Indeed, that appears to be the case:
using Turing, Random
@model poisson_model(y) = begin
theta_1 ~ Gamma(3, 1/5)
y ~ Poisson(2*theta_1)
end
Random.seed!(58844)
model_p = poisson_model(3)
chain2 = sample(model_p, NUTS(), 50000);
Output:
Summary Statistics
parameters mean std naive_se mcse ess rhat
Symbol Float64 Float64 Float64 Float64 Float64 Float64
theta_1 0.8557 0.3500 0.0016 0.0023 23968.1460 1.0000
Quantiles
parameters 2.5% 25.0% 50.0% 75.0% 97.5%
Symbol Float64 Float64 Float64 Float64 Float64
theta_1 0.3098 0.6009 0.8094 1.0604 1.6653