TY  - BOOK
AU  - Castillo,Ismaël
ED  - SpringerLink (Online service)
TI  - Bayesian Nonparametric Statistics: École d’Été de Probabilités de Saint-Flour LI - 2023 
T2  - École d'Été de Probabilités de Saint-Flour
SN  - 9783031740350
AV  - QA276-280 
PY  - 2024///
CY  - Cham
PB  - Springer Nature Switzerland, Imprint: Springer
KW  - Statistics
KW  - Machine learning
KW  - Mathematical optimization
KW  - Calculus of variations
KW  - Statistical Physics
KW  - Probabilities
KW  - Statistical Theory and Methods
KW  - Machine Learning
KW  - Calculus of Variations and Optimization
KW  - Probability Theory
N1  - -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
N2  - 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.
UR  - https://doi.org/10.1007/978-3-031-74035-0
ER  -