Continuous Probability Distributions and Markov Chains (Week 6)

Topics

Discrete-Time Markov Chains

• Markov property
• Transition matrices
• Stationarity
• Reversibility

Continuous Probability Distributions

• Uniform
• Normal
• Exponential
• Beta
• Gamma

Continuous-Time Markov Chains

• Exponential waiting times
• Poisson processes

Reading

• Yang, Ch. 1
• Yang, Ch. 12.5-12.6 (as needed)

Assignment

Modify the code that we covered in class to simulate a discrete-time Markov chain in order to simulate nucleotide evolution (four states - A,C,G,T) in a continuous-time Markov chain. You can assume a Jukes-Cantor model of sequence evolution.

Pseudocode first! Use the example we walked through in class (see slides) as a guide to the steps involved in simulation.