Parameter estimation and model selection for Neyman-Scott point processes

Area of Science:

• Spatial statistics
• Stochastic processes
• Point process modeling

Background:

• Neyman-Scott and similar point processes are widely used for modeling spatial data.
• Parameter estimation for these processes can be computationally challenging.
• Existing methods may struggle with complex spatial structures.

Purpose of the Study:

• To propose an approximative method for maximum likelihood estimation of parameters for Neyman-Scott and related point processes.
• To provide a computationally feasible and accurate approach for parameter estimation.
• To validate the method using simulated and real-world biological data.

Main Methods:

• Constructing a difference point pattern from pairs of points within the observation window.
• Expressing the intensity function of the constructed process using second-order characteristics of the original process.
• Treating the difference pattern as a non-homogeneous Poisson process for parameter estimation.

Main Results:

• The proposed method demonstrates computational feasibility and accuracy through simulations.
• The approach is successfully applied to two biological datasets.
• Comparison of various cluster process models based on goodness-of-fit was performed.

Conclusions:

• The approximative method offers a viable alternative for parameter estimation in Neyman-Scott and similar point processes.
• The technique is robust and applicable to complex spatial data, including biological patterns.
• The study facilitates a more effective analysis of clustered spatial phenomena.