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From Mikkel Meyer Andersen <m...@mikl.dk>
Subject Re: [math] Distributions over sample spaces other than R
Date Wed, 02 Nov 2011 07:39:50 GMT
I see your point, Phil, and agree with you. Thanks for clarifying.

Cheers, Mikkel.
Den 01/11/2011 18.24 skrev "Phil Steitz" <phil.steitz@gmail.com>:

> On 11/1/11 1:05 AM, Mikkel Meyer Andersen wrote:
> > 2011/10/30 Phil Steitz <phil.steitz@gmail.com>:
> >> On 10/29/11 10:20 AM, cwinter wrote:
> >>> Phil Steitz wrote:
> >>>> I would say pull DiscreteDistribution out.  That is where the
> >>>> difference really lies.  I have thought about suggesting that we
> >>>> eliminate it altogether; but I still think there may be value in
> >>>> supporting discrete distributions over sample spaces that are not
> >>>> embedded in the integers.
> >>>>
> >>>> Phil
> >>>>
> >>> Empirical distributions are discrete by nature. Depending on the
> underlying
> >>> data, the domain is usually (a subset of) the reals or the integers.
> >>> However, after moving probability(double) to Distribution,
> >>> DiscreteDistribution will be an empty interface. Thus there is in fact
> the
> >>> question whether it should be eliminated. Otherwise it would be just a
> >>> "flag" for discrete distributions and that's indeed independent of the
> >>> sample space.
> >> Maybe it would be best to eliminate IntegerDistribution then and
> >> merge Distribution and ContinuousDistribution, so we have two roots
> >> - DiscreteDistribution and ContinuousDistribution.   The only reason
> >> really to have DiscreteDistribution is if we want to support
> >> distributions of RVs over sample spaces that are not subsets of Z.
> >> There does not seem to be much enthusiasm for that (i.e.
> >> parameterizing the type of the domain of the distribution and pmf),
> >> so we might as well just collapse Discrete and Integer.   Once you
> >> pull out Discrete/Integer, there is not much value any more in
> >> Distribution as a parent, so why not just drop both
> >> IntegerDistribution and Distribution and move to two roots with
> >> doubles / ints as domains and contracts cleaned up to deal with
> >> discrete vs continuous cases consistently.
> > If we have these two roots, I would propose an Distribution interface
> > with e.g. with cdf and inverse cdf. Alternatively, an abstract class
> > implementing a default solver for the inverse cdf. We might be able to
> > make this generic parameterising the argument to cdf and others.
>
> The only way for this to work is to parameterize the type of the
> sample space, which will then force Double to be used for the
> continuous case.  Why is it so bad to have two roots?
>
> What exactly do we gain by having the common parent?  The inverse
> cdf machinery will work only for the continuous (by that, I mean
> real-valued RV) case.  Note how it is overriden now in
> AbstractIntegerDistribution.  So why not just leave that alone and
> separate out the discrete/integer/whatever-we-want-to-call-it case?
> Discrete distributions are fundamentally different.  They have
> pmfs.  They have discrete value sets.  Inversion works differently.
> Inequalities work differently.  Why not just cleanly separate?
>
> Phil
> >
> > In my opinion, we benefit from having one such common ancestor instead
> > of two "independent" linages.
> >
> >> Phil
> >>> Christian
> >>>
> >>> --
> >>> View this message in context:
> http://apache-commons.680414.n4.nabble.com/math-Distributions-over-sample-spaces-other-than-R-tp3931349p3951273.html
> >>> Sent from the Commons - Dev mailing list archive at Nabble.com.
> >>>
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> >
>
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