This lecturer talks about maximum likelihood estimation (MLE), maximum a posteriori (MAP) estimation and Bayes rule, and uses the tilde symbol in a statement.

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Does tilde here mean "follows", likelihood follows the binomial distribution? If yes, How to verify this?

  • $\begingroup$ Yes, in my experience $X~$... has always meant something (like a R.V. $X$) is distributed via a certain distribution. So, a use case is $X~b(x;n,p)$ where $X$ is distributed binomially with $n$ independent Bernoulli trials with a probability of success $p$. You can verify this by asking the lecturer. $\endgroup$
    – user214190
    Oct 30, 2019 at 13:00

1 Answer 1


Your interpretation of the author's use of $\sim$ seems about right. Based on how the slide is typeset, it seems like saving space was more important than precision.

A binomial distribution is characterized by three attributes:

  1. a fixed number of binary trials is conducted such that
  2. each trial is independent
  3. with a fixed probability of success.

So it's appropriate to use a binomial model in these circumstances. Suppose an experiment consists of flipping a coin (assume each flip is independent) with fixed probability of heads a fixed number of times and recording the number of heads. The number of heads you observe has a binomial distribution.

The appearance of a binomial likelihood in Bayes' rule, as opposed to appearing in a different context (such as MLE), does not change how the binomial distribution is characterized. So if you're familiar with a binomial likelihood elsewhere, there's not a difference when it appears in a Bayesian context.


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