In article <[EMAIL PROTECTED]>, [EMAIL PROTECTED] (Eddie Jaye) wrote:
> Bill Jefferys <[EMAIL PROTECTED]> wrote in message > news:<[EMAIL PROTECTED]>... > > In article <[EMAIL PROTECTED]>, > > [EMAIL PROTECTED] (Eddie Jaye) wrote: > > > > > Hi Bill > > thank you for your response. You say that as the questions stands > that it cannot be solved or calculated using the fisrt 3 lines of > explanation. prehaps i should have made myself clearer. what i mean to > say what is the probability of A given the evidence of B and C and D > which are all conditional probalities and dependent on A but which ARE > NOT mutually exclusive and independent on each other. Thus as i > mentioned before a student can belong to a series of stastics that are > grouped together in terms of age, gender, ethnicity and so on. if the > solution to this problem is already in some form provided by you as > given below > > P(A|B&C&D)=P(B|A&C&D)P(C|A&D)P(A|D)/[P(B|C&D)P(C|D)], > > i do apologise and then ask if you could tell me where i can find the > other mathetical formulas you hinted about. and politely ask for a > brief explaination as to why it cannot be solved soley using the input > sources given. I have replied to Eddie off-list. There seems to be some confusion here. Eddie wants to derive P(A|B&C&D) from P(A|B), P(A|C) and P(A|D). Now of course there is the well-known formula P(B&C&D|A)=P(B|A)P(C|A)P(D|A) when B, C and D are independent; but there is not to my knowledge anything analogous, involving only P(B|A), P(C|A) and P(D|A), when you switch the order. One does have, by an obvious application of Bayes' rule to each term in the above formula: P(A|B&C&D)=P(A|B)P(A|C)P(A|D)xP(B)P(C)P(D)/(P(B&C&D)P(A)^2), But this involves additional quantities not mentioned by Eddie. If B, C and D are unconditionally independent, one can further simplify this by factorizing P(B&C&D). The result is P(A|B&C&D)=P(A|B)P(A|C)P(A|D)/P(A)^2. That's as close as I can get to what you want, Eddie! You need some strong assumptions about independence, and you need the unconditional P(A), in addition to what you stated originally. Bill -- Bill Jefferys/Department of Astronomy/University of Texas/Austin, TX 78712 Email: replace 'warthog' with 'clyde' | Homepage: http://quasar.as.utexas.edu I report spammers to [EMAIL PROTECTED] Finger for PGP Key: F7 11 FB 82 C6 21 D8 95 2E BD F7 6E 99 89 E1 82 Unlawful to use this email address for unsolicited ads: USC Title 47 Sec 227 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
