What's the conventional notation for most probable/likely value as opposed to expectation value?

Question

Say I want to distinguish the expected value for some random variable $\mathbb{E}(\eta)$ from its most likely / probable value.

Is there a conventional, succinct way to refer to the latter, other than: $MostProbableValue(\eta)=\cdots$ ?

Answer 1

As already noted by MPW in the comments. The value is not unique. Also it does not need to exist (e.g. exponential distribution on $(0,\infty)$, which does not assume it's max on the definition range.). Hence a functional notation $MaxProb(P)$ would not be missleading.

On the other hand, a Maximum-Likelyhood-estimator of a statistic $\theta$ is often written as $\hat{\theta}$.

If you view the identity random variable $I: \Omega \rightarrow \Omega$, as statistic, you can write $\hat{I}$ for the most probable value.