Can anyone explain the concept of Bayes theorm to me (preferably with an example)?
Unable to get the formula for calculation and even the examples given in books are complicated and not clear.
Assume:
event A = pass Level I of CFA
event B = pass Part I of FRM
P(A) = 0.38
P(B) = 0.47
P(A | B) = 0.57
Now say you wanna find the probability of passing the part I FRM given that you’ve already passed the first level of the CFA (instead of the other way around). That is P(B | A), and Bayes’ is one way to find it. This is called updating the prior (unconditional) probability of event B in light of the information you have (ie. given that you passed L.I of CFA).
P(B | A) = P(A|B) * P(B) / P(A) = 0.705
So, the likelihood of passing the FRM Part I given that you’ve passed the CFA Level I is 0.71. This is higher than the probability of passing the CFA Level I given that you’ve passed the FRM Part 1, which was assumed to be 0.57.
orang3eph wrote:
Assume:
event A = pass Level I of CFA
event B = pass Part I of FRM
P(A) = 0.38
P(B) = 0.47
P(A | B) = 0.57
Now say you wanna find the probability of passing the part I FRM given that you’ve already passed the first level of the CFA (instead of the other way around). That is P(B | A), and Bayes’ is one way to find it. This is called updating the prior (unconditional) probability of event B in light of the information you have (ie. given that you passed L.I of CFA).
P(B | A) = P(A|B) * P(B) / P(A) = 0.705
So, the likelihood of passing the FRM Part I given that you’ve passed the CFA Level I is 0.71. This is higher than the probability of passing the CFA Level I given that you’ve passed the FRM Part 1, which was assumed to be 0.57.
Thanks @Orang3eph the example was quite intuitive.
orang3eph wrote:
Assume:
event A = pass Level I of CFA
event B = pass Part I of FRM
P(A) = 0.38
P(B) = 0.47
P(A | B) = 0.57
Now say you wanna find the probability of passing the part I FRM given that you’ve already passed the first level of the CFA (instead of the other way around). That is P(B | A), and Bayes’ is one way to find it. This is called updating the prior (unconditional) probability of event B in light of the information you have (ie. given that you passed L.I of CFA).
P(B | A) = P(A|B) * P(B) / P(A) = 0.705
So, the likelihood of passing the FRM Part I given that you’ve passed the CFA Level I is 0.71. This is higher than the probability of passing the CFA Level I given that you’ve passed the FRM Part 1, which was assumed to be 0.57.
VERY NICE!
orang3eph wrote:
Assume:
event A = pass Level I of CFA
event B = pass Part I of FRM
P(A) = 0.38
P(B) = 0.47
P(A | B) = 0.57
Now say you wanna find the probability of passing the part I FRM given that you’ve already passed the first level of the CFA (instead of the other way around). That is P(B | A), and Bayes’ is one way to find it. This is called updating the prior (unconditional) probability of event B in light of the information you have (ie. given that you passed L.I of CFA).
P(B | A) = P(A|B) * P(B) / P(A) = 0.705
So, the likelihood of passing the FRM Part I given that you’ve passed the CFA Level I is 0.71. This is higher than the probability of passing the CFA Level I given that you’ve passed the FRM Part 1, which was assumed to be 0.57.
Very clear and well simple!!
Although this example is very simple and to a certain degree understandable but still,
the example and explanation “updating prior probability” given are not correct (correct me If Im wrong).
There are two interpretations of Bayes’ Formula and both interpretations are explained with two examples in schweser book 1 pages 220 and 221. One is related with updating prior probability and second is related with inverse representations of the probabilities concerning two events. First Interpretation is called “Bayesian interpretation” and second is called “frequentist interpretation” (this is not written in the books - Curriculum and Schweser- , and in level one, curriculum only gives an example of ”Bayesian interpretation” which is related with updating prior probability)
The example given above is related with second interpretation where you just find sth which is unknown in already known probs (just reversing and finding unknown). There is not any new info which affects the events and their probabilities. Even if you look at the formula, it is written there
Updated prob. = prior prob. of event X ( prob. of new info given event / unconditional prob. of new info)
The example given is also incorrect. Events must be mutually exclusive and exhaustive. Mentioning only Pass scenario is not exhaustive. There must be another event Bc (read C is complement of B, which means not B) which is, not passing part 1 of FRM.
So there would be 2 unconditional Probs., 4 conditional Probs., 4 Joint probs. and from them 2 unconditional probs.
I heard from a CFA charterholder that there is less probability that this Bayes’ formula will be tested in level 1 because this formula is coming again in level 2 or 3. So don’t worry about this in level 1 just remember the formula and that’s it. Very easy way to remember the formula is;
E stands for Event and
I stands for Info.
P(E | I) = P(I | E) / P(I) X prior/old P(E)
发表于 2013-4-28 08:42
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