349,99 zł
Bayesian analysis of complex models based on stochastic processes has in recent years become a growing area. This book provides a unified treatment of Bayesian analysis of models based on stochastic processes, covering the main classes of stochastic processing including modeling, computational, inference, forecasting, decision making and important applied models. Key features: * Explores Bayesian analysis of models based on stochastic processes, providing a unified treatment. * Provides a thorough introduction for research students. * Computational tools to deal with complex problems are illustrated along with real life case studies * Looks at inference, prediction and decision making. Researchers, graduate and advanced undergraduate students interested in stochastic processes in fields such as statistics, operations research (OR), engineering, finance, economics, computer science and Bayesian analysis will benefit from reading this book. With numerous applications included, practitioners of OR, stochastic modelling and applied statistics will also find this book useful.
Ebooka przeczytasz w aplikacjach Legimi na:
Liczba stron: 458
Contents
Cover
Series
Title Page
Copyright
Preface
Part One: Basic Concepts and Tools
1: Stochastic processes
1.1 Introduction
1.2 Key concepts in stochastic processes
1.3 Main classes of stochastic processes
1.4 Inference, prediction, and decision-making
1.5 Discussion
References
2: Bayesian analysis
2.1 Introduction
2.2 Bayesian statistics
2.3 Bayesian decision analysis
2.4 Bayesian computation
2.5 Discussion
References
Part Two: Models
3: Discrete time Markov chains and extensions
3.1 Introduction
3.2 Important Markov chain models
3.3 Inference for first-order, time homogeneous, Markov chains
3.4 Special topics
3.5 Case study: Wind directions at Gijón
3.6 Markov decision processes
3.7 Discussion
References
4: Continuous time Markov chains and extensions
4.1 Introduction
4.2 Basic setup and results
4.3 Inference and prediction for CTMCs
4.4 Case study: Hardware availability through CTMCs
4.5 Semi-Markovian processes
4.6 Decision-making with semi-Markovian decision processes
4.7 Discussion
References
5: Poisson processes and extensions
5.1 Introduction
5.2 Basics on Poisson processes
5.3 Homogeneous Poisson processes
5.4 Nonhomogeneous Poisson processes
5.5 Compound Poisson processes
5.6 Further extensions of Poisson processes
5.7 Case study: Earthquake occurrences
5.8 Discussion
References
6: Continuous time continuous space processes
6.1 Introduction
6.2 Gaussian processes
6.3 Brownian motion and FBM
6.4 Diffusions
6.5 Case study: Predator–prey systems
6.6 Discussion
References
Part Three: Applications
7: Queueing analysis
7.1 Introduction
7.2 Basic queueing concepts
7.3 The main queueing models
7.4 Bayesian inference for queueing systems
7.5 Bayesian inference for the system
7.6 Inference for non-Markovian systems
7.7 Decision problems in queueing systems
7.8 Case study: Optimal number of beds in a hospital
7.9 Discussion
References
8: Reliability
8.1 Introduction
8.2 Basic reliability concepts
8.3 Renewal processes
8.4 Poisson processes
8.5 Other processes
8.6 Maintenance
8.7 Case study: Gas escapes
8.8 Discussion
References
9: Discrete event simulation
9.1 Introduction
9.2 Discrete event simulation methods
9.3 A Bayesian view of DES
9.4 Case study: A queueing system
9.5 Bayesian output analysis
9.6 Simulation and optimization
9.7 Discussion
References
10: Risk analysis
10.1 Introduction
10.2 Risk measures
10.3 Ruin problems
10.4 Case study: Estimation of finite-time ruin probabilities in the Sparre Andersen model
10.5 Discussion
References
Appendix A: Main distributions
Discrete distributions
Continuous distributions
Multivariate distributions
References
Appendix B: Generating functions and the Laplace–Stieltjes transform
Probability generating function
Moment generating function
Laplace–Stieltjes transform
References
Index
Series List
WILEY SERIES IN PROBABILITY AND STATISTICS
Established by WALTER A. SHEWHART and SAMUEL S. WILKS
Editors: David J. Balding, Noel A.C. Cressie, Garrett M. Fitzmaurice, Harvey Goldstein, Iain M. Johnstone, Geert Molenberghs, David W. Scott, Adrian F.M. Smith, Ruey S. Tsay, Sanford Weisberg
Editors Emeriti: Vic Barnett, Ralph A. Bradley, J. Stuart Hunter, J.B. Kadane, David G. Kendall, Jozef L. Teugels
A complete list of the titles in this series appears at the end of this volume.
