Spatial point process vs. spatial point pattern

• Spatial point process: a stochastic process \(\{X_1, X_2, ..., X_{N(A)}\}\) taking values in a planar region \(A \subset \mathbb{R}^2\).

  !! \(N(A)\) is a random variable !!

• Spatial point pattern: a single realization of a spatial point process.

  Each realization has a different number of points and different locations.

  The points are also often referred to as events.