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BUG: table has some problems in Bayes example #8

Closed buggsley closed 8 years ago

buggsley commented 8 years ago

The Bayesian example table and conditional probabilities seems to have a = problem.

One case in bottom right is duplicate.

Begin forwarded message: =20 From: "Chris J. Myers" myers@ece.utah.edu Subject: Re: HW 4 question Date: February 11, 2015 at 3:42:51 PM MST To: Cody MacDonald icmacd@gmail.com =20 Actually, the problem is you have this backwards. The entry is: =20 P(cro=3D1 | cI=3D0) =3D P(cI=3D0,cro=3D1) / P(cI=3D0) =3D .21/.52 =3D = .4 (book says .43 which I believe is a mistake). =20 Chris =20

On Feb 11, 2015, at 2:50 PM, Cody MacDonald <icmacd@gmail.com = mailto:icmacd@gmail.com> wrote: =20 Hi Chris, =20 Conceptually this helps yes, but I'm still having issues back = calculating to match the notes. or getting my two probabilities to add = to 1. =20 P(cI=3D0 | cro=3D1) =3D P(cI=3D0, cro=3D1) / P(cro=3D1) =3D .21/.35 =3D= .6 which doesn't equal what is in the notes and doesn't add up to 1 = with P( cro=3D0 | cI=3D0) =20 I didn't have problems anywhere else so I must be missing something. Any additional thoughts would be great. =20 Thank you, Cody =20 =20 On Wed, Feb 11, 2015 at 2:05 PM, Chris J. Myers <myers@ece.utah.edu = mailto:myers@ece.utah.edu> wrote: =20

On Feb 11, 2015, at 2:00 PM, Cody MacDonald <icmacd@gmail.com = mailto:icmacd@gmail.com> wrote:

Hi Chris,

I've been struggling to back calculate from the example in class. = Specifically when you are calculating the probability further down the = bayesian network.

Take cro from the example in class. The probability of cro=3D1 when = cI is 0 is calculated by adding up probabilities of this case given in = the chart and then dividing by what? I'm hung up on how to come to a = number to divide by in this more complicated case.

For the case you mention, you add the probabilities of all cases = where cro=3D1 and cI=3D0, then you divide by those where cro=3D1. =20 This makes use of Baye=E2=80=99s Rule which states: =20 P(ci | cro) =3D P(cI,cro) / P(cro) =20 So, your case is: =20 P(cI=3D0 | cro=3D1) =3D P(ci=3D0, cro=3D1) / P(cro=3D1) =20 Does this help? =20 Chris =20 =20 =20