Hi Jo
Thanks for the link! It is new to me. Jaines merely consideres two colors,
while I consider I=2, 3, 4, ...colors. Jaines writes R and N-R where I write
K_1 and K_2. And r and n-r where I write k_1 and k_2. Jaines' formula (6.1) is
the special case I=2 of the Deduction Vandermonde Convolution on page 9 in my
article, and 'the general summation formula' (6.16) is the special case I=2 of
the Induction Vandermonde Convolution on page 10 in my article.The case 'Both N
and R unknown' treated by Jaines on page 601 is not treated by me. I stick to
the case where N and n are known as treated by Jaines on page 604 : 'uniform
prior'.
Jaines' equation (6-29) is the special case Q=2 of my Induction Absorption
identity (page 10). Jaines estimate (6-32) is the same result as my induction
formula. But it seems as if Jaines is unaware that the induction estimate
formula is produced by the deduction estimate formula by this simple
transformation:
(k,K) <===> - (1+(K,k))
1. swap the sample and the population counts
2. add 1 to every count
3. change signs. This is my main discovery.
- Bo
>________________________________
> Fra: Jo van Schalkwyk <[email protected]>
>Til: [email protected]
>Sendt: 9:57 mandag den 13. maj 2013
>Emne: Re: [Jprogramming] Deduction, Induction, and Prediction.
>
>
>Hi Bo
>
>What do you think of Jaynes' Chapter 6 (At e.g.
>http://www-biba.inrialpes.fr/Jaynes/prob.html ) where he discusses the
>Bayesian approach to inversion of urn distributions?
>
>Any use to you?
>
>Regards Jo.
>
>On 13 May 2013 19:23, Bo Jacoby
<[email protected]> wrote:
>
>> Dear J'ers
>> I have uploaded an induction formula proof here:
>>
>> www.academia.edu/3247833/Statistical_induction_and_prediction
>>
>> I appreciate your comments in december, and invite you to comment on the
>> proof too.
>> 1. Did you already know the induction and prediction formulas from the
>> literature?
>> 2. Do you have suggestions for improving the article?
>> Thank you!
>> - Bo
>>
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