More explanation

Author: penelopeysm

usage/predictive-distributions/index.qmd

@@ -115,13 +115,21 @@ Depending on your data, you may naturally want to create different visualisation
 
 ## Prior predictive distribution
 
-Alternatively, if we use the prior distribution of the parameters, we obtain the *prior predictive distribution*:
+Alternatively, if we use the prior distribution of the parameters $p(\theta)$, we obtain the *prior predictive distribution*:
 
 $$
 p(\tilde{x}) = \int p(\tilde{x} | \theta) p(\theta) d\theta,
 $$
 
-This is simpler, as there is no need to pass a chain in: we can sample from the deconditioned model directly, using Turing's `Prior` sampler.
+In exactly analogous fashion to above, you could sample from the prior distribution of the conditioned model, and _then_ pass that to `predict`:
+
+```{julia}
+prior_params = sample(model, Prior(), 1_000; progress=false)
+prior_predictive_samples = predict(predictive_model, prior_params)
+```
+
+In fact there is a simpler way: you can directly sample from the deconditioned model, using Turing's `Prior` sampler.
+This will, in a single call, generate prior samples for both the parameters as well as the new data.
 
 ```{julia}
 prior_predictive_samples = sample(predictive_model, Prior(), 1_000; progress=false)