Fitting multiple cones to 2D data, how to impose ordering constraint on parameters

Questions v5
14

Is this what you were suggesting (I used Uniform instead of Dirichlet for starters)?

index_proportions = pm.Uniform("index_proportions", 0, 1,
                                  transform=pm.distributions.transforms.multivariate_ordered,
                                  initval=[0.4,0.6], size=2)
  
indices = pm.Deterministic("indices",
                           pm.math.floor(N*index_proportions))

This seems to achieve the effect I wanted (first index has most weight at 0 and decreases as it increases and vice versa for the other). At least almost always. Since there is rounding involved, even if the index_proportions satisfy x<y it is possible that pm.math.floor(x) = pm.math.floor(y). I guess when there are only two indices, one can floor the first one and ceil the other but that would not work beyond sampling two indices. In any case, I can work with the off chance of indices being the same once in a while.

I also tried Dirichlet as such:

index_proportions = pm.Dirichlet("index_proportions", a=[1/4,3/4],
                                   transform=pm.distributions.transforms.multivariate_ordered,
                                   initval=[1/4,3/4])

but this was sampling almost exclusively 0 for the first index and others for the second index.