In explaining MLE, some texts (such as this) formulate the likelihood function as: $\prod_{i=1}^n f(x_i; \theta)$

while some texts (such as this) formulale the likelihood function as: $\prod_{i=1}^n f(x_i| \theta)$

The basic difference is that, in the latter, $f$ is given as a conditional probability. Do they mean the same thing? What are their differences?


1 Answer 1


This is merely a matter of convention for denoting the dependence of the density on the unknown parameter. This dependence becomes a probabilistic dependence on the random variable $\theta$ only when $\theta$ itself is a random variable, namely in the Bayesian setting.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

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