Complex Stochastic Systems
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Summary
Complex stochastic systems comprises a vast area of research, from modelling specific applications to model fitting, estimation procedures, and computing issues. The exponential growth in computing power over the last two decades has revolutionized statistical analysis and led to rapid developments and great progress in this emerging field. In Complex Stochastic Systems, leading researchers address various statistical aspects of the field, illustrated by some very concrete applications.
A Primer on Markov Chain Monte Carlo by Peter J. Green provides a wide-ranging mixture of the mathematical and statistical ideas, enriched with concrete examples and more than 100 references.
Causal Inference from Graphical Models by Steffen L. Lauritzen explores causal concepts in connection with modelling complex stochastic systems, with focus on the effect of interventions in a given system.
State Space and Hidden Markov Models by Hans R. Künschshows the variety of applications of this concept to time series in engineering, biology, finance, and geophysics.
Monte Carlo Methods on Genetic Structures by Elizabeth A. Thompson investigates special complex systems and gives a concise introduction to the relevant biological methodology.
Renormalization of Interacting Diffusions by Frank den Hollander presents recent results on the large space-time behavior of infinite systems of interacting diffusions.
Stein's Method for Epidemic Processes by Gesine Reinert investigates the mean field behavior of a general stochastic epidemic with explicit bounds.
Individually, these articles provide authoritative, tutorial-style exposition and recent results from various subjects related to complex stochastic systems. Collectively, they link these separate areas of study to form the first comprehensive overview of this rapidly developing field.
Table of Contents
A PRIMER ON MARKOV CHAIN MONTE CARLO, Peter J. Green
Introduction
Getting Started: Bayesian Inference and the Gibbs Sampler
MCMC-The General Idea and the Main Limit Theorems
Recipes for Constructing MCMC Methods
The Role of Graphical Models
Performance of MCMC Methods
Reversible Jump Methods
Some Tools for Improving Performance
Coupling from the Past (CFTP)
Miscellaneous Topics
Some Notes on Programming MCMC
Conclusions
CAUSAL INFERENCE FROM GRAPHICAL MODELS, Steffen L. Lauritzen
Introduction
Graph Terminology
Conditional Independence
Markov Properties for Undirected Graphs
The Directed Markov Property
Causal Markov Models
Assessment of Treatment Effects in Sequential Trials
Identifiability of Causal Effects
Structural Equation Models
Potential Responses and Counterfactuals
Other Issues
STATE SPACE AND HIDDEN MARKOV MODELS, Hans R. Künsch
Introduction
The General State Space Model
Filtering and Smoothing Recursions
Exact and Approximate Filtering and Smoothing
Monte Carlo Filtering and Smoothing
Parameter Estimation
Extensions of the Model
MONTE CARLO METHODS ON GENETIC STRUCTURES, Elizabeth A. Thompson
Genetics, Pedigrees, and Structured Systems
Computations on Pedigrees
MCMC Methods for Multilocus Genetic Data
Conclusion
RENORMALIZATION OF INTERACTING DIFFUSIONS, Frank den Hollander
Introduction
The Model
Interpretation of the Model
Block Averages and Renormalization
The Hierarchical Lattice
The Renormalization Transformation
Analysis of the Orbit
Higher-Dimensional State Spaces
Open Problems
Conclusion
STEIN'S METHOD FOR EPIDEMIC PROCESSES, Gesine Reinert
Introduction
A Brief Introduction to Stein's Method
The Distance of the GSE to its Mean Field Limit
Discussion
Editorial Reviews
"…this book has achieved its aim of providing well-written tutorial papers for researchers by leading experts in several important areas of statistics…the book as a whole is well deserving of a position on any researcher statistician's bookshelf…"
--N. Sheehan, Biometrics, June 2001
"…[includes] an outstanding primer on Markov chain Monte Carlo (MCMC)…it is one of the best available tutorial sources on contemporary MCMC procedures."
--Journal of Mathematical Psychology
"One often has reservations about edited volumes, but this one is an excellent introduction to some of the most important tools of modern statistics."
-Short Book Reviews, Vol. 21, No. 2, August 2001
