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020 _a9783031740350
_9978-3-031-74035-0
024 7 _a10.1007/978-3-031-74035-0
_2doi
050 4 _aQA276-280
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
100 1 _aCastillo, Ismaël.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_987715
245 1 0 _aBayesian Nonparametric Statistics
_h[electronic resource] :
_bÉcole d’Été de Probabilités de Saint-Flour LI - 2023 /
_cby Ismaël Castillo.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXII, 216 p. 14 illus., 7 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aÉcole d'Été de Probabilités de Saint-Flour ;
_v2358
505 0 _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.
520 _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. .
650 0 _aStatistics.
_965982
650 0 _aMachine learning.
_955059
650 0 _aMathematical optimization.
_965522
650 0 _aCalculus of variations.
_967268
650 0 _aStatistical Physics.
_970323
650 0 _aProbabilities.
_965724
650 1 4 _aStatistical Theory and Methods.
650 2 4 _aMachine Learning.
_955059
650 2 4 _aCalculus of Variations and Optimization.
_967270
650 2 4 _aStatistical Physics.
_970323
650 2 4 _aProbability Theory.
_967428
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031740343
776 0 8 _iPrinted edition:
_z9783031740367
830 0 _aÉcole d'Été de Probabilités de Saint-Flour ;
_v2358
_987716
856 4 0 _uhttps://doi.org/10.1007/978-3-031-74035-0
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-LNM
999 _c65049
_d65049