LFD Book Forum Q19
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#11
06-09-2013, 11:33 AM
 sptripathi Junior Member Join Date: Apr 2013 Posts: 8
Re: Q20

Need help in verifying if below understanding is correct ?

The Bayesian:
P(h=f | D) = P(D | h=f) * P(h=f) / P(D)

For this Q, we are given:
P(h=f) is uniform in [0,1]
D: one-person-with-heart-attack
Pick f = c (constant)

To simplify, I assume that h and f are a discrete random-variables with 10 possible values from (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0)
and each is equally likely with P=1/10. Essentially simplifying here to make P(h=f) a pmf which is actually a pdf.

Now:

P (D | h=f)
= Pr( one-person-with-heart-attack | h=f )
= Probability of one-person-with-heart-attack, given (h=f)
= c

( because if h=f were given, then the Prob of one picked person getting heart-attack is c, as defined by f )

Plug in above to get:
P(h=f | D) = c * P(h=f) / P(D)

Does above sound correct ?
Also P(D) =1 in this case ?

Thanks.