03818nam 22007575 450 991090838120332120260121143931.09783031740350(electronic bk.)978303174034310.1007/978-3-031-74035-0(MiAaPQ)EBC31786551(Au-PeEL)EBL31786551(CKB)36601345100041(DE-He213)978-3-031-74035-0(PPN)281830452(EXLCZ)993660134510004120241119d2024 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierBayesian Nonparametric Statistics École d’Été de Probabilités de Saint-Flour LI - 2023 /by Ismaël Castillo1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Springer,2024.1 online resource (225 pages)École d'Été de Probabilités de Saint-Flour ;2358Print version: Castillo, Ismaël Bayesian Nonparametric Statistics Cham : Springer,c2024 9783031740343 -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. .École d'Été de Probabilités de Saint-Flour ;2358StatisticsMachine learningMathematical optimizationCalculus of variationsStatistical physicsProbabilitiesStatistical Theory and MethodsMachine LearningCalculus of Variations and OptimizationStatistical PhysicsProbability TheoryEstadística bayesianathubEstadística no paramètricathubLlibres electrònicsthubStatistics.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.Estadística bayesianaEstadística no paramètrica519.5Castillo Ismaël1775936MiAaPQMiAaPQMiAaPQ9910908381203321Bayesian Nonparametric Statistics4291109UNINA