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        "Approach 1: Two-Stage (brms + shrinkr)",
        "Stage 1: Fit Cox Model",
        "Stage 2: Apply Hierarchical Shrinkage",
        "Step 1: Extract posterior samples",
        "Step 2: Fit a Gaussian mixture approximation",
        "Step 3: Apply a hierarchical prior",
        "Approach 2: Full Hierarchical (brms)",
        "Approach 3: Two-Stage (Frequentist + shrinkr)",
        "Compare Three Approaches",
        "Numerical comparison",
        "Visual comparison",
        "Sensitivity Analysis: Exploring Different Priors",
        "Prior densities",
        "Heterogeneity estimates",
        "Impact on cell type estimates",
        "Key Takeaways",
        "Session Info"
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      "title": "Working with shrinkr in the Tidy Bayesian Ecosystem",
      "author": "Jacob M. Maronge",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Overview",
        "Example: Multi-Region Clinical Trial",
        "Simulate Stage 1 Results",
        "Fit shrinkr Model",
        "Working with posterior Package",
        "Extract Draws",
        "Basic Summaries",
        "Check Convergence",
        "Diagnostic Plots with bayesplot",
        "Trace Plots",
        "Density Plots",
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        "Tidy Analysis with tidybayes",
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        "Computing Contrasts",
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        "Quantile Dotplots",
        "Gradient Intervals",
        "Comparing Pre- and Post-Shrinkage",
        "Extract Both Estimates",
        "Custom Comparison Plot",
        "Complete Workflow Example",
        "Advanced: Custom Analyses",
        "Probability Statements",
        "Tail Probabilities",
        "Ranking Analysis",
        "Further Reading"
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      "modified": "2026-06-12 15:00:34",
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