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Full Description
Highly Structured Stochastic Systems (HSSS) is a modern strategy for building statistical models for challenging real-world problems, for computing with them, and for interpreting the resulting inferences. Complexity is handled by working up from simple local assumptions in a coherent way, and that is the key to modelling, computation, inference and interpretation; the unifying framework is that of Bayesian hierarchical models. The aim of this book is to make recent developments in HSSS accessible to a general statistical audience.
Graphical modelling and Markov chain Monte Carlo (MCMC) methodology are central to the field, and in this text they are covered in depth. The chapters on graphical modelling focus on causality and its interplay with time, the role of latent variables, and on some innovative applications. Those on Monte Carlo algorithms include discussion of the impact of recent theoretical work on the evaluation of performance in MCMC, extensions to variable dimension problems, and methods for dynamic problems based on particle filters. Coverage of these underlying methodologies is balanced by substantive areas of application - in the areas of spatial statistics (with epidemiological, ecological and image analysis applications) and biology (including infectious diseases, gene mapping and evolutionary genetics). The book concludes with two topics (model criticism and Bayesian nonparametrics) that seek to challenge the parametric assumptions that otherwise underlie most HSSS models.
Altogether there are 15 topics in the book, and for each there is a substantial article by a leading author in the field, and two invited commentaries that complement, extend or discuss the main article, and should be read in parallel. All authors are distinguished researchers in the field, and were active participants in an international research programme on HSSS.
This is the 27th volume in the Oxford Statistical Science Series, which includes texts and monographs covering many topics of current research interest in pure and applied statistics. These texts focus on topics that have been at the forefront of research interest for several years. Other books in the series include: J.Durbin and S.J.Koopman: Time series analysis by State Space Models; Peter J. Diggle, Patrick Heagerty, Kung-Yee Liang, Scott L. Zeger: Analysis of Longitudinal Data 2/e; J.K. Lindsey: Nonlinear Models in Medical Statistics; Peter J. Green, Nils L. Hjort & Sylvia Richardson: Highly Structured Stochastic Systems; Margaret S. Pepe: Statistical Evaluation of Medical Tests.
Contents
Introduction ; 1. Some modern applications of graphical models ; Analysing social science data with graphical Markov models ; Analysis of DNA mixtures using Bayesian networks ; 2. Causal inference using influence diagrams: the problem of partial compliance ; Commentary: causality and statistics ; Semantics of causal DAG models and the identification of direct and indirect effects ; 3. Causal inference via ancestral graph models ; Other approaches to description of conditional independence structures ; On ancestral graph Markov models ; 4. Causality and graphical models in times series analysis ; Graphical models for stochastic processes ; Discussion of "Causality and graphical models in times series analysis" ; 5. Linking theory and practice of MCMC ; Advances in MCMC: a discussion ; On some current research in MCMC ; 6. Trans-dimensional Markov chain Monte Carlo ; Proposal densities and product space methods ; Trans-dimensional Bayesian nonparametrics with spatial point processes ; 7. Particle filtering methods for dynamic and static Bayesian problems ; Some further topics on Monte Carlo methods for dynamic Bayesian problems ; General principles in sequential Monte Carlo methods ; 8. Spatial models in epidemiological applications ; Some remarks on Gaussian Markov random field models ; A compariosn of spatial point process models in epidemiological applications ; 9. Spatial hierarchical Bayesian modeld in ecological applications ; Likelihood analysis of binary data in space and time ; Some further aspects of spatio-temporal modelling ; 10. Advances in Bayesian image analysis ; Probabilistic image modelling ; Prospects in Bayesian image analysis ; 11. Preventing epidemics in heterogeneous environments ; MCMC methods for stochastic epidemic models ; Towards Bayesian inference in epidemic models ; 12. Genetic linkage analysis using Markov chain Monte Carlo techniques ; Graphical models for mapping continuous traits ; Statistical approaches to Genetic Mapping ; 13. The genealogy of neutral mutation ; Linked versus unlinked DNA data - a comparison based on ancestral inference ; The age of a rare mutation ; 14. HSSS model criticism ; What 'base' distribution for model criticism? ; Some comments on model criticism ; 15. Topics in nonparametric Bayesian statistics ; Asymptotics of Nonparametirc Posteriors ; A predictive point of view on Bayesian nonparametrics
