You are viewing a plain text version of this content. The canonical link for it is here.
Posted to dev@commons.apache.org by Phil Steitz <ph...@gmail.com> on 2012/10/18 22:19:00 UTC
[math] multivariate cdf
I just realized that when we defined RealMultivariateDistribution we
neglected to actually model the distribution function. If we
forced ourselves to support this and provide an integration-based
default in the abstract base class, that might also force us to
implement some useful multivariate integration algorithms :)
Volunteers? (Honestly, I am not sure this is realistic for many /
most multivariate distributions, but it is worth at least thinking
about).
Phil
---------------------------------------------------------------------
To unsubscribe, e-mail: dev-unsubscribe@commons.apache.org
For additional commands, e-mail: dev-help@commons.apache.org
Re: [math] multivariate cdf
Posted by Sébastien Brisard <se...@m4x.org>.
Hi Phil,
2012/10/19 Phil Steitz <ph...@gmail.com>:
> On 10/19/12 12:20 AM, Sébastien Brisard wrote:
>> Hi Phil,
>>
>>> that might also force us to implement some useful multivariate
>>> integration algorithms :)
>>>
>> Is there any, general purpose multidimensional integration algorithm?
>> MC would be flexible enough, but I doubt this would be efficient enough...
>> How would you define the domain? Would you restrict it to products of
>> intervals, or more general domains?
>
> I have not really looked into multivariate integration algorithms.
> Note that we do not provide this convenience now for univariate
> distributions (though I did recently add some integration tests that
> verify consistency of the distribution and density impls). I would
> define the cdf to take dimension vectors are arguments, so F(x_1,
> ..., x_n) = P(X_1 <=x_1, ..., X_n <= x_n). Other things to
> consider are marginal and conditional densities and distributions.
> Here again, defaults could in theory be provided; but without
> actually hacking some examples, I am not sure it is practical.
>
Even in one-d, I would not recommend that we implement a default
integration scheme to be used in *all situations* on an unbounded
integration domain (-infty, x]. Indeed, I think it will always be
possible to find a distribution with a pdf which goes to zero so
slowly as x tends to -\infty that our integration scheme fails (or is
grossly in error). Or am I missing something?
Sébastien
>
> Phil
>>
>> Sébastien
>>
>>
>> ---------------------------------------------------------------------
>> To unsubscribe, e-mail: dev-unsubscribe@commons.apache.org
>> For additional commands, e-mail: dev-help@commons.apache.org
>>
>>
>
>
> ---------------------------------------------------------------------
> To unsubscribe, e-mail: dev-unsubscribe@commons.apache.org
> For additional commands, e-mail: dev-help@commons.apache.org
>
---------------------------------------------------------------------
To unsubscribe, e-mail: dev-unsubscribe@commons.apache.org
For additional commands, e-mail: dev-help@commons.apache.org
Re: [math] multivariate cdf
Posted by Phil Steitz <ph...@gmail.com>.
On 10/19/12 12:20 AM, Sébastien Brisard wrote:
> Hi Phil,
>
>> that might also force us to implement some useful multivariate
>> integration algorithms :)
>>
> Is there any, general purpose multidimensional integration algorithm?
> MC would be flexible enough, but I doubt this would be efficient enough...
> How would you define the domain? Would you restrict it to products of
> intervals, or more general domains?
I have not really looked into multivariate integration algorithms.
Note that we do not provide this convenience now for univariate
distributions (though I did recently add some integration tests that
verify consistency of the distribution and density impls). I would
define the cdf to take dimension vectors are arguments, so F(x_1,
..., x_n) = P(X_1 <=x_1, ..., X_n <= x_n). Other things to
consider are marginal and conditional densities and distributions.
Here again, defaults could in theory be provided; but without
actually hacking some examples, I am not sure it is practical.
Phil
>
> Sébastien
>
>
> ---------------------------------------------------------------------
> To unsubscribe, e-mail: dev-unsubscribe@commons.apache.org
> For additional commands, e-mail: dev-help@commons.apache.org
>
>
---------------------------------------------------------------------
To unsubscribe, e-mail: dev-unsubscribe@commons.apache.org
For additional commands, e-mail: dev-help@commons.apache.org
Re: [math] multivariate cdf
Posted by Sébastien Brisard <se...@m4x.org>.
Hi Phil,
>
> that might also force us to implement some useful multivariate
> integration algorithms :)
>
Is there any, general purpose multidimensional integration algorithm?
MC would be flexible enough, but I doubt this would be efficient enough...
How would you define the domain? Would you restrict it to products of
intervals, or more general domains?
Sébastien
---------------------------------------------------------------------
To unsubscribe, e-mail: dev-unsubscribe@commons.apache.org
For additional commands, e-mail: dev-help@commons.apache.org