Series on Concrete and Applicable Mathematics - Vol. 4
STOCHASTIC MODELS WITH APPLICATIONS TO GENETICS, CANCERS, AIDS AND OTHER BIOMEDICAL SYSTEMS
by Tan Wai-Yuan (University of Memphis, USA)
Table of Contents (195k)
Preface (78k)
Chapter 1: Introduction
Chapter 1.1: Some Basic Concepts of Stochastic Processes and Examples (187k)
Chapter 1.2: Markovian and Non-Markovian Processes, Markov Chains and Examples (317k)
Chapter 1.3: Diffusion Processes and Examples (183k)
Chapter 1.4: State Space Models and Hidden Markov Models (191k)
Chapter 1.5: The Scope of the Book (145k)
Chapter 1.6: Complements and Exercises (205k)
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.
Contents:
- Discrete Time Markov Chain Models in Genetics and Biomedical
Systems
- Stationary Distributions and MCMC in Discrete Time Markov Chains
- Continuous-Time Markov Chain Models in Genetics, Cancers and AIDS
- Absorption Probabilities and Stationary Distributions in Continuous-Time Markov Chain Models
- Diffusion Models in Genetics, Cancer and AIDS
- Asymptotic Distributions, Stationary Distributions and Absorption Probabilities in Diffusion Models
- State Space Models and Some Examples from Cancer and AIDS
- Some General Theories of State Space Models and Applications
Readership: Graduate students and researchers in probability & statistics and
the life sciences.
"Its strengths include the large number of models described, many of which have previously been published only in research journals; its clear presentation of many detailed analyses; and good accounts of the biology behind the models."
| 460pp |
Pub. date: Feb 2002 |
|
