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:

$$|A_i| \cdot \Lambda(s)_{A_i} \sim \mathcal{Poisson}(|A_i| \cdot \mu_s)$$