Typing this on my phone. Sorry about format.  The sampling part of the mixture 
model makes it a true distribution according to the abstract class and 
interface. It will also come in handy for simulating data, I think. I am 
already using it to simulate mri images.
_

I support adding get dimension function to interface. I can't do anything for a 
few days though.

_______________________________________
From: Phil Steitz [phil.ste...@gmail.com]
Sent: Thursday, October 18, 2012 2:50 PM
To: Commons Developers List
Subject: Re: [Math] MATH-816 (mixture model distribution)=?utf-8?B?LiAgICAu?    
=

On 10/18/12 8:55 AM, Gilles Sadowski wrote:
> On Thu, Oct 18, 2012 at 06:59:22AM -0700, Phil Steitz wrote:
>> On 10/18/12 1:41 AM, Gilles Sadowski wrote:
>>> On Wed, Oct 17, 2012 at 10:26:55PM -0700, Phil Steitz wrote:
>>>> On 10/17/12 8:36 PM, Becksfort, Jared wrote:
>>>>> I see.  I am planning to submit the EM fit for multivariate normal 
>>>>> mixture models in the next couple of weeks (Math-817).  A Gibbs sampling 
>>>>> DP fit may be a bit further out.   I am not opposed to allowing the 
>>>>> number of components to change, but I also like the simplicity of this 
>>>>> class.  Whatever you guys decide is probably fine.
>>>> I like the interface as implemented for what it represents,
>>> By "interface", do you mean the class
>>>    MixtureMultivariateRealDistribution"
>>> as implemented in the file on the JIRA page?
>> Yes, the most recent one.  I like the way you set up the
>> constructors, handling the weights and distribution type parameter.
>>>> but I
>>>> agree with Ted's point above.  I also wonder if implementing the
>>>> multivariate distribution interface is really buying you anything.
>>>> Certainly not for the Gibbs sampler.  It might be better to just
>>>> directly implement EM with an interface that is natural for fitting
>>>> and using mixture models.   I am not sure this stuff belongs in the
>>>> distribution package in any case.
>>> As implemented, it seems quite natural.
>>> How this class will be used by non-existing code is beyond the scope of
>>> MATH-816.
>>> [And when the code exists, we can always revisit the design if necessary.]
>> It works for fixed component models, which I guess is OK by
>> consensus to start. The question I was asking is what exactly do you
>> get by having it extend the multivariate real distribution?
> Is it not a kind of distribution?
> [It's obvious that one can sample from it but maybe there are some required
> properties (for a distribution) which are missing from such a mixture (?).]

What is implemented is a legitimate distribution (or more precisely,
a legitimate density, which is all we really model in
RealMultivariateDistribution).  I just wonder whether there is value
in it as a distribution per se, rather than just a container for the
weights and component distribution parameters.  The sample()
implementation is legitimate - I just don't know if it has any
practical value.  I guess the density will be used by the EM impl.
As I said above, I am fine committing and then seeing how the EM
impl uses the class.  Assuming it does turn out to be practically
valuable as a distribution, a natural thing to add would be a
univariate version; but that would require an actual distribution
function.

Phil
>
>> I guess
>> that will become clear when we get the EM implementation.
> Hopefully.
>
>> I am OK committing this, I just wanted to get a clearer picture of
>> how the class was going to be used.
> I wouldn't be able to answer.
>
>
> Gilles
>
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