What is the notation for calculating the mode?

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Question:

What is appropriate notation for calculating the mode of a function? In this case, I use the mode of a Gamma(a,b) distribution in a cost-function.

I am looking for something analogous to $\bar{x}$ or $\tilde{x}$ notation that is commonly used for the mean and medians, respectively, if something like $\bar{\text{G}(a,b)}$ would make sense.

What I have tried:

1. Google results are confounded by mode $\simeq$ model and results for latex's 'math mode'

2. It is not on the following wikipedia pages:

   • Greek letters used in mathematics, science, and engineering

   • Table of mathematical symbols

   • Latin letters used in mathematics

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2 Answers

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One possibility for the notation for a mode is $$\underset{x}{\operatorname{arg\,max}} f(x)$$ but I thought that was ugly, so here I used a hat $$\hat{X}$$ to indicate the peak in the probability density or mass function, even though this can also be used for other meanings.

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In Bayesian estimation, the mode is given by the maximum a posteriori (MAP) estimate. Using the "MAP" subscript would suffice.

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