Trouble understanding how to use sample_posterior_predictive to generate a prediction

1

I’m quite new to PyMC and admitteldy much more comfortable in R and Stan than Py so I’m probably doing something rudimentary wrong and I’m not tracking all the variations between different versions of PyMC. I have a very simple model that I’ve been toying with to learn that I’ve copied from here. I had started with more complex modeling but realized that I was in way over my head.

Anyhow, here is my attempt to get some predictions:

# Predictions - generate new data
new_data = np.random.randn(3, 3)

#concat my existing features with new ones?
tmp = np.concatenate((features, new_data))

# should coords have 3 or 103? Neither seems to work confusingly.
new_coords = {
          # dim 1: len of df
          'obs_id': np.arange(0,3), #is this all coords from concat'd set or just for new?
          # dim 2: feature cats.
          'features': ['treatment', 'cov1', 'cov2']
}

with hierarchical_model:
    # set it over the feature data? Is this needed? doesn’t work anyways.
    hierarchical_model.set_data(name = "feature_data", values = tmp, coords=new_coords)
    # generate preds, seems to work
    predictions = pm.sample_posterior_predictive(hierarchical_trace, predictions=True)
    # this doesn’t exist any more, not sure how to replace it?
    preds = az.from_pymc3_predictions(predictions,
                              coords=new_coords,
                              idata_orig=lm_idata,
                              inplace=False)

# # get y-hat for new X data
preds.predictions['y'].median(dim=('chain', 'draw')).values

# # view y-hat as 94% HDI
az.plot_posterior(preds, group="predictions");

I’m guessing that there’s some trickery with how we set the co-ordinates that I can’t seem to puzzle out from the docs and sadly much of the code that I can find to reference no longer seems to work. Any advice much apprecated!

2

The syntax from the example you linked is somewhat out of date. coords are now deeply integrated into PyMC, so you don’t have to do all this juggling with az.from_pymc. Here’s a simplified model:

coords = {'features': ['treatment', 'cov1', 'cov2']}
coords_mutable = {'obs_id': np.arange(len(target))}

with pm.Model(coords=coords, coords_mutable=coords_mutable) as sk_lm:
    feature_data = pm.MutableData('feature_data', features, dims=('obs_id', 'features'))

    alpha = pm.Normal('alpha', mu=0, sigma=1)
    betas = pm.Normal('betas', mu=[40, 90, 50], sigma=5, dims='features')
    sigma = pm.Exponential("sigma", lam=1)

    mu = pm.Deterministic("mu", alpha + feature_data @ betas, dims='obs_id')

    y = pm.Normal("y", mu=mu, sigma=sigma, observed=target, dims='obs_id')

    idata = pm.sample(init='jitter+adapt_diag')

Since you’re planning to do out-of-sample stuff, you want to set the index coordinate with coords_mutable. That lets you change it down the road. Down the road is here:

new_data = np.random.randn(3, 3)

with sk_lm:
    pm.set_data({"feature_data": new_data}, 
                coords={'obs_id':np.arange(3) + len(target)})
    idata = pm.sample_posterior_predictive(idata, predictions=True, extend_inferencedata=True)

Since I used coords_mutable, I can pass new coords to pm.set_data. This is a common gotcha with out-of-sample prediction – you have to make sure the shapes of the targets somehow get updated to match the new data, even though you’re not using targets. This is discussed a bit more in-depth here.

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