Considering intensity as a stochastic variable
However we can approach intensity as a (locally) stochastic variable with a Poisson distribution:
\[\Lambda(s) \sim \mathcal{Poisson}(\mu_s)\]
To fit this model, we use the number of events in subregions \(A_i\) of \(A\) and use the area of \(A_i\) as an offset:
\[|A_i| \cdot \Lambda(s)_{A_i} \sim \mathcal{Poisson}(|A_i| \cdot \mu_s)\]