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Topographical Estimation of Visual Population Receptive Fields by fMRI

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Published on: February 3, 2015

Parameter estimation and model selection for Neyman-Scott point processes.

Ushio Tanaka¹, Yosihiko Ogata, Dietrich Stoyan

¹The Graduate University for Advanced Studies, Minami-Azabu 4-6-7, Minato-Ku, Tokyo 106-8569, Japan.

Biometrical Journal. Biometrische Zeitschrift

|July 21, 2007

Summary

This study introduces a new approximation for estimating parameters in Neyman-Scott point processes. The method uses difference patterns to analyze spatial data, proving effective in simulations and biological applications.

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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.