Bayesian Statistics

  1. Multi-Parameter Models
    1. Joint Posterior Distributions
      1. Definition and Notation
        1. Interpretation in Multivariate Contexts
          1. Correlation Structure
            1. Contour Plots and Visualization
            2. Marginal Posterior Distributions
              1. Marginalization Process
                1. Integration over Nuisance Parameters
                  1. Practical Calculation Methods
                    1. Numerical Integration
                    2. Conditional Posterior Distributions
                      1. Definition and Use
                        1. Conditioning on Other Parameters
                          1. Role in Gibbs Sampling
                            1. Full Conditional Distributions
                            2. The Multivariate Normal Distribution
                              1. Properties and Parameterization
                                1. Mean Vector and Covariance Matrix
                                  1. Bayesian Inference with Multivariate Normals
                                    1. Conjugate Analysis
                                      1. Marginal and Conditional Distributions
                                      2. The Multinomial Model
                                        1. Model Structure
                                          1. Categorical Data Analysis
                                            1. Dirichlet-Multinomial Conjugacy
                                              1. Dirichlet Prior Distribution
                                                1. Multinomial Likelihood
                                                  1. Posterior Dirichlet Distribution
                                                    1. Parameter Interpretation
                                                  2. The Normal Model with Unknown Mean and Variance
                                                    1. Model Structure
                                                      1. Joint Inference Problem
                                                        1. Normal-Inverse-Gamma Prior
                                                          1. Parameterization
                                                            1. Prior Specification
                                                              1. Posterior Derivation
                                                                1. Marginal Posteriors
                                                                2. Normal-Inverse-Chi-Squared Prior
                                                                  1. Alternative Parameterization
                                                                    1. Relationship to Inverse-Gamma
                                                                  2. Bivariate and Multivariate Extensions
                                                                    1. Multivariate Normal with Unknown Parameters
                                                                      1. Wishart and Inverse-Wishart Distributions
                                                                        1. Matrix-Normal Distributions

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                                                                      2. Single-Parameter Models

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                                                                      4. Bayesian Computation