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I am reading "Statistical methods in bioinformatics"

I came across this formula: enter image description here

As explained in the book O are the observations: enter image description here

My question is why the author only specified $prob(O)$ for a sequence of length=1 ?, I assume he is only talking about one observation, but generally we have a sequence $O_1 ,O_2,O_3,...$.

I assume that $Prob(sequence)= P(O_1).P(O_2)...$ but I am not sure.

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  • $\begingroup$ The capital non-indexed O seems to refer to the whole observed sequence (O = O1, O2, ...), so the probability P(O) is of observing the whole sequence of unspecified length. Or, am I missing something? $\endgroup$
    – Kamil S Jaron
    Commented Sep 2, 2020 at 12:43

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The author writes in the quote that $O$ is to be taken for the whole set of positions $O_{i}$.

In the extracts that you provide there is no reason to believe that it is only for a sequence of length 1. The author writes "the observed sequence $O = O_1, O_2...$"

Thus as you say $Pr(sequence) = Pr(O) = Pr(O_1) * Pr(O_2)...$ according to my understanding of the quotes.

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