Stochastic Processes for Biology

Introduce randomness into biological modelling. Begin with random variables and stochastic processes, then develop discrete- and continuous-time Markov chains, birth–death and Poisson processes, waiting times, transition and generator matrices, Kolmogorov equations, Gillespie simulation, Monte Carlo methods and extinction or outbreak probabilities.

01Why biological randomness matters 02Random variables 03Stochastic processes 04Markov property 05Discrete-time Markov chains 06Continuous-time Markov chains 07Birth–death processes 08Poisson processes 09Exponential waiting times 10Transition matrices 11Generator matrices 12Kolmogorov equations 13Gillespie algorithm 14Monte Carlo simulation 15Extinction and outbreak probabilities