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        "4. Comparing Different Resolution Fits",
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      "headings": [
        "Introduction",
        "Walkthrough of Basic Usage",
        "1. Preparing and Validating the Input Data",
        "Location Hierarchy (locations_sim)",
        "Coverage Observations (observations_sim)",
        "Observation Metadata (populations_sim)",
        "Validation Failure Examples",
        "2. Exploring the Synthetic Dataset and Latent Features",
        "State-Level Observations & Latent Propensity",
        "County-Level Observations & Offsets",
        "School-Level Observations Across Counties",
        "3. Fitting the Model",
        "Basis Spline Coefficients ($\\beta_{\\text{bs}}$)",
        "Hierarchy Layer Variances ($\\sigma$)",
        "Vaccination Uptake Rates ($\\lambda_{\\text{raw}}$)",
        "4. Defining a Target for Predictions",
        "5. Predicting Coverage"
      ],
      "created": "2026-06-22 18:31:44",
      "modified": "2026-09-02 18:48:18",
      "commits": 2
    }
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