000			02271nam a22002177a 4500
005			20250510171159.0
008			250507b |||||||| |||| 00| 0 eng d
020			_a9783031740343
082			_a519.542 _bCAS
100			_aCastillo, Ismaël _923955
245			_aBayesian nonparametric statistics
260			_bSpringer _aCham _c2024
300			_axii, 214 p.
365			_aEURO _b59.99
490			_aLecture Notes in Mathematics (Springer-Verlag), 2358
500			_aTable 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]
520			_aThis 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)
650			_aNonparametric statistics _97513
650			_aBayesian statistical--Decision theory
942			_cBK _2ddc
999			_c9643 _d9643