Charlesmartin14

Could you address the points at talk:empirical Bayes method? Michael Hardy 22:42, 27 September 2006 (UTC)

Use of TeX

Hello. Could I call your attention to the difference between

this:

$E({\frac {X}{n}})=E[E({\frac {X}{n}}|\theta )]=E(\theta )=\mu$

$\mathrm {var} ({\frac {X}{n}})=E[\mathrm {var} ({\frac {X}{n}}|\theta )]+\mathrm {var} [E({\frac {X}{n}}|\theta )]$

$=E[({\frac {1}{n}})\theta (1-\theta )|\mu ,M]+\mathrm {var} (\theta |\mu ,M)$

$={\frac {1}{n}}(\mu (1-\mu ))+{\frac {n_{i}-1}{n_{i}}}{\frac {(\mu (1-\mu ))}{M+1}}$

$={\frac {\mu (1-\mu )}{n}}(1+{\frac {n-1}{M+1}}).$

and this:

$E\left({\frac {X}{n}}\right)=E\left[E\left({\frac {X}{n}}|\theta \right)\right]=E(\theta )=\mu$

$\mathrm {var} \left({\frac {X}{n}}\right)=E\left[\mathrm {var} \left({\frac {X}{n}}|\theta \right)\right]+\mathrm {var} \left[E\left({\frac {X}{n}}|\theta \right)\right]$

$=E\left[\left({\frac {1}{n}}\right)\theta (1-\theta )|\mu ,M\right]+\mathrm {var} \left(\theta |\mu ,M\right)$

$={\frac {1}{n}}\left(\mu (1-\mu )\right)+{\frac {n_{i}-1}{n_{i}}}{\frac {(\mu (1-\mu ))}{M+1}}$

$={\frac {\mu (1-\mu )}{n}}\left(1+{\frac {n-1}{M+1}}\right).$

I changed the former to the latter in Beta-binomial model. Michael Hardy 20:14, 19 October 2006 (UTC)

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)

The link from the Empirical Bayes Page to here seems to be broken now? Charlesmartin14 22:43, 19 October 2006 (UTC)