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Book
xxv, 592 p. : ill. ; 26 cm.
  • Foreword Stephen P. Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng Introduction to MCMC, Charles J. Geyer A short history of Markov chain Monte Carlo: Subjective recollections from in-complete data, Christian Robert and George Casella Reversible jump Markov chain Monte Carlo, Yanan Fan and Scott A. Sisson Optimal proposal distributions and adaptive MCMC, Jeffrey S. Rosenthal MCMC using Hamiltonian dynamics, Radford M. Neal Inference and Monitoring Convergence, Andrew Gelman and Kenneth Shirley Implementing MCMC: Estimating with confidence, James M. Flegal and Galin L. Jones Perfection within reach: Exact MCMC sampling, Radu V. Craiu and Xiao-Li Meng Spatial point processes, Mark Huber The data augmentation algorithm: Theory and methodology, James P. Hobert Importance sampling, simulated tempering and umbrella sampling, Charles J.Geyer Likelihood-free Markov chain Monte Carlo, Scott A. Sisson and Yanan Fan MCMC in the analysis of genetic data on related individuals, Elizabeth Thompson A Markov chain Monte Carlo based analysis of a multilevel model for functional MRI data, Brian Caffo, DuBois Bowman, Lynn Eberly, and Susan Spear Bassett Partially collapsed Gibbs sampling & path-adaptive Metropolis-Hastings in high-energy astrophysics, David van Dyk and Taeyoung Park Posterior exploration for computationally intensive forward models, Dave Higdon, C. Shane Reese, J. David Moulton, Jasper A. Vrugt and Colin Fox Statistical ecology, Ruth King Gaussian random field models for spatial data, Murali Haran Modeling preference changes via a hidden Markov item response theory model, Jong Hee Park Parallel Bayesian MCMC imputation for multiple distributed lag models: A case study in environmental epidemiology, Brian Caffo, Roger Peng, Francesca Dominici, Thomas A. Louis, and Scott Zeger MCMC for state space models, Paul Fearnhead MCMC in educational research, Roy Levy, Robert J. Mislevy, and John T. Behrens Applications of MCMC in fisheries science, Russell B. Millar Model comparison and simulation for hierarchical models: analyzing rural-urban migration in Thailand, Filiz Garip and Bruce Western.
  • (source: Nielsen Book Data)9781420079418 20160605
Since their popularization in the 1990s, Markov chain Monte Carlo (MCMC) methods have revolutionized statistical computing and have had an especially profound impact on the practice of Bayesian statistics. Furthermore, MCMC methods have enabled the development and use of intricate models in an astonishing array of disciplines as diverse as fisheries science and economics. The wide-ranging practical importance of MCMC has sparked an expansive and deep investigation into fundamental Markov chain theory. The Handbook of Markov Chain Monte Carlo provides a reference for the broad audience of developers and users of MCMC methodology interested in keeping up with cutting-edge theory and applications. The first half of the book covers MCMC foundations, methodology, and algorithms. The second half considers the use of MCMC in a variety of practical applications including in educational research, astrophysics, brain imaging, ecology, and sociology. The in-depth introductory section of the book allows graduate students and practicing scientists new to MCMC to become thoroughly acquainted with the basic theory, algorithms, and applications. The book supplies detailed examples and case studies of realistic scientific problems presenting the diversity of methods used by the wide-ranging MCMC community. Those familiar with MCMC methods will find this book a useful refresher of current theory and recent developments.
(source: Nielsen Book Data)9781420079418 20160605
Science Library (Li and Ma)
STATS-362-01
Book
xvii, 600 p. : ill. ; 26 cm.
  • Preface-- Notation-- 1. Introduction-- 2. Quasi-Monte Carlo integration, discrepancy and reproducing kernel Hilbert spaces-- 3. Geometric discrepancy-- 4. Nets and sequences-- 5. Discrepancy estimates and average type results-- 6. Connections to other discrete objects-- 7. Duality Theory-- 8. Special constructions of digital nets and sequences-- 9. Propagation rules for digital nets-- 10. Polynomial lattice point sets-- 11. Cyclic digital nets and hyperplane nets-- 12. Multivariate integration in weighted Sobolev spaces-- 13. Randomisation of digital nets-- 14. The decay of the Walsh coefficients of smooth functions-- 15. Arbitrarily high order of convergence of the worst-case error-- 16. Explicit constructions of point sets with best possible order of L2-discrepancy-- Appendix A. Walsh functions-- Appendix B. Algebraic function fields-- References-- Index.
  • (source: Nielsen Book Data)9780521191593 20160604
Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi-Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and illustrations.
(source: Nielsen Book Data)9780521191593 20160604
Science Library (Li and Ma)
STATS-362-01
Book
xvii, 486 p. : ill., maps ; 25 cm.
  • INTRODUCING MARKOV CHAIN MONTE CARLO Introduction The Problem Markov Chain Monte Carlo Implementation Discussion HEPATITIS B: A CASE STUDY IN MCMC METHODS Introduction Hepatitis B Immunization Modelling Fitting a Model Using Gibbs Sampling Model Elaboration Conclusion MARKOV CHAIN CONCEPTS RELATED TO SAMPLING ALGORITHMS Markov Chains Rates of Convergence Estimation The Gibbs Sampler and Metropolis-Hastings Algorithm INTRODUCTION TO GENERAL STATE-SPACE MARKOV CHAIN THEORY Introduction Notation and Definitions Irreducibility, Recurrence, and Convergence Harris Recurrence Mixing Rates and Central Limit Theorems Regeneration Discussion FULL CONDITIONAL DISTRIBUTIONS Introduction Deriving Full Conditional Distributions Sampling from Full Conditional Distributions Discussion STRATEGIES FOR IMPROVING MCMC Introduction Reparameterization Random and Adaptive Direction Sampling Modifying the Stationary Distribution Methods Based on Continuous-Time Processes Discussion IMPLEMENTING MCMC Introduction Determining the Number of Iterations Software and Implementation Output Analysis Generic Metropolis Algorithms Discussion INFERENCE AND MONITORING CONVERGENCE Difficulties in Inference from Markov Chain Simulation The Risk of Undiagnosed Slow Convergence Multiple Sequences and Overdispersed Starting Points Monitoring Convergence Using Simulation Output Output Analysis for Inference Output Analysis for Improving Efficiency MODEL DETERMINATION USING SAMPLING-BASED METHODS Introduction Classical Approaches The Bayesian Perspective and the Bayes Factor Alternative Predictive Distributions How to Use Predictive Distributions Computational Issues An Example Discussion HYPOTHESIS TESTING AND MODEL SELECTION Introduction Uses of Bayes Factors Marginal Likelihood Estimation by Importance Sampling Marginal Likelihood Estimation Using Maximum Likelihood Application: How Many Components in a Mixture? Discussion Appendix: S-PLUS Code for the Laplace-Metropolis Estimator MODEL CHECKING AND MODEL IMPROVEMENT Introduction Model Checking Using Posterior Predictive Simulation Model Improvement via Expansion Example: Hierarchical Mixture Modelling of Reaction Times STOCHASTIC SEARCH VARIABLE SELECTION Introduction A Hierarchical Bayesian Model for Variable Selection Searching the Posterior by Gibbs Sampling Extensions Constructing Stock Portfolios With SSVS Discussion BAYESIAN MODEL COMPARISON VIA JUMP DIFFUSIONS Introduction Model Choice Jump-Diffusion Sampling Mixture Deconvolution Object Recognition Variable Selection Change-Point Identification Conclusions ESTIMATION AND OPTIMIZATION OF FUNCTIONS Non-Bayesian Applications of MCMC Monte Carlo Optimization Monte Carlo Likelihood Analysis Normalizing-Constant Families Missing Data Decision Theory Which Sampling Distribution? Importance