1
$\begingroup$

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

enter image description here

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

$\endgroup$
1
  • $\begingroup$ 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

0
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.