Inference for Stationary Log-Gaussian Cox Point Processes using Bayesian Deep Learning: Application to Human Oral...

Area of Science:

• Spatial statistics
• Computational biology
• Machine learning

Background:

• Spatial point patterns often exhibit aggregation, requiring advanced models for analysis.
• Log-Gaussian Cox processes (LGCPs) are effective for modeling spatial aggregation but face computational challenges in Bayesian inference.
• High-dimensional LGCPs pose significant computational hurdles for traditional likelihood-based methods.

Purpose of the Study:

• To develop a computationally efficient inference method for Log-Gaussian Cox processes (LGCPs).
• To leverage amortized posterior estimation using invertible neural networks for LGCP parameter inference.
• To address the computational challenges in high-dimensional spatial point pattern analysis.

Main Methods:

• Implementation of a likelihood-free inference approach using the BayesFlow framework.
• Utilizing invertible neural networks for amortized posterior estimation of LGCP parameters.
• Validation through comprehensive numerical studies and application to real-world data.

Main Results:

• The proposed BayesFlow approach achieves substantial computational gains, especially for 2D LGCPs.
• Demonstrated reliability and efficiency of the neural simulation-based method.
• Successful application to analyze oral microbial biofilm images, showcasing practical utility.

Conclusions:

• BayesFlow offers a computationally efficient and reliable alternative for LGCP inference.
• The method accelerates the analysis of spatial point patterns, particularly in high dimensions.
• This approach has significant implications for understanding spatial heterogeneity and biological processes.