Re: [Boost-users] [distributions]: Inverse Gamma

Subject: Re: [Boost-users] [distributions]: Inverse Gamma
From: Thomas Mang (Thomas.Mang_at_[hidden])
Date: 2010-08-03 10:06:52

On 30.07.2010 18:51, Paul A. Bristow wrote:
>
>
>> -----Original Message-----
>> From: boost-users-bounces_at_[hidden] [mailto:boost-users-bounces_at_[hidden]] On Behalf Of Thomas Mang
>> Sent: Friday, July 30, 2010 4:29 PM
>> To: boost-users_at_[hidden]
>> Subject: [Boost-users] [distributions]: Inverse Gamma
>>
>> Hi,
>>
>> 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/Inverse-gamma_distribution
>
> But you obviously have one ;-)

Yes I truly have one ;) The inverse gamma distribution and its special 
case, the scaled inverse chi-square 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_chi-square_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.

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).

>
>> What about  multivariate (in particular the multivariate normal and t
>> distributions and Wishart and Dirichlet ) ?
>
> A previous offer to do some multivariate distributions seems have fizzled out - perhaps because it is *much* more
> difficult, particularly with the templated and 'policied ' (to control the troublesome parameter cases) structure used
> for the Boost.Math library.  There may be no analytic expressions for some like inverse and CDF.
>
> So some strong motivation and support would be needed to embarge on this.
>
> Paul

I think the multivariate normal is fairly obvious, use for the others 
equally arises in Bayesian statistics. But I understand that everything 
is much more complicated.
What about 'vegetarian' versions offering say only the pdf (that is 
needed a lot. Personally I have never had the need for CDFs / inverse 
CDFs as these are truly a big mess. But the pdf - yes would be cool).

best,
Thomas

>
>
> ---
> Paul A. Bristow
> Prizet Farmhouse
> Kendal, UK   LA8 8AB
> [phone], mobile [phone]
> pbristow_at_[hidden]