
Boost Users : 
Subject: Re: [Boostusers] [distributions]: Inverse Gamma
From: Paul A. Bristow (pbristow_at_[hidden])
Date: 20100804 04:37:30
> Original Message
> From: boostusersbounces_at_[hidden] [mailto:boostusersbounces_at_[hidden]] On Behalf Of Thomas Mang
> Sent: Tuesday, August 03, 2010 3:07 PM
> To: boostusers_at_[hidden]
> Subject: Re: [Boostusers] [distributions]: Inverse Gamma
>
>>
> >> any plans of implementing the inverse gamma distribution as part of the distributions library ?
> >
> > This looks possible  but I'm curious about applications  you obviously have one, but Wikipedia doesn't mention any
> >
> > http://en.wikipedia.org/wiki/Inversegamma_distribution
> >
> > But you obviously have one ;)
>
> Yes I truly have one ;) The inverse gamma distribution and its special
> case, the scaled inverse chisquare distribution, is the conjugate prior
> to the normal distribution variance parameter in Bayesian statistics.
> Pretty much as uncommon and unheard of as it is outside Bayes world [to
> the best of my knowledge], it's very much central to Bayesian stats and
> appears in every textbook right after the introduction chapter ;)
>
> http://en.wikipedia.org/wiki/Scaled_inverse_chisquare_distribution
> http://en.wikipedia.org/wiki/Conjugate_prior
>
> Hence I wonder it has not been requested so far  but being a Bayesian
> C++ / booster I definitely want / need it :).
>
> @John: Yes it is a transformation deviate of the gamma, and an easy so.
> And it should be fairly easy to implement IMHO.
The pdf and pdf etc looks fairly straightforward (only uses exp, pow and gamma?) so I might be persuaded to do these.
But the inverses (qhantiles) may prove more troublesome if have to be done by brute force numerically
R library does it numerically http://rss.acs.unt.edu/Rdoc/library/pscl/html/igamma.html
 or are there analytic expressions for these?
Or can it use the inverse of the gamma distribution?
> Is contribution on my side expected (can be done just notice I am a
> [heavy !] user of the stats library only, not familiar with code /
> numerical stability issues).
I'm not mathematician enough to deal with this  but I can deal with the obfuscated code (by templating and policies) if
you can provide the equations.
(And there is the question of testing  some parameters and value combinations (preferably exact) are needed for sanity
and accuracy checks).
Are there use cases for the inverses?
Paul
 Paul A. Bristow Prizet Farmhouse Kendal, UK LA8 8AB +44 1539 561830, mobile +44 7714330204 pbristow_at_[hidden]
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