Sampling Discussion STOCHASTIC EM: METHOD AND APPLICATION Introduction The EM Algorithm The Stochastic EM Algorithm Examples GENERALIZED LINEAR MIXED MODELS Introduction Generalized Linear Models (GLMs) Bayesian Estimation of GLMs Gibbs Sampling for GLMs Generalized Linear Mixed Models (GLMMs) Specification of Random-Effect Distributions Hyperpriors and the Estimation of Hyperparameters Some Examples Discussion HIERARCHICAL LONGITUDINAL MODELLING Introduction Clinical Background Model Detail and MCMC Implementation Results Summary and Discussion MEDICAL MONITORING Introduction Modelling Medical Monitoring Computing Posterior Distributions Forecasting Model Criticism Illustrative Application Discussion MCMC FOR NONLINEAR HIERARCHICAL MODELS Introduction Implementing MCMC Comparison of Strategies A Case Study from Pharmacokinetics-Pharmacodynamics Extensions and Discussion BAYESIAN MAPPING OF DISEASE Introduction Hypotheses and Notation Maximum Likelihood Estimation of Relative Risks Hierarchical Bayesian Model of Relative Risks Empirical Bayes Estimation of Relative Risks Fully Bayesian Estimation of Relative Risks Discussion MCMC IN IMAGE ANALYSIS Introduction The Relevance of MCMC to Image Analysis Image Models at Different Levels Methodological Innovations in MCMC Stimulated by Imaging Discussion MEASUREMENT ERROR Introduction Conditional-Independence Modelling Illustrative examples Discussion GIBBS SAMPLING METHODS IN GENETICS Introduction Standard Methods in Genetics Gibbs Sampling Approaches MCMC Maximum Likelihood Application to a Family Study of Breast Cancer Conclusions MIXTURES OF DISTRIBUTIONS: INFERENCE AND ESTIMATION Introduction The Missing Data Structure Gibbs Sampling Implementation Convergence of the Algorithm Testing for Mixtures Infinite Mixtures and Other Extensions AN ARCHAEOLOGICAL EXAMPLE: RADIOCARBON DATING Introduction Background to Radiocarbon Dating Archaeological Problems and Questions Illustrative Examples Discussion Index.
  • (source: Nielsen Book Data)9780412055515 20160528
In a family study of breast cancer, epidemiologists in Southern California increase the power for detecting a gene-environment interaction. In Gambia, a study helps a vaccination program reduce the incidence of Hepatitis B carriage. Archaeologists in Austria place a Bronze Age site in its true temporal location on the calendar scale. And in France, researchers map a rare disease with relatively little variation.Each of these studies applied Markov chain Monte Carlo methods to produce more accurate and inclusive results. General state-space Markov chain theory has seen several developments that have made it both more accessible and more powerful to the general statistician. Markov Chain Monte Carlo in Practice introduces MCMC methods and their applications, providing some theoretical background as well. The authors are researchers who have made key contributions in the recent development of MCMC methodology and its application. Considering the broad audience, the editors emphasize practice rather than theory, keeping the technical content to a minimum. The examples range from the simplest application, Gibbs sampling, to more complex applications. The first chapter contains enough information to allow the reader to start applying MCMC in a basic way. The following chapters cover main issues, important concepts and results, techniques for implementing MCMC, improving its performance, assessing model adequacy, choosing between models, and applications and their domains.Markov Chain Monte Carlo in Practice is a thorough, clear introduction to the methodology and applications of this simple idea with enormous potential. It shows the importance of MCMC in real applications, such as archaeology, astronomy, biostatistics, genetics, epidemiology, and image analysis, and provides an excellent base for MCMC to be applied to other fields as well.
(source: Nielsen Book Data)9780412055515 20160528
Science Library (Li and Ma)
STATS-362-01