Fix predictive checks in Turing 0.21 (#65)

Closes #64.

_literate/04_Turing.jl

@@ -113,7 +113,9 @@ setprogress!(false) # hide
     p ~ Dirichlet(6, 1)
 
     #Each outcome of the six-sided dice has a probability p.
-    y ~ filldist(Categorical(p), length(y))
+    for i in eachindex(y)
+        y[i] ~ Categorical(p)
+    end
 end;
 
 # Here we are using the [Dirichlet distribution](https://en.wikipedia.org/wiki/Dirichlet_distribution) which
@@ -134,10 +136,9 @@ sum(mean(Dirichlet(6, 1)))
 
 # Also, since the outcome of a [Categorical distribution](https://en.wikipedia.org/wiki/Categorical_distribution) is an integer
 # and `y` is a $N$-dimensional vector of integers we need to apply some sort of broadcasting here.
-# `filldist()` is a nice Turing function which takes any univariate or multivariate distribution and returns another distribution that repeats the input distribution.
-# We could also use the familiar dot `.` broadcasting operator in Julia:
+# We could use the familiar dot `.` broadcasting operator in Julia:
 # `y .~ Categorical(p)` to signal that all elements of `y` are distributed as a Categorical distribution.
-# But doing that does not allow us to do predictive checks (more on this below). So, instead we use `filldist()`.
+# But doing that does not allow us to do predictive checks (more on this below). So, instead we use a `for`-loop.
 
 # ### Simulating Data
 
@@ -240,21 +241,15 @@ savefig(joinpath(@OUTPUT, "chain.svg")); # hide
 prior_chain = sample(model, Prior(), 2_000);
 
 # Now we can perform predictive checks using both the prior (`prior_chain`) or posterior (`chain`) distributions.
-# To draw from the prior and posterior predictive distributions we instantiate a "predictive model", *i.e.* a Turing model but with the observations set to `missing`[^missing], and then calling `predict()` on the predictive model and the previously drawn samples.
+# To draw from the prior and posterior predictive distributions we instantiate a "predictive model", *i.e.* a Turing model but with the observations set to `missing`, and then calling `predict()` on the predictive model and the previously drawn samples.
 # First let's do the *prior* predictive check:
 
-missing_data = Vector{Missing}(missing, length(data)) # vector of `missing`
-model_missing = dice_throw(missing_data)
-model_predict = DynamicPPL.Model{(:y,)}(:model_predict_missing_data,
-    model_missing.f,
-    model_missing.args,
-    model_missing.defaults) # instantiate the "predictive model"
-prior_check = predict(model_predict, prior_chain);
+missing_data = similar(data, Missing) # vector of `missing`
+model_missing = dice_throw(missing_data) # instantiate the "predictive model
+prior_check = predict(model_missing, prior_chain);
 
 # Here we are creating a `missing_data` object which is a `Vector` of the same length as the `data` and populated with type `missing` as values.
 # We then instantiate a new `dice_throw` model with the `missing_data` vector as the `data` argument.
-# We proceed by instantiating a new Turing `DynamicPPL.Model` model with the `missing_data` vector as the `data` argument.
-# The boilerplate around `DynamicPPL.Model` is the default arguments that a `DynamicPPL.Model` model needs to have.
 # Finally, we call `predict()` on the predictive model and the previously drawn samples, which in our case are the samples from the prior distribution (`prior_chain`).
 
 # Note that `predict()` returns a `Chains` object from `MCMCChains.jl`:
@@ -267,7 +262,7 @@ summarystats(prior_check[:, 1:5, :]) # just the first 5 prior samples
 
 # We can do the same with `chain` for a *posterior* predictive check:
 
-posterior_check = predict(model_predict, chain);
+posterior_check = predict(model_missing, chain);
 summarystats(posterior_check[:, 1:5, :]) # just the first 5 posterior samples
 
 # ## Conclusion
@@ -284,7 +279,6 @@ summarystats(posterior_check[:, 1:5, :]) # just the first 5 posterior samples
 # [^MCMC]: see [5. **Markov Chain Monte Carlo (MCMC)**](/pages/5_MCMC/).
 # [^visualization]: we'll cover those plots and diagnostics in [5. **Markov Chain Monte Carlo (MCMC)**](/pages/5_MCMC/).
 # [^workflow]: note that this workflow is a extremely simplified adaptation from the original workflow on which it was based. I suggest the reader to consult the original workflow of Gelman et al. (2020).
-# [^missing]: in a real-world scenario, you'll probably want to use more than just **one** observation as a predictive check, so you should use something like `Vector{Missing}(missing, length(y))` or `fill(missing, length(y)`.
 
 # ## References