TY  - BOOK
AU  - Tan,W.Y.
TI  - Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems
T2  - Series on concrete and applicable mathematics
SN  - 9789814390958
AV  - R853.M3 T36 2015eb
U1  - 610.1/5195 23
PY  - 2015///
CY  - New Jersey
PB  - World Scientific
KW  - Medicine
KW  - Mathematical models
KW  - Stochastic processes
KW  - Genetics
KW  - AIDS (Disease)
KW  - Cancer
KW  - Stochastic Processes
KW  - Médecine
KW  - Modèles mathématiques
KW  - Processus stochastiques
KW  - Sida
KW  - HEALTH & FITNESS
KW  - Holism
KW  - bisacsh
KW  - Reference
KW  - MEDICAL
KW  - Alternative Medicine
KW  - Atlases
KW  - Essays
KW  - Family & General Practice
KW  - Holistic Medicine
KW  - Osteopathy
KW  - fast
KW  - Electronic books
N1  - Includes bibliographical references and index; 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; 1.5. 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; 2.3. The Structure and Decomposition of Markov Chains; 2.4. Classification of States and the Dynamic Behavior of Markov Chains2.5. The Absorption Probabilities of Transient States; 2.5.1. The case when CT is finite; 2.5.2. The case when CT is infinite; 2.6. 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; 2.9. 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 populations2.10.Complements and Exercises; 2.11. Appendix; 2.11.1. The Hardy-Weinberg law in population genetics; 2.11.1.1. The Hardy-Weinberg law for a single locus in diploid populations; 2.11.1.2. The Hardy-Weinberg law for linked loci in diploid populations; 2.11.2. The inbreeding mating systems; 2.11.3. Some mathematical methods for computing An, the nth power of a square matrix A; References; 3 Stationary Distributions and MCMC in Discrete Time Markov Chains; 3.1. Introduction; 3.2. The Ergodic States and Some Limiting Theorems3.3. Stationary Distributions and Some Examples; 3.4. Applications of Stationary Distributions and Some MCMC Methods; 3.4.1. The Gibbs sampling method; 3.4.2. The weighted bootstrap method for generating random samples; 3.4.3. The Metropolis-Hastings algorithm; 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; References; 4 Continuous-Time Markov Chain Models in Genetics, Cancers and AIDS; 4.1. Introduction; 4.2. The Infinitesimal Generators and an Embedded Markov Chain4.3. The Transition Probabilities and Kolmogorov Equations; 4.4. Kolmogorov Equations for Finite Markov Chains with Continuous Time; 4.5. Complements and Exercises; References; 5 Absorption Probabilities and Stationary Distributions in Continuous-Time Markov Chain Models; 5.1. Absorption Probabilities and Moments of First Absorption Times of Transient States; 5.1.1. The case when CT is finite; 5.2. The Stationary Distributions and Examples; 5.3. Finite Markov Chains and the HIV Incubation Distribution
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