Hi all, given a rate matrix Q (instantaneous rates of change) of a nucleotide substitution model, one can calculate the transition probabilities between any pair of nucleotides by calculating a probability matrix that is derived from matrix exponentiation given a certain time interval t:
P(t) = exp(Q*t)
which can further be calculated numerically by Eigen-decomposition of Q and so on.. But I just want to know how exactly one arrives at this step with the exponentiation, or in other words, why does it work? I could not find a reference for this, everybody just takes it as granted.
cheers, Peter
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Peter •
1 answer
The fundamental assumption behind this formula is that nucleotide substitution can be modeled as a continuous time Markov chain. This handout from Stanford gives a good introduction to the topic.
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