MixtureModel with Continuous and Discrete

[dfagnan]

Is there a reason not to allow for mixtures with both continuous and discrete underlying distributions?

It seems like right now it would break the model, since it would be neither discrete nor continuous in terms of ValueSupport. I guess this would be a major change.

MixtureModel([Normal(); Geometric(0.5)])

ERROR: `variate_form` has no method matching variate_form(::Type{Sampleable{F<:V
ariateForm,S<:ValueSupport}})
 in MixtureModel at C:\Users\David\.julia\v0.3\Distributions\src\mixturemodel.jl
:20
 in MixtureModel at C:\Users\David\.julia\v0.3\Distributions\src\mixturemodel.jl
:29

[lindahua]

Yes, all components should be on the same space. We haven't explicitly enforced this constraint yet, but need to work on this.

[abraunst]

What about atomic distributions, are they continuous or discrete? More in particular, how does a distribution which is a mixture of continuous and point-mass fits here? Is it continuous or discrete? (math answer IMO: it is neither -- continuous and discrete are not complementary)

Real example: I'm interested in spike-and-slab or Gauss-Bernoulli (mixture of an atomic point-mass distribution and a normal). Right now it seems the only way of producing this is by using a degenerate normal with sigma=0 instead of a point-mass. Is this intended?

[matbesancon]

@abraunst I think in that case you should construct your own mixture type in that case, not use the common one, assuming same space for the two distributions seems expectable

[abraunst]

@matbesancon While I agree with your statement, I think that "continuous" is a bit ambiguous: it may mean that the distribution is defined on the real line (i.e. a distinction on the space on which is defined, as you mention) or that it is absolutely continuous. I think that the former is more useful.

So, in my humble opinion, discrete should mean that the distribution is defined on a subset of Z or Z^n (and continuous all other cases). In this interpretation the point mass (and mixtures of point mass) should be continuous.

[mschauer]

The absolute continuity is best seen as a property of the pdf. Continuous then just means that the pdf is given with respect to the Lebesgue measure.

[abraunst]

The absolute continuity is best seen as a property of the pdf. Continuous then just means that the pdf is given with respect to the Lebesgue measure.

@mschauer I don't understand. If a measure has a pdf wrt. to the Lebesgue measure, then it is absolutely continuous. So using this interpretation of "continuous" something like spike-and-slab is neither discrete nor continuous. Or am I missing something?