Generalized Joint Distribution

[brandon willard]

I couldn't find anything in the api that looked like a generalized joint distribution.  I was looking because I have a particle filter that's producing a discrete/mixture distribution of state distributions, where the state distributions are simple products of conditionally independent distributions.  

[Dixon, Kevin R]

Hi Brandon,

 

I’m not sure what you mean by “generalized joint distribution”.  Let me take a stab and see if I’m in the ballpark: When I want a joint distribution p(a,b), I’ll just represent it in the Foundry using the chain rule: p(a|b)*p(b)

 

Data-structure-wise, I usually do this with the prior (p(b)) as the appropriate distribution, a DataDistribution or UnivariateGaussian etc. and then the conditionals (p(a|b)) in a HashMap for discrete b or some type of other lookup for continuous b.

 

Does that make sense?

 

Let me know if I can help!

Kevin

 

--

Kevin R. Dixon

Sandia National Laboratories

Critical Systems Security (05621)

MS0672, TA-I: 729/134

tel: (505) 284-5615

fax: (505) 284-3258

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[brandon willard]

I was thinking of an interface or an abstract class implementing Distribution that specifies a support with elements, like (a,b), for which distributions are defined so that operations like "mean" will return a mean in (a,b) and pdf.evaluate returns p(a|b)p(b).

  

There are a lot of ways to implement this with the current api, but I'm more interested in the interface/generic side of things, because, for instance, it would be nice to build/use compound distributions and know something about their structure.  It would also be possible to generalize more of the basic operations.

As a related aside:

Compound distributions like MultivariateMixtureDensityModel come close, but it stops short by only handling ClosedFormComputableDistribution<Vector>, where Vector is the limiting factor.  Specifying a generic RingType instead of Vector would probably fix that, though.  Then, for my use case, specifying RingType to be my home-made joint distribution would work.