Ordered transform does not return ordered samples

Questions version agnostic
1

I am trying to do inference with OrderedLogistic observations as per the following code

# Samples
yo = np.random.choice( np.arange(5), p=[0.1,0.25,0.05,0.4,0.2], size=500 )

# PYMC model
with pm.Model() as model_0:
    # Priori
    cutpoints= pm.Normal(
        "cutpoints",
        0.0,
        1.5,
        transform=pm.distributions.transforms.ordered,
        shape=4,
        initval=np.arange(4)
    )

    # Cumulative probabilities
    q = pm.Deterministic( 'q', pm.math.invlogit(cutpoints) )
    
    # Likelihood
    Y = pm.OrderedLogistic("y", 0.0, cutpoints, observed=yo)

    # Prior predictive
    prior_ppc = pm.sample_prior_predictive( samples=1000 )

# Plot Prior predictive
fig, ax = plt.subplots( figsize=(15,5), ncols=3 )
_ = sns.kdeplot( prior_ppc.prior['cutpoints'][0,:], ax=ax[0] )
_ = sns.kdeplot( prior_ppc.prior['y_probs'][0,:], ax=ax[1] )
_ = sns.histplot( prior_ppc.prior_predictive['y'][0,:,100], stat='probability', ax=ax[2] )

The posterior results (not included in the code) look good, since the number of observations overshadow the priors. However the prior predictions do not make sense, since they predict negative probabilities for each category a priori.

pymc_oredered_output
pymc_oredered_output1242×428 67.1 KB

Inspecting prior samples for the cutpoints of the model, it looks like the model is not sampling in increasing order as I would assume by the pm.distributions.transforms.ordered

pymc_oredered_output2
pymc_oredered_output2716×327 18.5 KB

pymc_oredered_output3
pymc_oredered_output3715×428 14 KB

I have tried different initvals for the Normal distribution, but it doesn’t change the output.

Any guidance would be helpful. Thanks!

2

Transforms do not play a role in prior or posterior predictive sampling, only pm.sample

3

Thanks for the reply.

Is there a way to do a correct prior predictive analysis when using transforms?

4

You can use pm.sample in the same model, but without passing the observed argument to your likelihood. That will result in a sample from the prior that will respects your transforms.

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