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Preface Introduction Bayesian Modelling Statistical Model Bayes Model Advantages Sequential Analysis Big Data Hierarchical Models List of Problems Choice of Prior Subjective Priors Conjugate Priors Non-informative Priors Laplace Prior Jeffreys Prior Reference Priors List of Problems Decision Theory Basics of Decision Theory Bayesian Decision Theory Common Bayes Decision Rules Quadratic Loss Absolute Error Loss Prediction The 0–1 Loss Intrinsic Losses The Minimax Criterion Bridges List of Problems Asymptotic Theory Consistency Schwartz’ Theorem List of Problems Normal Linear Models Univariate Linear Models Bayes Linear Models Conjugate Prior: Parameter θ = β, σ2 Known Conjugate Prior: Parameter θ = (β, σ2) Jeffreys Prior Linear Mixed Models Bayes Linear Mixed Model, Marginal Model Bayes Hierarchical Linear Mixed Model Multivariate Linear Models Bayes Multivariate Linear Models Conjugate Prior Jeffreys Prior List of Problems Estimation Maximum a Posteriori (MAP) Estimator Regularized Estimators Bayes Rules Estimation in Univariate Linear Models Estimation in Multivariate Linear Models Credible Sets Credible Sets in Linear Models Prediction Prediction in Linear Models List of Problems Testing and Model Comparison Bayes Rule Bayes Factor Point Null Hypothesis Bayes Factor in Linear Model Improper Prior Bayes Information Bayesian Information Criterion (BIC) Deviance Information Criterion (DIC) List of Problems Computational Techniques Deterministic Methods Brute-Force Laplace Approximation Independent Monte Carlo Methods Importance Sampling (IS) Sampling from the Posterior Sampling Importance Resampling (SIR) Rejection Algorithm Markov Chain Monte Carlo (MCMC) Metropolis–Hastings Algorithms Gibbs Sampling Approximative Bayesian Computation (ABC) Variational Inference (VI) List of Problems Solutions Appendix Discrete Distributions Continuous Distributions Multivariate Distributions Matrix-Variate Distributions Bibliography Index