The Resource Stochastic models with applications to genetics, cancers, AIDS and other biomedical systems, Tan WaiYuan
Stochastic models with applications to genetics, cancers, AIDS and other biomedical systems, Tan WaiYuan
 Summary
 This book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and stochastic differential equations. It illustrates how these processes and approaches are applied to many problems in genetics, carcinogenesis, AIDS epidemiology and other biomedical systems. One feature of the book is that it describes the basic MCMC (Markov chain and Monte Carlo) procedures and illustrates how to use the Gibbs sampling method and the multilevel Gibbs sampling method to solve many problems in genetics, carcinogenesis, AIDS and other biomedical systems. As another feature, the book develops many state space models for many genetic problems, carcinogenesis, AIDS epidemiology and HIV pathogenesis. It shows in detail how to use the multilevel Gibbs sampling method to estimate (or predict) simultaneously the state variables and the unknown parameters in cancer chemotherapy, carcinogenesis, AIDS epidemiology and HIV pathogenesis. As a matter of fact, this book is the first to develop many state space models for many genetic problems, carcinogenesis and other biomedical problems
 Language
 eng
 Extent
 1 online resource (xv, 441 pages)
 Contents

 1. Introduction. 1.1. Some basic concepts of stochastic processes and examples. 1.2. Markovian and nonMarkovian processes, Markov chains and examples. 1.3. Diffusion processes and examples. 1.4. State space models and hidden Markov models. 1.5. The scope of the book. 1.6. Complements and exercises
 2. Discrete time Markov chain models in genetics and biomedical systems. 2.1. Examples from genetics and AIDS. 2.2. The transition probabilities and computation. 2.3. The structure and decomposition of Markov chains. 2.4. Classification of states and the dynamic behavior of Markov chains. 2.5. The absorption probabilities of transient states. 2.6. The moments of first absorption times. 2.7. Some illustrative examples. 2.8. Finite Markov chains. 2.9. Stochastic difference equation for Markov chains with discrete time. 2.10. Complements and exercises
 3. Stationary distributions and MCMC in discrete time Markov chains. 3.1. Introduction. 3.2. The ergodic states and some limiting theorems. 3.3. Stationary distributions and some examples. 3.4. Applications of stationary distributions and some MCMC methods. 3.5. Some illustrative examples. 3.6. Estimation of linkage fraction by Gibbs sampling method. 3.7. Complements and exercises. 3.8. Appendix: A lemma for finite Markov chains
 4. Continuoustime Markov chain models in genetics, cancers and AIDS. 4.1. Introduction. 4.2. The infinitesimal generators and an embedded Markov chain. 4.3. The transition probabilities and Kolmogorov equations. 4.4. Kolmogorov equations for finite Markov chains with continuous time. 4.5. Complements and exercises
 5. Absorption probabilities and stationary distributions in continuoustime Markov chain models. 5.1. Absorption probabilities and moments of first absorption times of transient states. 5.2. The stationary distributions and examples. 5.3. Finite Markov chains and the HIV incubation distribution. 5.4. Stochastic differential equations for Markov chains with continuons time. 5.5. Complements and exercises
 6. Diffusion models in genetics, cancer and AIDS. 6.1. The transition probabilities. 6.2. The Kolmogorov forward equation. 6.3. The Kolmogorov backward equation. 6.4. Diffusion approximation of models from genetics, cancers and AIDS. 6.5. Diffusion approximation of evolutionary processes. 6.6. Diffusion approximation of finite birthdeath processes. 6.7. Complements and exercises
 7. Asymptotic distributions, stationary distributions and absorption probabilities in diffusion models. 7.1. Some approximation procedures and asymptotic distributions in diffusion models. 7.2. Stationary distributions in diffusion processes. 7.3. The absorption probabilities and moments of first absorption times in diffusion processes. 7.4. Complements and exercises
 8. State space models and some examples from cancer and AIDS. 8.1. Some HIV epidemic models as discretetime linear state space models. 8.2. Some state space models with continuoustime stochastic system model. 8.3. Some state space models in carcinogenesis. 8.4. Some classical theories of discrete and linear state space models. 8.5. Estimation of HIV prevalence and AIDS cases in the San Francisco homosexual population. 8.6. Complements and exercises
 9. Some general theories of state space models and applications. 9.1. Some classical theories of linear state space models with continuoustime stochastic system model. 9.2. The extended state space models with continuoustime stochastic system model. 9.3. Estimation of CD4(+) T cell counts and number of HIV in blood in HIVinfected individuals. 9.4. A general Bayesian procedure for estimating the unknown parameters and the state variables by state space models simultaneously. 9.5. Simultaneous estimation in the San Francisco population. 9.6. Simultaneous estimation in the cancer drugresistant model. 9.7. Complements and exercises
 Isbn
 9789812777966
 Label
 Stochastic models with applications to genetics, cancers, AIDS and other biomedical systems
 Title
 Stochastic models with applications to genetics, cancers, AIDS and other biomedical systems
 Statement of responsibility
 Tan WaiYuan
 Language
 eng
 Summary
