Clarify extra computation in returned()

Author: penelopeysm

usage/tracking-extra-quantities/index.qmd

@@ -15,7 +15,7 @@ Pkg.instantiate();
 
 Often, there are quantities in models that we might be interested in viewing the values of, but which are not random variables in the model that are explicitly drawn from a distribution.
 
-As a motivating example, the most natural parameterization for a model might not the most computationally feasible.
+As a motivating example, the most natural parameterization for a model might not be the most computationally feasible.
 Consider the following (efficiently reparametrized) implementation of Neal's funnel [(Neal, 2003)](https://arxiv.org/abs/physics/0009028):
 
 ```{julia}
@@ -96,9 +96,9 @@ There are some pros and cons of using `returned`, as opposed to `:=`.
 Firstly, `returned` is more flexible, as it allows you to track any type of object; `:=` only works with variables that can be inserted into an `MCMCChains.Chains` object.
 (Notice that `x` is a vector, and in the first case where we used `:=`, reconstructing the vector value of `x` can also be rather annoying as the chain stores each individual element of `x` separately.)
 
-However, if used carelessly, `returned` can lead to unnecessary computation.
-For example, in `Neal_return()` above, the `x` and `y` variables are also calculated during the inference process (i.e. the call to `sample()`), but are then thrown away.
-They are then calculated _again_ when `returned()` is called.
+A drawback is that naively using `returned` can lead to unnecessary computation during inference.
+This is because during the sampling process, the return values are also calculated (since they are part of the model function), but then thrown away.
+So, if the extra quantities are expensive to compute, this can be a problem.
 
 To avoid this, you will essentially have to create two different models, one for inference and one for post-inference.
 The simplest way of doing this is to add a parameter to the model argument: