Custom prior for isotonic regression

Questions
2

I’m not sure you need a custom prior for this. Would it make sense to model this something like:

with pm.Model() as model:
    y0       = pm.Normal('y0',mu=some_representative_mu,sd=some_representative_sd)
    delta    = pm.HalfNormal('delta',sd=some_representative_sd,shape=(length_of_data-1))
    y        = theano.tensor.extra_ops.cumsum(theano.tensor.stack([y0,delta]))
    observed = pm.Bernoulli('observed', p=y, observed=observed_y)

where I’ve assumed that each delta is independent of the others.