Bayesian nonparametric statistics

By:

Castillo, Ismaël

Material type: Text

TextSeries: Lecture Notes in Mathematics (Springer-Verlag), 2358Publication details: Springer Cham 2024Description: xii, 214 pISBN:

9783031740343

Subject(s):

DDC classification:

519.542 CAS

Summary: This up-to-date overview of Bayesian nonparametric statistics provides both an introduction to the field and coverage of recent research topics, including deep neural networks, high-dimensional models and multiple testing, Bernstein-von Mises theorems and variational Bayes approximations, many of which have previously only been accessible through research articles. Although Bayesian posterior distributions are widely applied in astrophysics, inverse problems, genomics, machine learning and elsewhere, their theory is still only partially understood, especially in complex settings such as nonparametric or semiparametric models. Here, the available theory on the frequentist analysis of posterior distributions is outlined in terms of convergence rates, limiting shape results and uncertainty quantification. Based on lecture notes for a course given at the St-Flour summer school in 2023, the book is aimed at researchers and graduate students in statistics and probability. (https://link.springer.com/book/10.1007/978-3-031-74035-0)

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Book	Indian Institute of Management LRC General Stacks	Operations Management & Quantitative Techniques	519.542 CAS (Browse shelf(Opens below))	1	Available		008585

Table of contents:
Introduction, Rates I
Ismaël Castillo
Pages 1-24
Rates II and First Examples
Ismaël Castillo
Pages 25-46
Adaptation I: Smoothness
Ismaël Castillo
Pages 47-65
Adaptation II: High-Dimensions and Deep Neural Networks
Ismaël Castillo
Pages 67-102
Bernstein-von Mises I: Functionals
Ismaël Castillo
Pages 103-123
Bernstein-von Mises II: Multiscale and Applications
Ismaël Castillo
Pages 125-150
Classification and Multiple Testing
Ismaël Castillo
Pages 151-172
Variational Approximations
Ismaël Castillo
Pages 173-188
[https://link.springer.com/book/10.1007/978-3-031-74035-0]

This up-to-date overview of Bayesian nonparametric statistics provides both an introduction to the field and coverage of recent research topics, including deep neural networks, high-dimensional models and multiple testing, Bernstein-von Mises theorems and variational Bayes approximations, many of which have previously only been accessible through research articles. Although Bayesian posterior distributions are widely applied in astrophysics, inverse problems, genomics, machine learning and elsewhere, their theory is still only partially understood, especially in complex settings such as nonparametric or semiparametric models. Here, the available theory on the frequentist analysis of posterior distributions is outlined in terms of convergence rates, limiting shape results and uncertainty quantification. Based on lecture notes for a course given at the St-Flour summer school in 2023, the book is aimed at researchers and graduate students in statistics and probability.

(https://link.springer.com/book/10.1007/978-3-031-74035-0)

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