Hurdle Model from Manual

[Cody Ross]

The hurdle model is define in the manual as:

The hurdle model is even more straightforward to program in Stan, as it does not
require an explicit mixture.

y[n] ~ bernoulli(theta);
if (y[n] > 0)
y[n] ~ poisson(lambda) T[1,];

The [1,] after the Poisson indicates that it is truncated below at 1; see Section 37.3.
Although the variable y[n] is being “sampled” twice, the effect on the log probability
fucntion follows the definition (on the log scale).

How is this possible? Is there a missing "(if y[n]=0)" statement before the first statement above? Or does y[n] actually need to be 'sampled twice'? How can y[n] be sampled from a Bernoulli if it is >1?

[Andrew Gelman]

Hi, I’m not sure but, just speaking generally, the statement “~” in a Stan model does _not_ represent sampling, it represents a term in the log-posterior.

A

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[Marco Inacio]

> How can y[n] be sampled from a Bernoulli if it is >1?

You're right, if you follow the notation of manual for Hurdle
distribution, it should be:

(y[n] == 0) ~ bernoulli(theta);

if (y[n] > 0)
y[n] ~ poisson(lambda) T[1,];

Example:

stanm2 <- stan_model(model_code="
data {
int y[3];
}
parameters {
real<lower=0, upper=1> theta;
real<lower=0> lambda;
}
model {
for (n in 1:3) {
(y[n] == 0) ~ bernoulli(theta);

if (y[n] > 0)
y[n] ~ poisson(lambda) T[1,];
}

}")

fit1 <- sampling(stanm2, chains = 2, iter = 1e4, data = list(y = c(1,2,0)))

[Cody Ross]

 Excellent,
Thanks for the quick reply.

[Bob Carpenter]

That was my fault --- I should've run it on simulated data.
Thanks for diagnosing, Marco.

- Bob

> On Dec 13, 2014, at 8:43 PM, Cody Ross <ctr...@ucdavis.edu> wrote:
>
>
> Excellent,
> Thanks for the quick reply.
>