law. I think my problem is I am not sure of the name of the thing I am trying to derive...

I have 2 variables a and b.
a = 1 or 0, b = 0...n
I have the data to calculate;
p(a = 1 and b) p(b)
for any b. Hence I can find p(a=1|b) = p(a = 1 and b)/p(b)

What I want is p(a=1|b), but 'given' that a = 1. I don't want this to be affected by p(b), hence I am not trying to find p(b|a=1).
To explain further what i mean; If event a = 1, what is the prob it will happen at a certain b, independant of the frequency of occurences of different b's.

So I normalise;
[tex]\sum_{b = 0}^n p(a=1|b).N = 1[/tex]

Where N is a constant.

[tex] N = \frac{1}{\sum_{b = 0}^n p(a=1|b) }[/tex]

[tex] p(a=1,b) = \frac{p(a=1|b)}{\sum_{b = 0}^n p(a=1|b)}[/tex]

is that alright and does it have a name?

Many thanks in advance for any advice...

Hugh
 
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  • #2
According to Bayes' Law p[a|B]p = p[a,B] = p[B|a]p[a]; in order for your formula to be Bayesian it must conform with this.

EnumaElish
___________________________________________
I would definitely have logged in as EnumaElish had PF administration awarded that account the privilege of posting replies, after I reset my e-mail address Tuesday, October 28, 2008.
 

Related to Calculating Conditional Probability for a given Event (a=1)

What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the two events occurring together by the probability of the first event occurring.

How is conditional probability different from regular probability?

Regular probability is the likelihood of an event occurring without any prior information. Conditional probability takes into account additional information, such as the occurrence of another event, when calculating the likelihood of an event.

What is the formula for calculating conditional probability?

The formula for calculating conditional probability is P(A|B) = P(A and B) / P(B), where A and B are two events and P(A|B) is the probability of event A occurring given that event B has occurred.

How can conditional probability be applied in real life?

Conditional probability can be applied in various fields, such as medicine, economics, and insurance. For example, in medicine, conditional probability can be used to calculate the likelihood of a patient having a certain disease given their symptoms and medical history.

What are some common misconceptions about conditional probability?

One common misconception about conditional probability is that it is the same as regular probability. Another misconception is that the probability of an event occuring is always higher when another event has already occurred, which is not always the case.

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