BMTRY 718 : Stochastic Processes in Biology and Medicine

DESCRIPTION

An overview of the role of stochastic processes is followed by review and extension of probability theory, including probability generating functions. The course will cover stochastic processes like random walk, branching processes, Markov processes, renewal theory, and hidden Markov process. Applications of these processes in genetics, clinical trial design and data analyses, and computer simulations are discussed throughout the course.

TOPICS:

• Review of random variable theory
• Condition moments, delta method
• Probability generating functions
• Multivariate p.g.f.’s, compound distributions
• Exponential family, MLE, Chiang’s lemma
• Branching processes
• Random walk, diffusion process
• Gambler’s ruin problem
• Classification of Markov states, of stoch. Proc.
• Transition probabilities and other functions
• Theorems. Stationarity. Genetics application.
• Markov characteristic matrix, adjoint matrices
• Higher order transitions, limiting distributions
• Application in Genetics
• Finite Markov Chain
• Limiting Probability
• Hidden Markov Model
• Review of Markov Processes
• Renewal Processes
• Poisson processes
• Sequential Design in Clinical Trials
• Applications in Simulation