From: ted.dunning@gmail.com   
      
   On Oct 1, 4:58 pm, smart  wrote:   
   > Page 8. He talked about Beta(0,0) as prior.   
   >   
   > But does Beta(0,0) exist? The integration in the definition of   
   > Beta(0,0) simply don't converge? Or do I make any misunderstanding?   
   >   
   > I'm confused.   
   >   
   > Wei   
   >   
      
   This is an improper, but it is still useful in some applications,   
   especially as a prior.   
      
   You are correct that the integral diverges.  Typically, though, you   
   don't want to integrate the distribution itself, but some other   
   distribution based on this distribution (as a posterior is based on a   
   prior, for instance).  Other useful improper priors include the   
   hyperbolic distribution (the limit of Gamma for constant shape * scale   
   as shape => 0) and the infinite uniform (the limit of the normal   
   distribution with 0 mean as \sigma => infinity).  These limits don't   
   properly exist, but the corresponding limits on other expressions   
   using these "distributions" may exist.   
      
   There is considerable controversy regarding the explicit use of these   
   distributions, but they are conceptually useful in certain cases.   
      
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