Answers.Body: <p>It means that <span class="math-container">$z$</span> has a (multivariate) normal distribution with 0 mean and identity covariance matrix. This essentially means each individual element of the vector <span class="math-container">$z$</span> has a standard normal distribution.</p>
  
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Body: <p>I know that the notation <span class="math-container">$\mathcal{N}(\mu, \sigma)$</span> stands for a normal distribution.
  But I'm reading the book &quot;An Introduction to Variational Autoencoders&quot; and in it, there is this notation:
  <span class="math-container">$$\mathcal{N}(z; 0, I)$$</span>
  What does it mean?</p>
  <p>picture of the book:
  <a href="https://i.sstatic.net/34JES.png" rel="noreferrer"><img src="https://i.sstatic.net/34JES.png" alt="picture of the book An Introduction to Variational Autoencoders" /></a></p>
  
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Comments.UserDisplayName: nbro
Tags: <terminology><variational-autoencoder><notation><random-variable><bayesian-statistics>
Title: What does the notation $\mathcal{N}(z; \mu, \sigma)$ stand for in statistics?
UserDisplayName: Peyman
ThreadText: # What does the notation $\mathcal{N}(z; \mu, \sigma)$ stand for in statistics?
  
  (Asked by: username_0 on 2020-08-23)
  
  I know that the notation $\mathcal{N}(\mu, \sigma)$ stands for a normal distribution.
  But I'm reading the book "An Introduction to Variational Autoencoders" and in it, there is this notation:
  $$\mathcal{N}(z; 0, I)$$
  What does it mean?
  
  picture of the book:
  [![picture of the book An Introduction to Variational Autoencoders](https://i.sstatic.net/34JES.png)](https://i.sstatic.net/34JES.png)
  
  **Tags:** terminology, variational-autoencoder, notation, random-variable, bayesian-statistics
  
  > **Comments:**
  > **username_1**: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/118284/discussion-on-question-by-username_0-what-does-the-notation-mathcalnz-mu-si).  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2020-08-23. Score: 7 | Accepted answer
  
  It means that $z$ has a (multivariate) normal distribution with 0 mean and identity covariance matrix. This essentially means each individual element of the vector $z$ has a standard normal distribution.
  
  > **Comments:**
  > **username_1**: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/118283/discussion-on-answer-by-username_2-ireland-what-does-the-notation-mathcalnz-mu).  
  
  ---
  
  