Help on Example 10.9 Race Equality in U.S. ...

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Help on Example 10.9 Race Equality in U.S. ...

Jun Wang
First of all, this book is great to learn Bayesian stats.

May I ask for help in working out the "results for all hypotheses, after normalization" in P332 (e.g., P(D|H1:S independent of V  and D)=0.007).
I can follow the steps in Box 10.9, but cannot work out the results for the  hypotheses.  

Thanks !

Jun Wang
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Re: Help on Example 10.9 Race Equality in U.S. ...

norman@eecs.qmul.ac.uk
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Jun Wang

Thanks for your kind comments on the book.

The results on page 322 'after normalization' come from the following:

-The joint probability for the data in the case of H1 (line 3, page 331) is shown to be 4.26E-6
-The joint probability for the data in the case of H2 (middle of page 331) is shown to be 4.67E-5
-The joint probability for the data in the case of H3 (line 1, page 332) is shown to be 1.93E-4
-The joint probability for the data in the case of H4 (last line of box, page 331) is shown to be 3.78E-4

When you normalize the four values 4.26E-6, 4.67E-5, 1.93E-4, 3.78E-4 (i.e. scale them to sum to 1) you end up (to 3 decimal places) with 0.007, 0.075, 0.310, 0.608
and these are the four values respectively for the probability of the data given H1, H2, H3, and H4.

What is confusing (and we will put thisin the errata) is that when we write P(D | H1) etc at the bottom of page 332 the D refers not to the Defendant's race but to the data observed.
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Re: Help on Example 10.9 Race Equality in U.S. ...

norman@eecs.qmul.ac.uk
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I have actually updated the errata page to take care of this now:

http://bayesianrisk.com/Errata.pdf

Norman Fenton
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Re: Help on Example 10.9 Race Equality in U.S. ...

Jun Wang
In reply to this post by Jun Wang
Thanks Norman for the quick help !

Two minor  typos ?

P330, Step 2: H1: "S dependent of ..." SHOULD be "S INdependent of ..." (?)
P331, H2: "S dependent on V" SHOULD be "S dependent on D" (?)
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Re: Help on Example 10.9 Race Equality in U.S. ...

norman@eecs.qmul.ac.uk
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Yun

Yes - thanks for pointing those errors out. I will update the errata page later today.

Norman Fenton
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Re: Help on Example 10.9 Race Equality in U.S. ...

Jun Wang
Jun NOT Yun thanks Norman.

No worries !

Jun
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