Meaning
Stochastic models generate random sets of locations within a defined geometric space according to specific probabilistic rules. A spatial point process defines the mathematical framework for analyzing the distribution of objects such as defects on a battery electrode or the placement of charging stations. The process is characterized by its intensity, which is the expected number of points per unit area, and its interaction structure.
Intensity Variable
Homogeneous models assume a constant intensity across the entire region. An intensity variable changes in non-homogeneous models to reflect underlying environmental gradients.
Interaction Rule
Interactions between points are modeled using gibbs or poisson structures. In a simple poisson process, the locations are independent. More complex models include inhibitory effects where points cannot be closer than a certain distance, or attractive effects where points tend to form groups.
These interactions are captured by the probability density function of the process. Estimating the parameters of the model allows for the simulation of new patterns that share the same statistical properties as the observed data.
Application Context
Validating a model involves comparing its summary statistics to the original dataset. An application context determines which type of process is most appropriate for the physical phenomenon.
