Question: Scaled Poisson expectation

I'm trying to implement the GP with a Poisson likelihood whose parameter may vary with the observations[^1]:
$$ y_i \sim Poisson(e_i exp(f_i))$$
where f_i is the GP. Is this possible?

[^1]:  [Approximate inference for disease mapping with sparse Gaussian processes](https://onlinelibrary.wiley.com/doi/10.1002/sim.3895), Jarno Vanhatalo, Ville Pietiläinen, Aki Vehtari (Eq. 1)

