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Bayesian Nonparametric Statistics: Theorems, Proofs, and Python Implementations (Computational Mathematics Library)

Higher Education

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Description

A rigorous, research-grade treatment of Bayesian nonparametric statistics for graduate students, statisticians, and machine learning researchers. From measure-theoretic foundations and de Finetti representation to completely random measures with Levy-Khintchine calculus, this text develops the theory of Dirichlet, Pitman Yor, and normalized random measures, beta and gamma processes for feature allocation, Gaussian and Polya tree priors, the Bayesian bootstrap, and species sampling models. Every chapter includes fully worked proofs and end of chapter Python demonstrations that implement samplers, posterior computations, and diagnostic checks. Chapters delve into exchangeable partition probability functions and size-biased stick-breaking, posterior consistency and contraction rates with sharp testing and entropy bounds, semiparametric Bernstein von Mises results and efficient influence functions, identifiability and LAN for functionals, and Poisson-Kingman and Gibbs-type priors that yield power law clustering. Advanced computation is covered in depth, including marginalized and blocked MCMC for mixtures and feature models, slice and retrospective samplers, split-merge moves, Poisson random measure augmentation for completely random measures, and scalable variational methods with principled truncation error control. Applications span hierarchical models, dependent processes with covariates, time series and HMMs, spatial mixtures and Cox processes, survival analysis with neutral to the right priors, and network models from Aldous Hoover representations. Designed as both a course text and a long term reference, it integrates measure theory, probability on Polish spaces, RKHS geometry, and modern asymptotics with reproducible code. Proofs are constructive, assumptions are explicit, and each chapter ends with Python demonstrations that mirror the theory for immediate experimentation.

Product Specifications

Format: paperback
ASIN: B0G24HSVFG
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Education > Higher Education
Domain: Amazon UK
Release Date: 12 November 2025
Listed Since: 13 November 2025

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Bayesian Nonparametric Statistics: Theorems, Proofs, and Python Implementations (Computational Mathematics Library)

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