00000nam a2200000 i 4500 UP-99946688289984575 Buklod 20220927130146.0 a r |||| u| ta 220920s2020 si r |||| u| d 9789813274600 DIM rda eng QH 323.5 W36 2020 Wan, Frederick Y M author. Stochastic models in the life sciences and their methods of analysis Frederick Y M Wan. Singapore World Scientific 2020 xvi, 460 pages 25 cm text rdacontent unmediated rdamedia volume rdacarrier Intro; Contents; Preface; Part 1. Discrete Stage Markov Chains; Chapter 1. Discrete Sample Space Probability; 1.1 Terminology; 1.1.1 Events and sample space; 1.1.2 Finite, countable and continuous experiments; 1.2 Intuitive Probability for Finite Sample Space; 1.2.1 Relative frequencies and equiprobable sample space; 1.2.2 Basic properties of probabilities; 1.2.3 Expected value and variance; 1.3 The Binomial Distribution; 1.4 Conditional Probability; Chapter 2. Discrete Stage Regular Markov Chains; 2.1 Introduction; 2.2 A Simple Mouse Experiment 2.2.1 The mathematical model of a mouse experiment2.3 Transition Matrix for a DMC; 2.3.1 Probability vectors and stochastic matrices; 2.3.2 Evolution of probability distribution; 2.3.3 Chapman-Kolmogorov equations; 2.4 Regular Markov Chains; 2.4.1 Convergence to a steady state; 2.4.2 The eigenvalues of a transition matrix; 2.4.3 Uniqueness and stability of the steady state; 2.4.4 Evolution and steady state of the mouse experiment; 2.4.4.1 Steady state of the mouse experiment; 2.4.4.2 Evolution of the probability distribution; 2.5 DNA Mutation; 2.5.1 The double helix 2.5.2 Mutation due to base substitutions2.5.3 Markov chain model; 2.5.4 Equal opportunity substitution; 2.6 Linear Difference Equations; 2.6.1 A single first order linear equation; 2.6.2 Linear systems with constant coefficients; 2.6.3 Reduction of order; 2.6.4 Variation of parameters; 2.7 Appendix A Proof of a Basic Existence Theorem for Regular MC; Chapter 3. Discrete Stage Absorbing Markov Chains; 3.1 Introduction; 3.2 Gambler's Ruin; 3.2.1 The model; 3.2.2 Solution of IVP; 3.2.3 Canonical transition and absorbing matrix; 3.3 Expected Transient Stops to an Absorbing State 3.4 Birth and Death Processes3.4.1 General birth and death processes; 3.4.1.1 The model; 3.4.1.2 Expected time to extinction; 3.4.1.3 Time-invariant systems; 3.5 A Simplified Infectious Disease Problem; 3.5.1 A simplified (SIS) model; 3.5.2 Probability of absorption; Chapter 4. Discrete Stage Nonlinear Markov Processes; 4.1 Mendelian Genetics and Difference Equation; 4.2 Hardy-Weinberg Stability Theorem; 4.3 Selective Breeding I; 4.4 Gene Frequencies; 4.5 Selective Breeding II; 4.6 Mutation; 4.7 A Nonlinear Infectious Disease Model; 4.8 Single Nonlinear Difference Equations 4.8.1 Taking logarithms4.8.2 Algebraic and trigonometric identities; 4.8.3 Raising the order; 4.8.4 Other ad hoc substitutions; 4.8.5 Evolving a few stages; Part 2. Continuous Time Markov Chains; Chapter 5. Continuous Time Birth and Death Type Processes; 5.1 The Poisson Process; 5.1.1 Stationary processes; 5.1.2 Independent increments; 5.1.3 Other probabilistic information; 5.1.3.1 The expected value; 5.1.3.2 Second moment and variance; 5.1.3.3 Probability generating function; 5.1.4 Waiting time; 5.2 Pure Birth and Pure Death Processes; 5.2.1 Pure birth processes Life sciences Statistical methods. Statistics process. Life sciences Mathematical models. FO UPD DIM QH 323.5 W36 2020 Book