Hjort N.L., Holmes C., Müller P., Walker S.G. (eds.) Bayesian Nonparametrics

Cambridge: Cambridge University Press, 2010. — 308 p.What is it all about?
Who needs it?
The aims, purposes and contents of this book
What does this book do?
How do alternative models relate to each other?
A brief history of Bayesian nonparametrics
From the start to the present
Applications
Where does this book fit in the broader picture?
Further topics
Challenges and future developmentsBayesian choices
Decision theory
Asymptotics
General posterior inferenceMotivation
Construction by normalization
Conjugacy
Limits of the posterior
Discreteness
Self-similarity
Dirichlet samples and ties
Sethuraman stick-breaking representation
Mixtures of Dirichlet processes
Dirichlet process mixtures
Hierarchical Dirichlet processes
Motivation and implications
Instances of inconsistency
Approaches to consistency
Schwartz's theory
Uniformly consistent tests
Entropy and sieves
Gaussian processes
Semiparametric applications
Non-iid observations
Martingale method
Motivation, description and consequences
Prior concentration rate
Sieves
Finite-dimensional models
Dirichlet mixtures
Misspecified models
Non-iid extensions
Motivation and description
Infinite-dimensional normal models
General theory of Bayesian adaptation
Density estimation using splines
Parametric Bernshten-von Mises theorems
Nonparametric Bernshten-von Mises theorems
Nonexistence of Bernshten-von Mises theorems
Concluding remarksExchangeability assumption
A concise account of completely random measures
Models for survival analysis
Neutral-to-the-right priors
Priors for cumulative hazards: the beta process
Priors for hazard rates
General classes of discrete nonparametric priors
Normalized random measures with independent increments
Exchangeable partition probability function
Poisson-Kingman models and Gibbs-type priors
Species sampling models
Models for density estimation
Mixture models
Polya trees
Random means
Concluding remarksConstruction and interpretation
Transitions and Markov processes
Hazard regression models
Semiparametric competing risks models
Quantile inference
Shape analysis
Time series with nonparametric correlation function
Concluding remarks
Mixtures of beta processes
From nonparametric Bayes to parametric survival modelsHierarchical Dirichlet processes
Stick-breaking construction
Chinese restaurant franchise
Posterior structure of the HDP
Information retrieval
Multipopulation haplotype phasing
Topic modeling
Hidden Markov models with infinite state spaces
Word segmentation
Trees and grammars
Pitman-Yor processes
Hierarchical Pitman-Yor processes
Applications of the hierarchical Pitman-Yor process
Image segmentation
The beta process and the Bernoulli process
The Indian buffet process
Stick-breaking constructions
Hierarchical beta processes
Sparse latent variable models
Relational models
Hierarchical DPs with random effects
Analysis of densities and transformed DPs
Inference for hierarchical Bayesian nonparametric models
Chinese restaurant franchise sampler
Posterior representation sampler
Inference for HDP hidden Markov models
Inference for beta processes
Inference for hierarchical beta processes
DiscussionConstruction of finite-dimensional measures on observables
Recent advances in computation for Dirichlet process mixture modelsIllustration for simple repeated measurement models
Posterior computation
General random effects models
Latent factor regression models
Background
Basis functions and clustering
Functional Dirichlet process
Kernel-based approaches
Joint modeling
Local borrowing of information and clustering
Borrowing information across studies and centers
Motivation
Dependent Dirichlet processes
Kernel-based approaches
Conditional distribution modeling through DPMs
Reproductive epidemiology application
Bioinformatics
Modeling of differential gene expression
Analyzing polymorphisms and haplotypes
New species discovery
Nonparametric hypothesis testing
DiscussionRandom partitions
Polya trees
More DDP models
The ANOVA DDP
Classification with DDP models
Other data formats
An R package for nonparametric Bayesian inference
DiscussionAuthor index
Subject index