Add probs methods to discrete distributions

[lindahua]

Computing pmf over a contiguous range can take advantage of the recursive relations in the pmf formula, and thus can be much more efficient than computing them individually using pdf.

Hence, I introduce the probs function for discrete distribution, with the following semantics:

probs(d, a:b)   # return a vector of probabilities corresponding to each value in the range a:b
probs(d)   # only for bounded distributions, equivalent to probs(minimum(d):maximum(d))

This function can be used to get an entire probability vector efficiently.

[coveralls]

Coverage decreased (-0.04%) when pulling 1efccbe on dh/probs into 67d5eae on master.

[coveralls]

Coverage decreased (-0.04%) when pulling 1efccbe on dh/probs into 67d5eae on master.

[StefanKarpinski]

I'm wondering if this couldn't reasonably be additional methods of the pdf function.

[kmsquire]

I was thinking the same thing as Stefan.

[lindahua]

This idea of using pdf did came to my mind but somehow I feel that pdf(d) producing a probability vector does not look very natural.

If the consensus is that it is ok to have pdf(d) yield a probability vector (for finite distributions), I can change it to pdf. I am pretty open to this.

[kmsquire]

To me this just seems like a vectorized version of the pdf function, which
seems fine to me.

On Saturday, November 8, 2014, Dahua Lin notifications@github.com wrote:

This idea of using pdf did came to my mind but somehow I feel that pdf(d)
producing a probability vector does not look very natural.

If the consensus is that it is ok to have pdf(d) yield a probability
vector (for finite distributions), I can change it to pdf. I am pretty
open to this.

—
Reply to this email directly or view it on GitHub
#305 (comment)
.

[StefanKarpinski]

The pdf(d) form does seem a little odd – and there's the issue of what, if anything, it should do for continuous distributions – but I think once you see it, it makes sense, and you'd have to look up probs anyway, so there seems to be little point in having an additional generic function for this.

[johnmyleswhite]

Since this special case would only make sense for discrete distributions, perhaps we should use pmf, which I believe we already support for evaluation at a point.

[lindahua]

Based on the feedback, I think I can take the following steps at this point:

1. Use pdf(d, a:b) instead of probs(d, a:b) (for this case, their semantics are essentially the same), but using an efficient implementation that takes advantage of the relation between pdf(x) and pdf(x + 1).
2. I will keep probs(d) as it is for now. This method was originally only for Categorical, Multinomial and MixtureModel to retrieve the associated probability vector. However, other bounded discrete distributions can be considered as a special case of Categorical distribution, and as I extend the probs method for them.

Whereas for Categorical, probs is the same as pdf. However, this is no longer the case for Multinomial and MixtureModel.

[lindahua]

Think about it all, I lean more towards just using pdf.

Whereas it might be too cute to have pdf(d), however, it doesn't seem that it will cause ambiguity or confusion.

And probs(d) is only reserved for the case where there is a probability vector as a parameter and one can use probs(d) to retrieve that parameter. This applies to distributions like Categorical, Multinomial, and MixtureModel. In such cases probs are not necessarily the same as pdf.

[lindahua]

As of v0.6.1, we are now using pdf in all these cases.