Bayesian Nonparametric Data Analysis (Springer Series in Statistics)

This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the bookℓ́ℓs structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in on-line software pages This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the bookĺls structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in on-line software pages Preface; Acronyms; Contents; 1 Introduction; References; 2 Density Estimation: DP Models; 2.1 Dirichlet Process; 2.1.1 Definition; 2.1.2 Posterior and Marginal Distributions; 2.2 Dirichlet Process Mixture; 2.2.1 The DPM Model; 2.2.2 Mixture of DPM; 2.3 Clustering Under the DPM; 2.4 Posterior Simulation for DPM Models; 2.4.1 Conjugate DPM Models; 2.4.2 Updating Hyper-Parameters; 2.4.3 Non-Conjugate DPM Models; 2.4.4 Neal's Algorithm 8; 2.4.5 Slice Sampler; 2.4.6 Finite DP; 2.5 Generalizations of the Dirichlet Processes; 2.5.1 Tail-Free Processes; 2.5.2 Species Sampling Models (SSM) Front Matter....Pages i-xiv Introduction....Pages 1-5 Density Estimation: DP Models....Pages 7-31 Density Estimation: Models Beyond the DP....Pages 33-50 Regression....Pages 51-75 Categorical Data....Pages 77-100 Survival Analysis....Pages 101-123 Hierarchical Models....Pages 125-143 Clustering and Feature Allocation....Pages 145-174 Other Inference Problems and Conclusion....Pages 175-178 Back Matter....Pages 179-193 Introduction -- Density Estimation: Dp Models -- Density Estimation: Models Beyond The Dp -- Regression -- Categorical Data -- Survival Analysis -- Hierarchical Models -- Clustering And Feature Allocation -- Other Inference Problems And Conclusion Peter Müller, Fernando Andréa Quintana, Alejandro Jara, Tim Hanson. Includes Bibliographical References And Index. Also Issued Online.