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    Area of Science:

    • Spatial statistics
    • Computational statistics
    • Bioinformatics

    Background:

    • Spatial point patterns exhibit aggregation, crucial for understanding heterogeneity and event processes.
    • Log-Gaussian Cox processes (LGCPs) model spatial aggregation but face computational challenges in Bayesian inference, especially in high dimensions.

    Purpose of the Study:

    • To develop a novel, computationally efficient likelihood-free inference method for LGCPs.
    • To leverage BayesFlow and invertible neural networks for amortized posterior estimation in spatial point pattern analysis.

    Main Methods:

    • Proposed a likelihood-free inference approach using the BayesFlow framework.
    • Employed invertible neural networks to approximate the posterior distribution of LGCP parameters.
    • Validated the method through comprehensive numerical studies and application to oral microbial biofilm images.

    Main Results:

    • The BayesFlow approach provides a significant computational gain, particularly for 2D LGCPs.
    • Demonstrated the reliability and robustness of the proposed framework.
    • Successfully applied the method to analyze oral microbial biofilm data.

    Conclusions:

    • BayesFlow offers a powerful and efficient alternative for Bayesian inference in LGCPs.
    • The method accelerates the analysis of spatial aggregation phenomena.
    • This approach has broad applicability in fields dealing with spatial point pattern data.