 This book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and stochastic differential equations. It illustrates how these processes and approaches are applied to many problems in genetics, carcinogenesis, AIDS epidemiology and other biomedical systems. One feature of the book is that it describes the basic MCMC (Markov chain and Monte Carlo) procedures and illustrates how to use the Gibbs sampling method and the multilevel Gibbs sampling method to solve many problems in genetics, carcinogenesis, AIDS and other biomedical systems. As another feature, the book develops many state space models for many genetic problems, carcinogenesis, AIDS epidemiology and HIV pathogenesis. It shows in detail how to use the multilevel Gibbs sampling method to estimate (or predict) simultaneously the state variables and the unknown parameters in cancer chemotherapy, carcinogenesis, AIDS epidemiology and HIV pathogenesis. As a matter of fact, this book is the first to develop many state space models for many genetic problems, carcinogenesis and other biomedical problems
 Cataloging source
 N$T
 Dewey number
 610/.1/5118
 Illustrations
 illustrations
 Index
 index present
 LC call number
 R853.M3
 LC item number
 T36 2002eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Series on concrete and applicable mathematics
 Series volume
 v. 4
 Label
 Stochastic models with applications to genetics, cancers, AIDS and other biomedical systems, Tan WaiYuan
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 http://library.link/vocab/branchCode

 net
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1. Introduction. 1.1. Some basic concepts of stochastic processes and examples. 1.2. Markovian and nonMarkovian processes, Markov chains and examples. 1.3. Diffusion processes and examples. 1.4. State space models and hidden Markov models. 1.5. The scope of the book. 1.6. Complements and exercises  2. Discrete time Markov chain models in genetics and biomedical systems. 2.1. Examples from genetics and AIDS. 2.2. The transition probabilities and computation. 2.3. The structure and decomposition of Markov chains. 2.4. Classification of states and the dynamic behavior of Markov chains. 2.5. The absorption probabilities of transient states. 2.6. The moments of first absorption times. 2.7. Some illustrative examples. 2.8. Finite Markov chains. 2.9. Stochastic difference equation for Markov chains with discrete time. 2.10. Complements and exercises  3. Stationary distributions and MCMC in discrete time Markov chains. 3.1. Introduction. 3.2. The ergodic states and some limiting theorems. 3.3. Stationary distributions and some examples. 3.4. Applications of stationary distributions and some MCMC methods. 3.5. Some illustrative examples. 3.6. Estimation of linkage fraction by Gibbs sampling method. 3.7. Complements and exercises. 3.8. Appendix: A lemma for finite Markov chains  4. Continuoustime Markov chain models in genetics, cancers and AIDS. 4.1. Introduction. 4.2. The infinitesimal generators and an embedded Markov chain. 4.3. The transition probabilities and Kolmogorov equations. 4.4. Kolmogorov equations for finite Markov chains with continuous time. 4.5. Complements and exercises  5. Absorption probabilities and stationary distributions in continuoustime Markov chain models. 5.1. Absorption probabilities and moments of first absorption times of transient states. 5.2. The stationary distributions and examples. 5.3. Finite Markov chains and the HIV incubation distribution. 5.4. Stochastic differential equations for Markov chains with continuons time. 5.5. Complements and exercises  6. Diffusion models in genetics, cancer and AIDS. 6.1. The transition probabilities. 6.2. The Kolmogorov forward equation. 6.3. The Kolmogorov backward equation. 6.4. Diffusion approximation of models from genetics, cancers and AIDS. 6.5. Diffusion approximation of evolutionary processes. 6.6. Diffusion approximation of finite birthdeath processes. 6.7. Complements and exercises  7. Asymptotic distributions, stationary distributions and absorption probabilities in diffusion models. 7.1. Some approximation procedures and asymptotic distributions in diffusion models. 7.2. Stationary distributions in diffusion processes. 7.3. The absorption probabilities and moments of first absorption times in diffusion processes. 7.4. Complements and exercises  8. State space models and some examples from cancer and AIDS. 8.1. Some HIV epidemic models as discretetime linear state space models. 8.2. Some state space models with continuoustime stochastic system model. 8.3. Some state space models in carcinogenesis. 8.4. Some classical theories of discrete and linear state space models. 8.5. Estimation of HIV prevalence and AIDS cases in the San Francisco homosexual population. 8.6. Complements and exercises  9. Some general theories of state space models and applications. 9.1. Some classical theories of linear state space models with continuoustime stochastic system model. 9.2. The extended state space models with continuoustime stochastic system model. 9.3. Estimation of CD4(+) T cell counts and number of HIV in blood in HIVinfected individuals. 9.4. A general Bayesian procedure for estimating the unknown parameters and the state variables by state space models simultaneously. 9.5. Simultaneous estimation in the San Francisco population. 9.6. Simultaneous estimation in the cancer drugresistant model. 9.7. Complements and exercises
 Control code
 ocn181646037
 Dimensions
 unknown
 Extent
 1 online resource (xv, 441 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9789812777966
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other physical details
 illustrations
 Quality assurance targets
 not applicable
 http://library.link/vocab/recordID
 .b36029506
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)181646037
 pebcs9812777962
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