03545nam a22006015i 4500 978-3-031-74035-0 DE-He213 20251030113318.0 cr nn 008mamaa 241119s2024 sz | s |||| 0|eng d 9783031740350 978-3-031-74035-0 10.1007/978-3-031-74035-0 doi QA276-280 PBT bicssc MAT029000 bisacsh PBT thema Castillo, Ismaël. author. aut http://id.loc.gov/vocabulary/relators/aut 87715 Bayesian Nonparametric Statistics [electronic resource] : École d’Été de Probabilités de Saint-Flour LI - 2023 / by Ismaël Castillo. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XII, 216 p. 14 illus., 7 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda École d'Été de Probabilités de Saint-Flour ; 2358 -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. . Statistics. 65982 Machine learning. 55059 Mathematical optimization. 65522 Calculus of variations. 67268 Statistical Physics. 70323 Probabilities. 65724 Statistical Theory and Methods. Machine Learning. 55059 Calculus of Variations and Optimization. 67270 Statistical Physics. 70323 Probability Theory. 67428 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031740343 Printed edition: 9783031740367 École d'Été de Probabilités de Saint-Flour ; 2358 87716 https://doi.org/10.1007/978-3-031-74035-0 ZDB-2-SMA ZDB-2-SXMS ZDB-2-LNM 65049 65049