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Bayesian nonparametric statistics : École d'été de probabilités de Saint-Flour LI - 2023 / Ismaël Castillo.

By: Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag). École d'été de probabilités de Saint-Flour. | Lecture notes in mathematics (Springer-Verlag) ; 2358.Publisher: Cham : Springer, [2024]Copyright date: ©2024Description: 1 online resource (xii, 216 pages) : illustrations (some color)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783031740350
  • 3031740351
Subject(s): DDC classification:
  • 519.5/42 23/eng/20241202
LOC classification:
  • QA278.8
Online resources:
Contents:
-1. Introduction, rates I.-2. Rates II and first examples.-3. Adaptation I: smoothness.-4. Adaptation II: high-dimensions and deep neural networks -- 5. Bernstein-von Mises I: functionals -- 6. Bernstein-von Mises II: multiscale and applications -- 7. classification and multiple testing -- 8. Variational approximations.
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. .
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
eBook eBook e-Library eBook LN Mathematic Available
Total holds: 0

Includes bibliographical references and index.

-1. Introduction, rates I.-2. Rates II and first examples.-3. Adaptation I: smoothness.-4. Adaptation II: high-dimensions and deep neural networks -- 5. Bernstein-von Mises I: functionals -- 6. Bernstein-von Mises II: multiscale and applications -- 7. classification and multiple testing -- 8. Variational approximations.

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. .

Online resource; title from PDF title page (SpringerLink, viewed December 2, 2024).

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