<p>The author writes in the quote that <span class="math-container">$O$</span> is to be taken for the whole set of positions <span class="math-container">$O_{i}$</span>.</p>
<p>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 &quot;the observed sequence <span class="math-container">$O = O_1, O_2...$</span>&quot;</p>
<p>Thus as you say <span class="math-container">$Pr(sequence) = Pr(O) = Pr(O_1) * Pr(O_2)...$</span> according to my understanding of the quotes.</p>

CC BY-SA 4.0
2020-08-25T20:35:40.233Z
2020-08-25T20:35:40.233Z
Maximilian Press
<p>I am reading "<code>Statistical methods in bioinformatics</code>"</p>

<p>I came across this formula:
<a href="https://i.sstatic.net/eSebp.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/eSebp.png" alt="enter image description here"></a></p>

<p>As explained in the book <strong>O</strong> are the observations:
<a href="https://i.sstatic.net/DnIgr.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DnIgr.png" alt="enter image description here"></a> </p>

<p>My question is why the author only specified <span class="math-container">$prob(O)$</span> for a sequence of length=1 ?, I assume he is only talking about one observation, but generally we have a sequence <span class="math-container">$O_1 ,O_2,O_3,...$</span>. </p>

<p>I assume that <span class="math-container">$Prob(sequence)= P(O_1).P(O_2)...$</span> but I am not sure.</p>

CC BY-SA 4.0
2020-09-02T12:43:27.527Z
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?
Kamil S Jaron
<ngs><hidden-markov-models>
probability of an entire sequence, not just one value
# probability of an entire sequence, not just one value

(Asked by: username_0 on 2020-01-26)

I am reading "`Statistical methods in bioinformatics`"

I came across this formula:
[![enter image description here](https://i.sstatic.net/eSebp.png)](https://i.sstatic.net/eSebp.png)

As explained in the book **O** are the observations:
[![enter image description here](https://i.sstatic.net/DnIgr.png)](https://i.sstatic.net/DnIgr.png)

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.

**Tags:** ngs, hidden-markov-models
> **Comments:**
> **username_1**: 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?  

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## 1 answers

### Answer by username_2 on 2020-08-25. Score: 2

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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