Bayesian Statistics

  1. Bayesian Regression Models
    1. Bayesian Linear Regression
      1. Model Specification
        1. Linear Model Structure
          1. Design Matrix
            1. Error Term Assumptions
            2. Prior Specification
              1. Priors for Regression Coefficients
                1. Conjugate Normal Priors
                  1. Weakly Informative Priors
                    1. Regularizing Priors
                    2. Priors for Error Variance
                      1. Inverse-Gamma Priors
                        1. Half-Cauchy Priors
                          1. Uniform Priors
                        2. Posterior Inference
                          1. Analytical Solutions
                            1. Conjugate Analysis
                              1. Numerical Methods
                              2. Posterior Predictive Distribution
                                1. Point Predictions
                                  1. Prediction Intervals
                                    1. Model Checking
                                    2. Model Diagnostics
                                      1. Residual Analysis
                                        1. Influential Observations
                                          1. Leverage and Cook's Distance
                                        2. Bayesian Generalized Linear Models
                                          1. GLM Framework
                                            1. Exponential Family Distributions
                                              1. Linear Predictor
                                              2. Logistic Regression
                                                1. Binomial Likelihood
                                                  1. Prior Specification
                                                    1. Posterior Inference
                                                      1. Interpretation of Coefficients
                                                        1. Classification Applications
                                                        2. Probit Regression
                                                          1. Data Augmentation
                                                            1. Latent Variable Interpretation
                                                            2. Poisson Regression
                                                              1. Count Data Modeling
                                                                1. Overdispersion Issues
                                                                  1. Negative Binomial Extensions
                                                                  2. Computational Methods
                                                                    1. MCMC for GLMs
                                                                      1. Data Augmentation Techniques
                                                                        1. Auxiliary Variable Methods
                                                                      2. Regularization and Shrinkage
                                                                        1. Motivation for Regularization
                                                                          1. Overfitting Prevention
                                                                            1. High-Dimensional Problems
                                                                              1. Variable Selection
                                                                              2. Ridge Regression
                                                                                1. Gaussian Shrinkage Priors
                                                                                  1. Prior Specification
                                                                                    1. Effect on Estimates
                                                                                      1. Bias-Variance Trade-off
                                                                                      2. Lasso Regression
                                                                                        1. Laplace Shrinkage Priors
                                                                                          1. Sparsity Induction
                                                                                            1. Variable Selection Properties
                                                                                              1. Computational Challenges
                                                                                              2. Elastic Net
                                                                                                1. Combining Ridge and Lasso
                                                                                                  1. Grouped Variable Selection
                                                                                                  2. Horseshoe Prior
                                                                                                    1. Motivation and Properties
                                                                                                      1. Global-Local Shrinkage
                                                                                                        1. Applications in Sparse Models
                                                                                                          1. Computational Implementation
                                                                                                          2. Spike-and-Slab Priors
                                                                                                            1. Variable Selection Framework
                                                                                                              1. Mixture Prior Specification
                                                                                                                1. Posterior Inclusion Probabilities
                                                                                                              2. Model Selection in Regression
                                                                                                                1. Variable Selection
                                                                                                                  1. Bayesian Variable Selection
                                                                                                                    1. Stochastic Search Variable Selection
                                                                                                                      1. Reversible Jump MCMC
                                                                                                                      2. Model Averaging
                                                                                                                        1. Bayesian Model Averaging
                                                                                                                          1. Accounting for Model Uncertainty
                                                                                                                            1. Prediction with Multiple Models

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                                                                                                                        7. Model Checking and Selection

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                                                                                                                        9. Advanced Topics