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Author Hjort, Nils Lid
Title Bayesian Nonparametrics
Imprint Cambridge : Cambridge University Press, 2010
©2010
book jacket
Descript 1 online resource (310 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Cambridge Series in Statistical and Probabilistic Mathematics ; v.28
Cambridge Series in Statistical and Probabilistic Mathematics
Note Cover -- Bayesian Nonparametrics -- Title -- Copyright -- Contents -- Contributors -- An invitation to Bayesian nonparametrics -- Bayesian nonparametrics -- What is it all about? -- Who needs it? -- Why now? -- The aims, purposes and contents of this book -- A background event -- What does this book do? -- How do alternative models relate to each other? -- How to teach from this book -- A brief history of Bayesian nonparametrics -- From the start to the present -- Applications -- Where does this book fit in the broader picture? -- Further topics -- Computation and software\sindexsoftware packages -- Challenges and future developments -- References -- 1 Bayesian nonparametric methods: motivation and ideas -- 1.1 Introduction -- 1.2 Bayesian choices -- 1.3 Decision theory -- 1.4 Asymptotics -- 1.5 General posterior inference -- 1.6 Discussion -- References -- 2 The Dirichlet process, related priors and posterior asymptotics -- 2.1 Introduction -- 2.2 The Dirichlet process -- 2.2.1 Motivation -- 2.2.2 Construction of the Dirichlet process\sindexDirichlet process!construction -- Naive construction -- Construction using a countable generator -- Construction by normalization -- 2.2.3 Properties -- Moments and marginal distribution -- Linear functionals -- Conjugacy -- Posterior mean -- Limits of the posterior -- Lack of smoothness -- Negative correlation -- Discreteness -- Support -- Self-similarity -- Limit types -- Dirichlet samples and ties -- Sethuraman stick-breaking representation -- Mutual singularity -- Tail of a Dirichlet process -- 2.3 Priors related to the Dirichlet process -- 2.3.1 Mixtures of Dirichlet processes -- 2.3.2 Dirichlet process mixtures -- 2.3.3 Hierarchical Dirichlet processes -- 2.3.4 Invariant and conditioned Dirichlet processes -- 2.4 Posterior consistency -- 2.4.1 Motivation and implications -- 2.4.2 Doob's theorem
2.4.3 Instances of inconsistency -- 2.4.4 Approaches to consistency -- 2.4.5 Schwartz's theory -- Kullback-Leibler property -- Bounding the numerator -- Uniformly consistent tests -- Entropy and sieves -- 2.4.6 Density estimation -- Dirichlet mixtures -- Gaussian processes -- Pólya tree processes -- 2.4.7 Semiparametric applications -- 2.4.8 Non-i.i.d. observations -- 2.4.9 Sieve-free approaches -- Martingale method -- Power-posterior distribution -- 2.5 Convergence rates of posterior distributions -- 2.5.1 Motivation, description and consequences -- 2.5.2 General theory -- Prior concentration rate -- Entropy and tests -- Sieves -- 2.5.3 Applications -- Optimal rates using brackets -- Finite-dimensional models -- Log-spline priors -- Dirichlet mixtures -- Gaussian processes -- 2.5.4 Misspecified models -- 2.5.5 Non-i.i.d. extensions -- 2.6 Adaptation and model selection -- 2.6.1 Motivation and description -- 2.6.2 Infinite-dimensional normal models -- 2.6.3 General theory of Bayesian adaptation -- 2.6.4 Density estimation using splines -- 2.6.5 Bayes factor consistency -- 2.7 Bernshteǐn-von Mises theorems -- 2.7.1 Parametric Bernshteǐn-von Mises theorems -- 2.7.2 Nonparametric Bernshteǐn-von Mises theorems -- 2.7.3 Semiparametric Bernshteǐn-von Mises theorems -- 2.7.4 Nonexistence of Bernshteǐn-von Mises theorems -- 2.8 Concluding remarks -- References -- 3 Models beyond the Dirichlet process -- 3.1 Introduction -- 3.1.1 Exchangeability assumption -- 3.1.2 A concise account of completely random measures -- 3.2 Models for survival analysis -- 3.2.1 Neutral-to-the-right priors -- 3.2.2 Priors for cumulative hazards: the beta process -- 3.2.3 Priors for hazard rates -- 3.3 General classes of discrete nonparametric priors -- 3.3.1 Normalized random measures with independent increments -- 3.3.2 Exchangeable partition probability function
