number generator

Duncan Smith buzzard at urubu.freeserve.co.uk
Wed Mar 14 15:40:41 CET 2007


Hendrik van Rooyen wrote:
> "Duncan Smith" <bu...ard at urubu.freeserve.co.uk> wrote:
> 
> 
> 
>>Yes, if the generating processes yield numbers from different
>>probability mass functions.  You could simply look at the likelihood
>>ratio.  Otherwise, the likelihood ratio will be 1.
>>
> 
>  I was thinking about the same random number generator being used in the two 
> disparate ways.
> 
> - Hendrik
> 

The code I posted for multinomial variates repeatedly generates
independent Poissons until the total is less than, or equal to, the
desired total.  Then the total is made up by repeatedly sampling from a
discrete distribution (multinomial with n==1).  If you replace the
second stage by just increasing a single count by the necessary amount,
then the two mass functions are clearly different.  I'm not sure that
I'd count this as two approaches using "the same random number generator".

Duncan



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