Complex Stochastic Systems: 1st Edition (Hardback) book cover

Complex Stochastic Systems

1st Edition

Edited by O.E. Barndorff-Nielsen, Claudia Kluppelberg

Chapman and Hall/CRC

304 pages

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Hardback: 9781584881582
pub: 2000-08-09
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Description

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.

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

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

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

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Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MAT029010
MATHEMATICS / Probability & Statistics / Bayesian Analysis