Fundamentals of Nonparametric Bayesian Inference

Erscheinungsjahr 2019
ISBN: 978-0-521-87826-5
Verlag: Cambridge University Press

Buch, Englisch, Band 44, 670 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 1438 g

Reihe: Cambridge Series in Statistical and Probabilistic Mathematics

Explosive growth in computing power has made Bayesian methods for infinite-dimensional models - Bayesian nonparametrics - a nearly universal framework for inference, finding practical use in numerous subject areas. Written by leading researchers, this authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors. Because understanding the behavior of posteriors is critical to selecting priors that work, the large sample theory is developed systematically, illustrated by various examples of model and prior combinations. Precise sufficient conditions are given, with complete proofs, that ensure desirable posterior properties and behavior. Each chapter ends with historical notes and numerous exercises to deepen and consolidate the reader's understanding, making the book valuable for both graduate students and researchers in statistics and machine learning, as well as in application areas such as econometrics and biostatistics.

Autoren/Hrsg.

Ghosal, Subhashis

Vaart, Aad van der

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftsstatistik, Demographie
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

Preface; Glossary of symbols; 1. Introduction; 2. Priors on function spaces; 3. Priors on spaces of probability measures; 4. Dirichlet processes; 5. Dirichlet process mixtures; 6. Consistency: general theory; 7. Consistency: examples; 8. Contraction rates: general theory; 9. Contraction rates: examples; 10. Adaptation and model selection; 11. Gaussian process priors; 12. Infinite-dimensional Bernstein–von Mises theorem; 13. Survival analysis; 14. Discrete random structures; Appendices; References; Author index; Subject index.

Über Autor(innen)

Vaart, Aad van der
Aad van der Vaart is Professor of Stochastics at Universiteit Leiden. He is the author of several books and lecture notes in topics ranging from asymptotic statistics to genetics and finance, and many research papers in statistics and its applications. He is a member of the Royal Netherlands Academy of Arts and Sciences, former president of Netherlands Statistical Society, and a recipient of the Spinoza Prize of the Netherlands Organisation of Scientific Research.

Ghosal, Subhashis
Subhashis Ghosal is Professor of Statistics at North Carolina State University. His primary research interest is in the theory, methodology and various applications of Bayesian nonparametrics. He has edited one book, written nearly one hundred papers, and serves on the editorial boards of the Annals of Statistics, Bernoulli, and the Electronic Journal of Statistics. He is an elected fellow of the Institute of Mathematical Statistics, the American Statistical Association and the International Society for Bayesian Analysis.