05426nam 2200745Ia 450 991045098700332120200520144314.0981-277-796-2(CKB)1000000000411039(EBL)1679538(OCoLC)879023609(SSID)ssj0000251562(PQKBManifestationID)11939249(PQKBTitleCode)TC0000251562(PQKBWorkID)10174119(PQKB)11778072(MiAaPQ)EBC1679538(WSP)00004894(Au-PeEL)EBL1679538(CaPaEBR)ebr10201221(CaONFJC)MIL505431(EXLCZ)99100000000041103920020621d2002 uy 0engur|n|---|||||txtccrStochastic models with applications to genetics, cancers, AIDS and other biomedical systems[electronic resource] /Tan Wai-YuanSingapore ;River Edge, N.J. World Scientificc20021 online resource (458 p.)Series on concrete and applicable mathematics ;v. 4Description based upon print version of record.981-02-4868-7 Includes bibliographical references and index.Contents ; Preface ; 1 Introduction ; 1.1. Some Basic Concepts of Stochastic Processes and Examples ; 1.2. Markovian and Non-Markovian Processes Markov Chains and Examples ; 1.3. Diffusion Processes and Examples ; 1.4. State Space Models and Hidden Markov Models1.5. The Scope of the Book 1.6. Complements and Exercises ; References ; 2 Discrete Time Markov Chain Models in Genetics and Biomedical Systems ; 2.1. Examples from Genetics and AIDS ; 2.2. The Transition Probabilities and Computation2.3. 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 ; 2.5.1. The case when CT is finite ; 2.5.2. The case when CT is infinite2.6. The Moments of First Absorption Times 2.6.1. The case when CT is finite ; 2.7. Some Illustrative Examples ; 2.8. Finite Markov Chains ; 2.8.1. The canonical form of transition matrix ; 2.8.2. Absorption probabilities of transient states in finite Markov chains2.9. Stochastic Difference Equation for Markov Chains With Discrete Time 2.9.1. Stochastic difference equations for finite Markov chains ; 2.9.2. Markov chains in the HIV epidemic in homosexual or IV drug user populations ; 2.10. Complements and Exercises ; 2.11. Appendix2.11.1. The Hardy-Weinberg law in population genetics 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 manSeries on concrete and applicable mathematics ;v. 4.MedicineMathematical modelsStochastic processesGeneticsMathematical modelsAIDS (Disease)Mathematical modelsCancerMathematical modelsElectronic books.MedicineMathematical models.Stochastic processes.GeneticsMathematical models.AIDS (Disease)Mathematical models.CancerMathematical models.519.2302457610.15118610/.1/5118Tan W. Y.1934-906941MiAaPQMiAaPQMiAaPQBOOK9910450987003321Stochastic models with applications to genetics, cancers, AIDS and other biomedical systems2028793UNINA