Answers.Body: <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>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-08-25T20:35:40.233Z
Answers.LastActivityDate: 2020-08-25T20:35:40.233Z
Answers.UserDisplayName: Maximilian Press
Body: <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>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-09-02T12:43:27.527Z
Comments.Text: 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?
Comments.UserDisplayName: Kamil S Jaron
Tags: <ngs><hidden-markov-models>
Title: probability of an entire sequence, not just one value
ThreadText: # 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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