I have a dataset that gives information of a population. For instance, I know the fraction of people that are males (M) and that are within a certain age range (A), P(M & A), and then I know the fraction of males that live in a certain area (L), P(M & L).

What I'm interested in computing is P(M & A & L), which is the fraction of people that are males, are within a certain age range and live in a certain area.

Using Baye's formula I can say that

P(M & A & L) = P(M & A | L) P(L)

But my dataset only gives P(L) and not P(M & A | L). However, if I assumed that M & A and L are independent I have

P(M & A | L) = P(M & A) P(L)

How large is the error on P(M & A | L) if I make this assumption. Do you know of any other method I could use to estimate P(M & A | L) without assuming independence?

  • $\begingroup$ When you say you have a dataset, do you mean you only have those descriptors of the dataset (the ones you mentioned)? $\endgroup$
    – jamesmf
    Commented Nov 16, 2015 at 22:40
  • $\begingroup$ Yes, I mean exactly that. $\endgroup$
    – Brian
    Commented Nov 17, 2015 at 7:47

1 Answer 1


Bayes Theorem applies to conditional probabilities. $ P(A|B) = \frac{P(A).P(B|A)}{P(B)} $

The question you have posed is one of multiple events occurring together. If the events can be considered to be independent of each other, then,

P(A & B & C) = P(A).P(B).P(C)

In your question above,

P(M & A & L) = P(M & A).P(L) = P(M).P(A).P(L)

Based on the data provided by you, you should have these probabilities or can derive them by appropriate summations.

Let's say that .1 probability of males are between 1-10 years of age. Further, probability of males in location L is 0.2. So the probability of males in 1-10 years of age in Location L is 0.1 X 0.2 = 0.02 . This is assuming that all locations have the same probability distribution of age ranges.

  • $\begingroup$ thanks, but this is not what I'm asking. I'm interesting in knowing P(M & A | L) and I know that M and A are dependent (I also know P(M & A)), but I don't know if L depends on M & A, so they only thing I could do was to assume P(M & A | L) = P(M & A) P(L). So now I need to understand how bad this assumption is. $\endgroup$
    – Brian
    Commented Nov 18, 2015 at 9:02

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.