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

[hughwf]

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, independent of the frequency of occurences of different b's.

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

Where N is a constant.

$$N = \frac{1}{\sum_{b = 0}^n p(a=1|b) }$$

$$p(a=1,b) = \frac{p(a=1|b)}{\sum_{b = 0}^n p(a=1|b)}$$

is that alright and does it have a name?

Many thanks in advance for any advice...

Hugh

 

[Enuma_Elish]

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
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