
Dependence Models via Hierarchical Structures
Luis E. Nieto-Barajas(Author)
Cambridge University Press
Published on 27. March 2025
Book
Hardback
149 pages
978-1-009-58411-1 (ISBN)
Description
Bringing together years of research into one useful resource, this text empowers the reader to creatively construct their own dependence models. Intended for senior undergraduate and postgraduate students, it takes a step-by-step look at the construction of specific dependence models, including exchangeable, Markov, moving average and, in general, spatio-temporal models. All constructions maintain a desired property of pre-specifying the marginal distribution and keeping it invariant. They do not separate the dependence from the marginals and the mechanisms followed to induce dependence are so general that they can be applied to a very large class of parametric distributions. All the constructions are based on appropriate definitions of three building blocks: prior distribution, likelihood function and posterior distribution, in a Bayesian analysis context. All results are illustrated with examples and graphical representations. Applications with data and code are interspersed throughout the book, covering fields including insurance and epidemiology.
Reviews / Votes
'Luis Nieto-Barajas has been making wonderful contributions to the Bayesian nonparametrics literature for many years, and it is exciting to see this new book on the important topic of inducing dependence in statistical models via intricate hierarchical structures. I plan to use this book as a reference for my students.' David B. Dunson, Duke University 'The book introduces Bayesian statistical modeling and inference from an unusual, but very meaningful perspective. The underlying organizing principle is based on increasingly more complex levels of modelling dependence subject to pre-specified marginals. The discussion starts with i.i.d. sampling and conjugate prior/likelihood pairs, continues with exchangeable models, moving on with Markov dependence, and finally arbitrary levels of dependence, including temporal and spatial dependence as special cases. The book could serve as a wonderful text for a second look at Bayesian statistical inference, from an unusual perspective. Using dependence structure as the main paradigm allows another view of familiar inference approaches. It is a great and inspiring text.' Peter Mueller, University of Texas at Austin 'This book presents a step-by-step approach to constructing dependence models with pre-specified marginals, covering a wide range of discrete-time stochastic processes, along with practical applications. It is a highly valuable and enriching resource for graduate students and researchers alike.' Igor Pruenster, University of Bocconi 'This monograph will be of interest to graduate or advanced undergraduate students that are looking for principled and elegant ways to construct models with stochastic dependence. The text goes from the simplest scenario (exchangeability) to more complicated spatio-temporal models. Many references and concrete examples are introduced and discussed in detail.' Fernando A. Quintana, Pontificia Universidad Catolica de ChileMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Illustrations
Worked examples or Exercises
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 13 mm
Weight
378 gr
ISBN-13
978-1-009-58411-1 (9781009584111)
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Schweitzer Classification
Person
Luis E. Nieto-Barajas is Full Professor and Head of the Department of Statistics at the Instituto Tecnologico Autonomo de Mexico (ITAM). He was previously President of the Mexican Statistical Association (2020-2021). For his thesis, he won the Savage Award (2001) and Francisco Aranda Ordaz Awards (2002-2004).
Content
1. Introduction; 2. Conjugate models; 3. Exchangeable sequences; 4. Markov sequences; 5. General dependent sequences; 6. Temporal dependent sequences; 7. Spatial dependent sequences; 8. Multivariate dependent sequences; Appendix. Data sets; References; Index.