Potential bug in assembleHypothesesElements!

[Affie]

@dehann , It looks like a [x, l1, l2] multihypo = [1,0.5,0.5] only uses 33% of x when solving for l1, or l2 I would expect 50% eg:

N = 100
mh = Categorical([0, 0.5,0.5])
certainidx, allelements, activehypo, mhidx = IIF.assembleHypothesesElements!(mh, N, 2, 3)

([1], Any[[2, 5, 8, 12, 14, 16, 17, 20, 21, 22  …  65, 66, 71, 81, 82, 91, 92, 93, 94, 99], Int64[], [1, 7, 13, 15, 18, 24, 25, 28, 29, 45  …  73, 75, 76, 77, 79, 80, 84, 85, 90, 96], [3, 4, 6, 9, 10, 11, 19, 31, 32, 33  …  78, 83, 86, 87, 88, 89, 95, 97, 98, 100]], Any[(0, [2]), (1, [1, 2]), (2, [1, 2]), (3, [2, 3])], [2, 0, 3, 3, 0, 3, 2, 0, 3, 3  …  0, 0, 0, 0, 3, 2, 3, 3, 0, 3])

julia> activehypo
4-element Vector{Any}:
 (0, [2])
 (1, [1, 2])
 (2, [1, 2])
 (3, [2, 3])

samples for 0: 30.599999999999998%
samples for 1: 0.0%
samples for 2: 32.7%
samples for 3: 36.7%

Sorry if I'm misunderstanding something but I thought I'd rather ask just in case.

[Affie]

Also, should we perhaps use the nullhypo (spreadNH) case in initialization:

certainidx, allelements, activehypo, mhidx = IIF.assembleHypothesesElements!(mh, N, 1, 3, Bool[0, 0, 1])
#currently:
#samples for 0: 0.0% <-- no 0 activehypo currenly exists for this case
#samples for 1: 0.0%
#samples for 2: 0.0%
#samples for 3: 100.0%

#suggested:
#samples for 0: 50.0%
#samples for 1: 0.0%
#samples for 2: 0.0%
#samples for 3: 50.0%

[dehann]

Perhaps you missed in the the discussion. We had forced a nullhypo case (0) previously, so currently you are effectively getting 60% nullhypo (0 + 2||3) -- when solving for one of the fractionals, not when solving for a certainidx.

samples for 0: 30.599999999999998% samples for 1: 0.0% samples for 2: 32.7% samples for 3: 36.7%

There is a less important bug, which is allocating the proper probability weight for "snap together case" in general n-ary use (currently "snap together" is being suppressed as nullhypo):

[Affie]

I didn’t miss it in the discussion. I understand that part. The issue is even if you give the probability of 0.999-0.001 it wil go to 33% nullhypo and 66% x