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If I have a markov chain transition matrix for 2 states. Specifically in my case, it is a transition matrix for a bacterial genome with 4 random variables being A,C,G and T. (The bases) If I want to calculate the probability of a random sequence like GATTACA occurring from the markov chain, how would I go about it?

I was thinking that I would have to do it by :

P(A|G) * P(T|A) * P(T|T) * P(A|T) * P(C|A) * P(A|C)

But I am not sure what to do with the first G. Do I take its probability as 1 or do I use the stationary distribution of transition matrix value for G?

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Do you mean 4 states ACGT, not 4 random variables? –  gt6989b Feb 28 '13 at 15:55
    
You would need either the initial distribution or the initial starting state. –  gt6989b Feb 28 '13 at 15:56
    
@gt6989b I actually used the word states for them first, but I thought it might be confusing since I already said that markov chain was for 2 states. (Ti and Ti-1). –  gaddaga Feb 28 '13 at 16:31
    
@gt6989b, can I use the stationary distribution matrix for P as the initial starting state? –  gaddaga Feb 28 '13 at 16:32
    
@gaddaga The Markov chain has 4 states, not 2. Your 2 does not enumerate the states, in fact it is 1 + the length of the memory of the Markov process. –  Did Feb 28 '13 at 16:45
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