Bayesian Nonparametrics

Name: Bayesian Nonparametrics
Availability: InStock
ISBN: 9780387955377

ISBN-10: 0387955372

ISBN-13: 9780387955377

Edition: 2003

Authors: J. K. Ghosh, R. V. Ramamoorthi

List price: $219.99

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Description:

The first systematic treatment of Bayesian nonparametric methods & the theory behind them, this volume is aimed at a broad audience of researchers interested in the continuous spectrum of robust alternatives to purely parametric & purely nonparametric methods of classical statistics.

Book details

List price: $219.99
Copyright year: 2003
Publisher: Springer New York
Publication date: 4/8/2003
Binding: Hardcover
Pages: 308
Size: 6.10" wide x 9.25" long x 0.75" tall
Weight: 1.254
Language: English



Introduction: Why Bayesian Nonparametrics-An Overview and Sum-mary



Preliminaries and the Finite Dimensional Case



Introduction



Metric Spaces



preliminaries



Weak Convergence



Posterior Distribution and Consistency



Preliminaries



Posterior Consistency and Posterior Robustness



Doob's Theorem



Wald-Type Conditions



Asymptotic Normality of MLE and Bernstein-von Mises Theorem



Ibragimov and Hasminski&ibreve; Conditions



Nonsubjective Priors



Fully Specified



Discussion



Conjugate and Hierarchical Priors



Exchangeability, De Finetti's Theorem, Exponential Families



<$>M({\cal X})<$> and Priors on <$>M({\cal X})<$>



Introduction



The Space M(X)



(Prior) Probability Measures on <$>M({\cal X})<$>



<$>{\cal X}<$> Finite



<$>{\cal X} = {\op R}<$>



Tail Free Priors



Tail Free Priors and 0-1 Laws



Space of Probability Measures on <$>M({\op R})<$>



De Finetti's Theorem



Dirichlet and Polya tree process



Dirichlet and Polya tree process



Finite Dimensional Dirichlet Distribution



Dirichlet Distribution via Polya Urn Scheme



Dirichlet Process on <$>M({\op R})<$>



Construction and Properties



The Sethuraman Construction



Support of D<sub>ï¿½</sub>



Convergence Properties of D<sub>ï¿½</sub>



Elicitation and Some Applications



Mutual Singularity of Dirichlet Priors



Mixtures of Dirichlet Process



Polya Tree Process



The Finite Case



<$>{\cal X} = {\op R}<$>



Consistency Theorems



Introduction



Preliminaries



Finite and Tail free case



Posterior Consistency on Densities



Schwartz Theorem



L<sub>1</sub>-Consistency



Consistency via LeCam's inequality



Density Estimation



Introduction



Polya Tree Priors



Mixtures of Kernels



Hierarchical Mixtures



Random Histograms



Weak Consistency



L<sub>1</sub>-Consistency



Mixtures of Normal Kernel



Dirichlet Mixtures: Weak Consistency



Dirichlet Mixtures: L<sub>1</sub>-Consistency



Extensions



Gaussian Process Priors



Inference for Location Parameter



Introduction



The Diaconis-Freedman Example



Consistency of the Posterior



Polya Tree Priors



Regression Problems



Introduction



Schwartz Theorem



Exponentially Consistent Tests



Prior Positivity of Neighborhoods



Polya Tree Priors



Dirichlet Mixture of Normals



Binary Response Regression with Unknown Link



Stochastic Regressor



Simulations



Uniform Distribution on Infinite-Dimensional Spaces



Introduction



Towards a Uniform Distribution



The Jeffreys Prior



Uniform Distribution via Sieves and Packing Numbers



Technical Preliminaries



The Jeffreys Prior Revisited



Posterior Consistency for Noninformative Priors for Infinite-Dimensional Problems



Convergence of Posterior at Optimal Rate



Survival Analysis-Dirichlet Priors



Introduction



Dirichlet Prior



Cumulative Hazard Function, Identifiability



Priors via Distributions of (Z, ï¿½)



Interval Censored Data



Neutral to the Right Priors



Introduction



Neutral to the Right Priors



Independent Increment Processes



Basic Properties



Beta Processes



Definition and Construction



Properties



Posterior Consistency



Exercises


References


Index