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Bayesian Nonparametric Statistics : École d’Été de Probabilités de Saint-Flour LI - 2023 / by Ismaël Castillo.
Springer Nature - Springer Mathematics and Statistics eBooks 2024 English International Available online
View online- Format:
- Book
- Author/Creator:
- Castillo, Ismaël.
- Series:
- École d'Été de Probabilités de Saint-Flour ; 2358
- Language:
- English
- Subjects (All):
- Statistics.
- Machine learning.
- Mathematical optimization.
- Calculus of variations.
- Statistical physics.
- Probabilities.
- Statistical Theory and Methods.
- Machine Learning.
- Calculus of Variations and Optimization.
- Statistical Physics.
- Probability Theory.
- Local Subjects:
- Statistical Theory and Methods.
- Machine Learning.
- Calculus of Variations and Optimization.
- Statistical Physics.
- Probability Theory.
- Physical Description:
- 1 online resource (225 pages)
- Edition:
- 1st ed. 2024.
- Place of Publication:
- Cham : Springer Nature Switzerland : Imprint: Springer, 2024.
- 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. .
- 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.
- Notes:
- Description based on publisher supplied metadata and other sources.
- Other Format:
- Print version: Castillo, Ismaël Bayesian Nonparametric Statistics
- ISBN:
- 9783031740350
- OCLC:
- 1472990141
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