Could you address the points at talk:empirical Bayes method? Michael Hardy 22:42, 27 September 2006 (UTC)[reply]
Hello. Could I call your attention to the difference between
this:
![{\displaystyle E({\frac {X}{n}})=E[E({\frac {X}{n}}|\theta )]=E(\theta )=\mu }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1515c55ffb85b873b52245bcd6f30caef241faa9)
![{\displaystyle \mathrm {var} ({\frac {X}{n}})=E[\mathrm {var} ({\frac {X}{n}}|\theta )]+\mathrm {var} [E({\frac {X}{n}}|\theta )]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/27d4265582f8d6fd43ada444e4d896fa2fef8a2d)
![{\displaystyle =E[({\frac {1}{n}})\theta (1-\theta )|\mu ,M]+\mathrm {var} (\theta |\mu ,M)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/679e56b31a60fe1c4cef9f6700c24e4e8abc36ef)
![{\displaystyle ={\frac {1}{n}}(\mu (1-\mu ))+{\frac {n_{i}-1}{n_{i}}}{\frac {(\mu (1-\mu ))}{M+1}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fa36b6568cf9ff22374036d530f0c11a1fdc659b)
![{\displaystyle ={\frac {\mu (1-\mu )}{n}}(1+{\frac {n-1}{M+1}}).}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cf8a1c45055915be50c9aa7c195d217023b04954)
and this:
![{\displaystyle E\left({\frac {X}{n}}\right)=E\left[E\left({\frac {X}{n}}|\theta \right)\right]=E(\theta )=\mu }](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe8a45c6c6c6fe1f222e05174c85eac787f0f2ea)
![{\displaystyle \mathrm {var} \left({\frac {X}{n}}\right)=E\left[\mathrm {var} \left({\frac {X}{n}}|\theta \right)\right]+\mathrm {var} \left[E\left({\frac {X}{n}}|\theta \right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7787bfdf6733a0354641bbdf67fa298c6f5f13aa)
![{\displaystyle =E\left[\left({\frac {1}{n}}\right)\theta (1-\theta )|\mu ,M\right]+\mathrm {var} \left(\theta |\mu ,M\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/49b2eb8babc6ed579334bca5f48d9460196815ee)
![{\displaystyle ={\frac {1}{n}}\left(\mu (1-\mu )\right)+{\frac {n_{i}-1}{n_{i}}}{\frac {(\mu (1-\mu ))}{M+1}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3e58266bfbee4f97c414c4307808ea8d266f583c)
![{\displaystyle ={\frac {\mu (1-\mu )}{n}}\left(1+{\frac {n-1}{M+1}}\right).}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b18789b8247eb7ef1b2b9ece0d36a58ec3dc02bc)
I changed the former to the latter in Beta-binomial model. Michael Hardy 20:14, 19 October 2006 (UTC)[reply]
I am not great with the MathML and editing the wikipedia so I will take a look at this more carefully. I'll try to take more care in the presentation. Please understand that this is a work in progress and it would also be helpful to check the derivations since I could make a mistake.
Thanks
Charlesmartin14 22:32, 19 October 2006 (UTC)[reply]
The link from the Empirical Bayes Page to here seems to be broken now?
Charlesmartin14 22:43, 19 October 2006 (UTC)[reply]