Bayesian Statistics

  1. Model Checking and Selection
    1. Philosophy of Model Checking
      1. Models as Approximations
        1. Iterative Model Building
          1. The Role of Domain Knowledge
          2. Assessing Model Fit
            1. Goodness-of-Fit Measures
              1. Deviance and Information Criteria
                1. Residual Analysis
                2. Identifying Model Misspecification
                  1. Systematic Patterns in Residuals
                    1. Outlier Detection
                      1. Influential Observations
                    2. Posterior Predictive Checks
                      1. Conceptual Framework
                        1. Replicating the Data Generation Process
                          1. Model Criticism Philosophy
                          2. Implementation
                            1. Generating Replicated Datasets
                              1. Test Statistics Selection
                              2. Graphical Checks
                                1. Visual Comparison Methods
                                  1. Histogram Comparisons
                                    1. Q-Q Plots
                                      1. Scatter Plots
                                      2. Numerical Summaries
                                        1. Bayesian p-values
                                          1. Posterior Predictive p-values
                                            1. Interpretation and Limitations
                                              1. Choice of Test Statistics
                                              2. Discrepancy Measures
                                                1. Standardized Residuals
                                                  1. Pearson Chi-Square Statistics
                                                    1. Custom Test Statistics
                                                  2. Model Comparison and Selection
                                                    1. Bayesian Model Comparison Philosophy
                                                      1. Model Uncertainty
                                                        1. Model Averaging vs. Selection
                                                        2. Bayes Factors
                                                          1. Definition and Calculation
                                                            1. Interpretation Guidelines
                                                              1. Jeffreys' Scale
                                                                1. Computational Challenges
                                                                  1. Marginal Likelihood Estimation
                                                                    1. Savage-Dickey Density Ratio
                                                                    2. Information Criteria
                                                                      1. Deviance Information Criterion
                                                                        1. Effective Number of Parameters
                                                                          1. Calculation and Use
                                                                            1. Limitations
                                                                            2. Widely Applicable Information Criterion
                                                                              1. Pointwise Predictive Accuracy
                                                                                1. Calculation and Use
                                                                                  1. Advantages over DIC
                                                                                  2. Leave-One-Out Cross-Validation
                                                                                    1. Procedure and Implementation
                                                                                      1. Pareto Smoothed Importance Sampling
                                                                                        1. Interpretation and Use
                                                                                        2. Expected Log Pointwise Predictive Density
                                                                                          1. Theoretical Foundation
                                                                                            1. Practical Estimation
                                                                                          2. Model Averaging
                                                                                            1. Bayesian Model Averaging
                                                                                              1. Weight Calculation
                                                                                                1. Prediction with Multiple Models
                                                                                                2. Sensitivity Analysis
                                                                                                  1. Prior Sensitivity
                                                                                                    1. Varying Prior Specifications
                                                                                                      1. Robustness Assessment
                                                                                                      2. Likelihood Sensitivity
                                                                                                        1. Alternative Model Specifications
                                                                                                        2. Computational Sensitivity
                                                                                                          1. MCMC Diagnostics
                                                                                                            1. Convergence Assessment

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                                                                                                      6. Hierarchical Models

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                                                                                                      8. Bayesian Regression Models