03344nam a22005535i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202072001500225100008800240245015200328250001800480264006900498300006400567336002600631337002600657338003600683347002400719490006300743505032600806520098701132650002302119650002902142650003802171650003502209650003202244650002602276650003602302650002902338650005202367650003202419650003102451710003402482773002602516776003602542776003602578830007002614856004602684912001402730912001502744912001402759999001702773978-3-031-74035-0DE-He21320251030113318.0cr nn 008mamaa241119s2024    sz |    s    |||| 0|eng d  a97830317403509978-3-031-74035-07 a10.1007/978-3-031-74035-02doi 4aQA276-280 7aPBT2bicssc 7aMAT0290002bisacsh 7aPBT2thema1 aCastillo, Ismaël.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98771510aBayesian Nonparametric Statisticsh[electronic resource] :bÉcole d’Été de Probabilités de Saint-Flour LI - 2023 /cby Ismaël Castillo.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXII, 216 p. 14 illus., 7 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aÉcole d'Été de Probabilités de Saint-Flour ;v23580 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.  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. . 0aStatistics.965982 0aMachine learning.955059 0aMathematical optimization.965522 0aCalculus of variations.967268 0aStatistical Physics.970323 0aProbabilities.96572414aStatistical Theory and Methods.24aMachine Learning.95505924aCalculus of Variations and Optimization.96727024aStatistical Physics.97032324aProbability Theory.9674282 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303174034308iPrinted edition:z9783031740367 0aÉcole d'Été de Probabilités de Saint-Flour ;v235898771640uhttps://doi.org/10.1007/978-3-031-74035-0  aZDB-2-SMA  aZDB-2-SXMS  aZDB-2-LNM  c65049d65049