This edition first published 2012 © 2012 John Wiley & Sons, Ltd
Registered officeJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom
For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.
The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.
Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought.
Library of Congress Cataloging-in-Publication Data
Ruggeri, Fabrizio. Bayesian analysis of stochastic process models / Fabrizio Ruggeri, Michael P. Wiper, David Rios Insua. pages cm Includes bibliographical references and index. ISBN 978-0-470-74453-6 (hardback) 1. Bayesian statistical decision theory. 2. Stochastic processes. I. Wiper, Michael P. II. Rios Insua, David, 1964– III. Title. QA279.5.R84 2012 519.5′42–dc23 2012000092
A catalogue record for this book is available from the British Library.
ISBN: 978-0-470-74453-6
Preface
To the best of our knowledge, this is the first book focusing on Bayesian analysis of stochastic process models at large. We believe that recent developments in the field and the growing interest in this topic deserve a book-length treatment.
The advent of cheap computing power and the developments in Markov chain Monte Carlo simulation produced a revolution within the field of Bayesian statistics around the beginning of the 1990s, allowing a true ‘model liberation’ that permitted treating models that previously we could only dream of dealing with. This has challenged analysts in trying to deal with more complex problems. Given this great advance in computing power, it is no surprise that several researchers have attempted to deal with stochastic processes in a Bayesian fashion, moving away from the usual assumptions of independent and identically distributed (IID) data. In 1998, this led us to organize the first Workshop on Bayesian Analysis of Stochastic Processes in Madrid. The seventh edition of this conference was held in 2011, which is an illustration of the great current interest in this subject area. Given the numerous papers written, we felt, therefore, that the time was right to provide a systematic account of developments in Bayesian analysis of stochastic processes. In doing this, it is interesting to note that most books in stochastic processes have referred mainly to probabilistic aspects and there are many fewer texts that treat them from a (classical) statistical perspective.
In this monograph, we have emphasized five salient aspects:
Our monograph is structured in three parts:
We are grateful to the many institutions that have supported at various points our research in this field. In particular, D.R.I. wants to acknowledge the Spanish Ministry of Science and Education (eColabora and Riesgos), the Spanish Ministry of Industry, the Government of Madrid through the Riesgos-CM program, the European Science Foundation through the ALGODEC program, the SECONOMICS project, the Statistical and Applied Mathematical Sciences Institute, Apara Software and MTP. F.R. wants to acknowledge the Statistical and Applied Mathematical Sciences Institute. M.P.W. wishes to acknowledge support from projects of the Spanish Ministry of Science and Education and the Government of Madrid.
We have also benefited of our collaboration in these areas over various years with many colleagues and former students. Specifically, D.R.I. would like to thank Javier Cano, Jesus Ríos, Miguel Herrero, Javier Girón, Concha Bielza, Peter Müller, Javier Moguerza, Dipak Dey, Mircea Grigoriu, Jim Berger, Armi Moreno, Simon French, Jacinto Martin, David Banks, Raquel Montes, and Miguel Virto. He specially misses many hours of discussion and collaboration with Sixto Ríos, Sixto Ríos Insua, and Jorge Muruzábal. F.R. would like to thank Sara Pasquali, Antonio Pievatolo, Renata Rotondi, Bruno Betrò, Refik Soyer, Siva Sivaganesan, Gianni Gilioli, Fernanda D’Ippoliti, Cristina Mazzali, Loretta Masini, Emanuela Saccuman, Davide Cavallo, Franco Caron, Enrico Cagno, and Mauro Mancini. Finally, M.P.W. has been much helped by Andrés Alonso, Conchi Ausín, Carmen Broto, José Antonio Carnicero, Pedro Galeano, Cristina García, Ana Paula Palacios, Pepa Rodríguez-Cobo, and Nuria Torrado.
The patience and competence of the personnel at Wiley, and in particular of Richard Davies and Heather Kay, is heartily appreciated, as well as the support from Kathryn Sharples and Ilaria Meliconi who played a fundamental role in the start of this project.
Last, but not least, our families (Susana, Isa, and Ota; Anna, Giacomo, and Lorenzo; Imogen, Pike†, and Bo) have provided us with immense support and the required warmth to complete this long-lasting project.
Valdoviño, Milano, and Getafe November 2011
Part One
BASIC CONCEPTS AND TOOLS
2
Bayesian analysis
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!
Lesen Sie weiter in der vollständigen Ausgabe!