Q19

[DeanS]

I was wondering if the problem assumes that some learning has been done to determine P(D|h=f) for some population or if the person with the heart attack is the only person in D. Obviously, I may not understand Bayesian analysis.

[yaser]

Originally Posted by DeanS

I was wondering if the problem assumes that some learning has been done to determine P(D|h=f) for some population or if the person with the heart attack is the only person in D. Obviously, I may not understand Bayesian analysis.

The set is the set of available data points, so in this case it is that one person with a heart attack. This problem will help you understand the Bayesian reasoning better.

[DeanS]

Thank you very much for the quick reply. This has been an amazing course!!

[fgpancorbo]

I am still a bit confused about the setup of the problem. Is it correct to assume that what we are trying to determine is the underlying probability of somebody picked at random from the population to have a heart attack out of a single sample? If so, shouldn't be relevant? If a single point is all we have, call it the binary variable - equal to 1 if the patient has a heart attach; 0 if he doesn't-, that would be the probability of generating a single point with a patient having a heart attack, given the underlying probability that a person has a heart attack, right? In that case, the posterior is going to have two cases and . The question refers only to case right?

[yaser]

Originally Posted by fgpancorbo

Is it correct to assume that what we are trying to determine is the underlying probability of somebody picked at random from the population to have a heart attack out of a single sample?

(emphasis added)

It should be based on rater than out of. A source of confusion here is that is a probability, but then we have a probability distribution over . Let us just call the fraction of heart attacks in the population. Then the problem is addressing the probability distribution of that fraction - Is the fraction more likely to be 0.1 or 0.5 or 0.9 etc. The prior is that that fraction is equally likely to be anything (uniform probability). The problem then asks how this probability is modified if we get a sample of a single patient and they happen to have a heart attack.

If I have not answered your question, please ask again perhaps in those terms.

[fgpancorbo]

Originally Posted by yaser

(emphasis added)
It should be based on rater than out of. A source of confusion here is that is a probability, but then we have a probability distribution over . Let us just call the fraction of heart attacks in the population. Then the problem is addressing the probability distribution of that fraction - Is the fraction more likely to be 0.1 or 0.5 or 0.9 etc. The prior is that that fraction is equally likely to be anything (uniform probability). The problem then asks how this probability is modified if we get a sample of a single patient and they happen to have a heart attack.

I see. If my understanding is correct, I think that I can safely assume that , in which is made of a single random variable say , has a Bernoulli distribution with parameter . Is that right?