Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems /:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New Jersey :
World Scientific,
2015.
|
| Edition: | 2nd edition. |
| Series: | Series on concrete and applicable mathematics ;
volume 19 |
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| Physical Description: | 1 online resource |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9789814390958 981439095X |
Staff View
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| 100 | 1 | |a Tan, W. Y., |d 1934- |1 https://id.oclc.org/worldcat/entity/E39PCjv7PRQrGhytgFTfxxb68C |0 http://id.loc.gov/authorities/names/n86001404 | |
| 245 | 1 | 0 | |a Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems / |c by Wai-Yuan Tan. |
| 250 | |a 2nd edition. | ||
| 264 | 1 | |a New Jersey : |b World Scientific, |c 2015. | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 0 | |a Series on concrete and applicable mathematics ; |v volume 19 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 650 | 0 | |a Medicine |x Mathematical models. |0 http://id.loc.gov/authorities/subjects/sh85083085 | |
| 650 | 0 | |a Stochastic processes. |0 http://id.loc.gov/authorities/subjects/sh85128181 | |
| 650 | 0 | |a Genetics |x Mathematical models. |0 http://id.loc.gov/authorities/subjects/sh85053879 | |
| 650 | 0 | |a AIDS (Disease) |x Mathematical models. | |
| 650 | 0 | |a Cancer |x Mathematical models. | |
| 650 | 2 | |a Stochastic Processes |0 https://id.nlm.nih.gov/mesh/D013269 | |
| 650 | 6 | |a Médecine |x Modèles mathématiques. | |
| 650 | 6 | |a Processus stochastiques. | |
| 650 | 6 | |a Sida |x Modèles mathématiques. | |
| 650 | 6 | |a Cancer |x Modèles mathématiques. | |
| 650 | 7 | |a HEALTH & FITNESS |x Holism. |2 bisacsh | |
| 650 | 7 | |a HEALTH & FITNESS |x Reference. |2 bisacsh | |
| 650 | 7 | |a MEDICAL |x Alternative Medicine. |2 bisacsh | |
| 650 | 7 | |a MEDICAL |x Atlases. |2 bisacsh | |
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| 650 | 7 | |a MEDICAL |x Family & General Practice. |2 bisacsh | |
| 650 | 7 | |a MEDICAL |x Holistic Medicine. |2 bisacsh | |
| 650 | 7 | |a MEDICAL |x Osteopathy. |2 bisacsh | |
| 650 | 7 | |a AIDS (Disease) |x Mathematical models |2 fast | |
| 650 | 7 | |a Cancer |x Mathematical models |2 fast | |
| 650 | 7 | |a Genetics |x Mathematical models |2 fast | |
| 650 | 7 | |a Medicine |x Mathematical models |2 fast | |
| 650 | 7 | |a Stochastic processes |2 fast | |
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| author | Tan, W. Y., 1934- |
| author_GND | http://id.loc.gov/authorities/names/n86001404 |
| author_facet | Tan, W. Y., 1934- |
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| 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 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. |
| ctrlnum | (OCoLC)928387326 |
| dewey-full | 610.1/5195 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 610 - Medicine and health |
| dewey-raw | 610.1/5195 |
| dewey-search | 610.1/5195 |
| dewey-sort | 3610.1 45195 |
| dewey-tens | 610 - Medicine and health |
| discipline | Medizin |
| edition | 2nd edition. |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn928387326 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-18T14:22:35Z |
| institution | BVB |
| isbn | 9789814390958 981439095X |
| language | English |
| oclc_num | 928387326 |
| open_access_boolean | |
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| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | World Scientific, |
| record_format | marc |
| series2 | Series on concrete and applicable mathematics ; |
| spelling | Tan, W. Y., 1934- https://id.oclc.org/worldcat/entity/E39PCjv7PRQrGhytgFTfxxb68C http://id.loc.gov/authorities/names/n86001404 Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems / by Wai-Yuan Tan. 2nd edition. New Jersey : World Scientific, 2015. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Series on concrete and applicable mathematics ; volume 19 Includes bibliographical references and index. Print version record. 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. Medicine Mathematical models. http://id.loc.gov/authorities/subjects/sh85083085 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Genetics Mathematical models. http://id.loc.gov/authorities/subjects/sh85053879 AIDS (Disease) Mathematical models. Cancer Mathematical models. Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Médecine Modèles mathématiques. Processus stochastiques. Sida Modèles mathématiques. Cancer Modèles mathématiques. HEALTH & FITNESS Holism. bisacsh HEALTH & FITNESS Reference. bisacsh MEDICAL Alternative Medicine. bisacsh MEDICAL Atlases. bisacsh MEDICAL Essays. bisacsh MEDICAL Family & General Practice. bisacsh MEDICAL Holistic Medicine. bisacsh MEDICAL Osteopathy. bisacsh AIDS (Disease) Mathematical models fast Cancer Mathematical models fast Genetics Mathematical models fast Medicine Mathematical models fast Stochastic processes fast Print version: Tan, W.Y., 1934- Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems. 2nd edition 9789814390941 (DLC) 2015031964 (OCoLC)926623329 |
| spellingShingle | Tan, W. Y., 1934- Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems / 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. Medicine Mathematical models. http://id.loc.gov/authorities/subjects/sh85083085 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Genetics Mathematical models. http://id.loc.gov/authorities/subjects/sh85053879 AIDS (Disease) Mathematical models. Cancer Mathematical models. Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Médecine Modèles mathématiques. Processus stochastiques. Sida Modèles mathématiques. Cancer Modèles mathématiques. HEALTH & FITNESS Holism. bisacsh HEALTH & FITNESS Reference. bisacsh MEDICAL Alternative Medicine. bisacsh MEDICAL Atlases. bisacsh MEDICAL Essays. bisacsh MEDICAL Family & General Practice. bisacsh MEDICAL Holistic Medicine. bisacsh MEDICAL Osteopathy. bisacsh AIDS (Disease) Mathematical models fast Cancer Mathematical models fast Genetics Mathematical models fast Medicine Mathematical models fast Stochastic processes fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85083085 http://id.loc.gov/authorities/subjects/sh85128181 http://id.loc.gov/authorities/subjects/sh85053879 https://id.nlm.nih.gov/mesh/D013269 |
| title | Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems / |
| title_auth | Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems / |
| title_exact_search | Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems / |
| title_full | Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems / by Wai-Yuan Tan. |
| title_fullStr | Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems / by Wai-Yuan Tan. |
| title_full_unstemmed | Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems / by Wai-Yuan Tan. |
| title_short | Stochastic models with applications to genetics, cancers, AIDS, and other biomedical systems / |
| title_sort | stochastic models with applications to genetics cancers aids and other biomedical systems |
| topic | Medicine Mathematical models. http://id.loc.gov/authorities/subjects/sh85083085 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Genetics Mathematical models. http://id.loc.gov/authorities/subjects/sh85053879 AIDS (Disease) Mathematical models. Cancer Mathematical models. Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Médecine Modèles mathématiques. Processus stochastiques. Sida Modèles mathématiques. Cancer Modèles mathématiques. HEALTH & FITNESS Holism. bisacsh HEALTH & FITNESS Reference. bisacsh MEDICAL Alternative Medicine. bisacsh MEDICAL Atlases. bisacsh MEDICAL Essays. bisacsh MEDICAL Family & General Practice. bisacsh MEDICAL Holistic Medicine. bisacsh MEDICAL Osteopathy. bisacsh AIDS (Disease) Mathematical models fast Cancer Mathematical models fast Genetics Mathematical models fast Medicine Mathematical models fast Stochastic processes fast |
| topic_facet | Medicine Mathematical models. Stochastic processes. Genetics Mathematical models. AIDS (Disease) Mathematical models. Cancer Mathematical models. Stochastic Processes Médecine Modèles mathématiques. Processus stochastiques. Sida Modèles mathématiques. Cancer Modèles mathématiques. HEALTH & FITNESS Holism. HEALTH & FITNESS Reference. MEDICAL Alternative Medicine. MEDICAL Atlases. MEDICAL Essays. MEDICAL Family & General Practice. MEDICAL Holistic Medicine. MEDICAL Osteopathy. AIDS (Disease) Mathematical models Cancer Mathematical models Genetics Mathematical models Medicine Mathematical models Stochastic processes |
| work_keys_str_mv | AT tanwy stochasticmodelswithapplicationstogeneticscancersaidsandotherbiomedicalsystems |