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    Statistical estimation methods in localization microscopy (LM) rely on models that often mismatch experimental data. This study introduces the Misspecified Cramér-Rao Bound (MCRB) to accurately assess localization accuracy under real-world imperfections.

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    Area of Science:

    • Optics and Photonics
    • Statistical Physics
    • Biophysical Imaging

    Background:

    • Localization microscopy (LM) uses statistical models to estimate emitter locations and theoretical accuracy bounds.
    • The Cramér-Rao lower bound (CRLB) is a standard performance metric, assuming perfect model-data agreement.
    • Experimental uncertainties frequently cause model-data mismatch, invalidating CRLB accuracy.

    Purpose of the Study:

    • To derive and analyze the Misspecified Cramér-Rao Bound (MCRB) for localization microscopy.
    • To quantify the impact of experimental imperfections on localization accuracy limits.
    • To provide a framework for understanding performance bounds under model mismatch.

    Main Methods:

    • Derivation of the MCRB for various LM configurations.
    • Analysis of MCRB behavior under different Poisson statistics.
    • Quantitative assessment of experimental uncertainty effects on localization precision.

    Main Results:

    • The MCRB provides a more accurate lower bound on localization error than CRLB when models are misspecified.
    • Experimental imperfections significantly affect achievable localization accuracy.
    • The derived MCRB framework elucidates the impact of aberrations, calibration errors, and misalignment.

    Conclusions:

    • The MCRB is essential for realistic performance evaluation in localization microscopy.
    • Understanding model-data mismatch is critical for advancing LM precision.
    • This work offers a quantitative tool for optimizing LM experimental designs and data analysis.