LEADER 05393nam 2200733Ia 450 001 9910785094603321 005 20230607221531.0 010 $a981-277-796-2 035 $a(CKB)1000000000411039 035 $a(EBL)1679538 035 $a(OCoLC)879023609 035 $a(SSID)ssj0000251562 035 $a(PQKBManifestationID)11939249 035 $a(PQKBTitleCode)TC0000251562 035 $a(PQKBWorkID)10174119 035 $a(PQKB)11778072 035 $a(MiAaPQ)EBC1679538 035 $a(WSP)00004894 035 $a(Au-PeEL)EBL1679538 035 $a(CaPaEBR)ebr10201221 035 $a(CaONFJC)MIL505431 035 $a(EXLCZ)991000000000411039 100 $a20020621d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStochastic models with applications to genetics, cancers, AIDS and other biomedical systems$b[electronic resource] /$fTan Wai-Yuan 210 $aSingapore ;$aRiver Edge, N.J. $cWorld Scientific$dc2002 215 $a1 online resource (458 p.) 225 1 $aSeries on concrete and applicable mathematics ;$vv. 4 300 $aDescription based upon print version of record. 311 $a981-02-4868-7 320 $aIncludes bibliographical references and index. 327 $aContents ; 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 Models 327 $a1.5. 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 Computation 327 $a2.3. 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 infinite 327 $a2.6. 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 chains 327 $a2.9. 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. Appendix 327 $a2.11.1. The Hardy-Weinberg law in population genetics 330 $a This book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and stochastic differential equations. It illustrates how these processes and approaches are applied to many problems in genetics, carcinogenesis, AIDS epidemiology and other biomedical systems. One feature of the book is that it describes the basic MCMC (Markov chain and Monte Carlo) procedures and illustrates how to use the Gibbs sampling method and the multilevel Gibbs sampling method to solve man 410 0$aSeries on concrete and applicable mathematics ;$vv. 4. 606 $aMedicine$xMathematical models 606 $aStochastic processes 606 $aGenetics$xMathematical models 606 $aAIDS (Disease)$xMathematical models 606 $aCancer$xMathematical models 615 0$aMedicine$xMathematical models. 615 0$aStochastic processes. 615 0$aGenetics$xMathematical models. 615 0$aAIDS (Disease)$xMathematical models. 615 0$aCancer$xMathematical models. 676 $a519.2302457 676 $a610.15118 676 $a610/.1/5118 700 $aTan$b W. Y.$f1934-$01521848 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910785094603321 996 $aStochastic models with applications to genetics, cancers, AIDS and other biomedical systems$93761273 997 $aUNINA