Bayesian Nonparametric Statistics: École d’Été de Probabilités de Saint-Flour LI - 2023

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Ismaël Castillo

Bayesian Nonparametric Statistics

École d’Été de Probabilités de Saint-Flour LI - 2023

Ismaël Castillo

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English

Springer International Publishing AG
19 November 2024

Probability & statistics; Optimisation; Stochastics; Statistical physics; Machine learning

Series: École d'Été de Probabilités de Saint-Flour

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.

By: Ismaël Castillo
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2024 ed.
Volume: 2358
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031740343
ISBN 10: 3031740343
Series: École d'Été de Probabilités de Saint-Flour
Pages: 216
Publication Date: 19 November 2024
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

-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.

Ismaël Castillo studied mathematics at the École Normale Supérieure de Lyon and obtained a PhD in statistics from the Université Paris-Sud at Orsay in 2006. After a postdoc at the Vrije Universiteit in Amsterdam, in 2009 he became CNRS researcher in Paris, France. Since 2015 he has been full professor of Statistics at Sorbonne Université in Paris. He has taught statistics courses worldwide, especially in Bayesian inference, including invited lectures at Cambridge, Columbia, Berlin, Lunteren and St-Flour. He is an IMS fellow and an honorary fellow of the Institut Universitaire de France.