Hurdle models are described in the examples section of the Stan manual (version 2.17.0, p. 199) with this code:

```
if (y[n] == 0)
1 ~ bernoulli(theta);
else {
0 ~ bernoulli(theta);
y[n] ~ poisson(lambda) T[1, ];
}
```

Yet, putting integers (such as 0 and 1) on the left-hand side of a sampling statement is not shown earlier in the manual. What does this mean? The description says:

“The Bernoulli statements are just shorthand for adding log \theta and log(1 - \theta) to the log density.” I’m not sure how this follows from the syntax: It seems to me like it is saying “0 is distributed Bernoulli with a probability of theta.”