Added text to clarify difference in posterior draws and posterior predictions

Author: bbbales2

knitr/hmm-example/hmm-example.Rmd

@@ -45,11 +45,11 @@ There are three functions
 
 - `hmm_marginal` - The likelihood of an HMM with the hidden discrete states
 integrated out
-- `hmm_latent_rng` - A function to generate draws of the hidden state that are
+- `hmm_latent_rng` - A function to generate posterior draws of the hidden state that are
 implicitly integrated out of the model when using `hmm_marginal` (this is
 different than sampling more states with a posterior draw of a transition matrix
 and initial state)
-- `hmm_hidden_state_prob` - A function to compute the distributions of the
+- `hmm_hidden_state_prob` - A function to compute the posterior distributions of the
 integrated out hidden states
 
 This guide will demonstrate how to simulate HMM realizations in R, fit the data
@@ -271,11 +271,16 @@ generated quantities {
 }
 ```
 
-Note, these are the probabilities and draws of the hidden state that was
-integrated out. This is different than sampling new HMM realizations using
-posterior draws of the initial condition and the transition matrix.
+Note that the probabilities from `hmm_hidden_state_prob` are the marginal
+probabilities of the hidden states, meaning they cannot be directly used to
+jointly sample hidden states. The posterior draws generated by `hmm_latent_rng`
+account for the correlation between hidden states.
 
-These can be plotted as well:
+Note further these are draws of the hidden state that was integrated out. This is
+different than sampling new HMM realizations using posterior draws of the initial
+condition and the transition matrix. 
+
+The draws of the hidden state can be plotted as well:
 
 ```{r}
 y_sim = fit$draws() %>%