LEADER 03816nam 22007575 450 001 996630872303316 005 20260121143931.0 010 $a9783031740350$b(electronic bk.) 010 $z9783031740343 024 7 $a10.1007/978-3-031-74035-0 035 $a(MiAaPQ)EBC31786551 035 $a(Au-PeEL)EBL31786551 035 $a(CKB)36601345100041 035 $a(DE-He213)978-3-031-74035-0 035 $a(PPN)281830452 035 $a(EXLCZ)9936601345100041 100 $a20241119d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBayesian Nonparametric Statistics $eÉcole d?Été de Probabilités de Saint-Flour LI - 2023 /$fby Ismaël Castillo 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (225 pages) 225 1 $aÉcole d'Été de Probabilités de Saint-Flour ;$v2358 311 08$aPrint version: Castillo, Ismaël Bayesian Nonparametric Statistics Cham : Springer,c2024 9783031740343 327 $a-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. 330 $aThis up-to-date overview of Bayesian nonparametric statistics provides both an introduction to the field and coverage of recent research topics, including deep neural networks, high-dimensional models and multiple testing, Bernstein-von Mises theorems and variational Bayes approximations, many of which have previously only been accessible through research articles. Although Bayesian posterior distributions are widely applied in astrophysics, inverse problems, genomics, machine learning and elsewhere, their theory is still only partially understood, especially in complex settings such as nonparametric or semiparametric models. Here, the available theory on the frequentist analysis of posterior distributions is outlined in terms of convergence rates, limiting shape results and uncertainty quantification. Based on lecture notes for a course given at the St-Flour summer school in 2023, the book is aimed at researchers and graduate students in statistics and probability. . 410 0$aÉcole d'Été de Probabilités de Saint-Flour ;$v2358 606 $aStatistics 606 $aMachine learning 606 $aMathematical optimization 606 $aCalculus of variations 606 $aStatistical physics 606 $aProbabilities 606 $aStatistical Theory and Methods 606 $aMachine Learning 606 $aCalculus of Variations and Optimization 606 $aStatistical Physics 606 $aProbability Theory 606 $aEstadística bayesiana$2thub 606 $aEstadística no paramètrica$2thub 608 $aLlibres electrònics$2thub 615 0$aStatistics. 615 0$aMachine learning. 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aStatistical physics. 615 0$aProbabilities. 615 14$aStatistical Theory and Methods. 615 24$aMachine Learning. 615 24$aCalculus of Variations and Optimization. 615 24$aStatistical Physics. 615 24$aProbability Theory. 615 7$aEstadística bayesiana 615 7$aEstadística no paramètrica 676 $a519.5 700 $aCastillo$b Ismaël$01775936 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a996630872303316 996 $aBayesian Nonparametric Statistics$94291109 997 $aUNISA