User talk: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)