Bayesian Nonparametric Statistics
École d’Été de Probabilités de Saint-Flour LI - 2023
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Beschreibung
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.
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.
Gives an accessible up-to-date introduction to Bayesian nonparametric statistics Provides complete mathematical proofs or describes the key ideas Discusses recent topics such as deep neural networks and variational Bayes approximations
Autor*in
Ismaël Castillo
Themen in »Bayesian Nonparametric Statistics«
Bayesian Inference Posterior Distributions Nonparametric Models Bernstein-von Mises Theorems High-Dimensional Models Bayesian Deep Neural Networks Variational Bayes Uncertainty Quantification