3.3.3 Poisson-Kingman models and Gibbs-type priors -- 3.3.4 Species sampling models -- 3.4 Models for density estimation -- 3.4.1 Mixture models -- 3.4.2 Pólya trees -- 3.5 Random means -- 3.6 Concluding remarks -- References -- 4 Further models and applications -- 4.1 Beta processes for survival and event history models -- 4.1.1 Construction and interpretation -- 4.1.2 Transitions and Markov processes -- 4.1.3 Hazard regression models -- 4.1.4 Semiparametric competing risks models -- 4.2 Quantile inference -- 4.3 Shape analysis -- 4.4 Time series with nonparametric correlation function -- 4.5 Concluding remarks -- 4.5.1 Bernshteǐn-von Mises theorems -- 4.5.2 Mixtures of beta processes -- 4.5.3 Bayesian kriging -- 4.5.4 From nonparametric Bayes to parametric survival models -- References -- 5 Hierarchical Bayesian nonparametric models with applications -- 5.1 Introduction -- 5.2 Hierarchical Dirichlet processes -- 5.2.1 Stick-breaking construction -- 5.2.2 Chinese restaurant franchise -- 5.2.3 Posterior structure of the HDP -- 5.2.4 Applications of the HDP -- Information retrieval -- Multipopulation haplotype phasing -- Topic modeling -- 5.3 Hidden Markov models with infinite state spaces -- 5.3.1 Applications of the HDP-HMM -- Speaker diarization -- Word segmentation -- Trees and grammars -- 5.4 Hierarchical Pitman-Yor processes -- 5.4.1 Pitman-Yor processes -- 5.4.2 Hierarchical Pitman-Yor processes -- 5.4.3 Applications of the hierarchical Pitman-Yor process -- 5.5 The beta process and the Indian buffet process -- 5.5.1 The beta process and the Bernoulli process -- 5.5.2 The Indian buffet process -- 5.5.3 Stick-breaking constructions -- 5.5.4 Hierarchical beta processes -- 5.5.5 Applications of the beta process -- Sparse latent variable models -- Relational models -- 5.6 Semiparametric models -- 5.6.1 Hierarchical DPs with random effects
5.6.2 Analysis of densities and transformed DPs -- 5.7 Inference for hierarchical Bayesian nonparametric models -- 5.7.1 Inference for hierarchical Dirichlet processes -- Chinese restaurant franchise sampler -- Posterior representation sampler -- 5.7.2 Inference for HDP hidden Markov models -- 5.7.3 Inference for beta processes -- 5.7.4 Inference for hierarchical beta processes -- 5.8 Discussion -- References -- 6 Computational issues arising in Bayesian nonparametric hierarchical models -- 6.1 Introduction -- 6.2 Construction of finite-dimensional measures on observables -- 6.3 Recent advances in computation for Dirichlet process mixture models -- References -- 7 Nonparametric Bayes applications to biostatistics -- 7.1 Introduction -- 7.2 Hierarchical modeling with Dirichlet process priors -- 7.2.1 Illustration for simple repeated measurement models -- 7.2.2 Posterior computation -- 7.2.3 General random effects models -- 7.2.4 Latent factor regression models -- 7.3 Nonparametric Bayes functional data analysis -- 7.3.1 Background -- 7.3.2 Basis functions and clustering -- 7.3.3 Functional Dirichlet process -- 7.3.4 Kernel-based approaches -- 7.3.5 Joint modeling -- 7.4 Local borrowing of information and clustering -- 7.5 Borrowing information across studies and centers -- 7.6 Flexible modeling of conditional distributions -- 7.6.1 Motivation -- 7.6.2 Dependent Dirichlet processes -- 7.6.3 Kernel-based approaches -- 7.6.4 Conditional distribution modeling through DPMs -- 7.6.5 Reproductive epidemiology application -- 7.7 Bioinformatics -- 7.7.1 Modeling of differential gene expression -- 7.7.2 Analyzing polymorphisms and haplotypes -- 7.7.3 New species discovery -- 7.8 Nonparametric hypothesis testing -- 7.9 Discussion -- References -- 8 More nonparametric Bayesian models for biostatistics -- 8.1 Introduction -- 8.2 Random partitions
8.3 Pólya trees -- 8.4 More DDP models -- 8.4.1 The ANOVA DDP -- 8.4.2 Classification with DDP models -- 8.5 Other data formats -- 8.6 An R package for nonparametric Bayesian inference -- 8.7 Discussion -- References -- Author index -- Subject index
The most intelligent guide to the hottest field in statistics
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Hjort, Nils Lid Bayesian Nonparametrics Cambridge : Cambridge University Press,c2010 9780521513463
Subject Bayesian statistical decision theory.;Nonparametric statistics
Electronic books
Alt Author Holmes, Chris
Müller, Peter
Walker, Stephen G
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