École d’Été de Probabilités de Saint-Flour LI - 2023 Castillo, Ismaël. creator author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 1st ed. 2024. monographic eng

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electronic resource

access XII, 216 p. 14 illus., 7 illus. in color. online resource. 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. . -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. by Ismaël Castillo. 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 QA276-280 9783031740350 https://doi.org/10.1007/978-3-031-74035-0 https://doi.org/10.1007/978-3-031-74035-0 241119 20251030113318.0 978-3-031-74035-0