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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:

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    @J.M. Thanks for th$e$ hint. But I am still unsuccessful.2011-05-06

2 Answers 2

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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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    thanks ... right now I am using mode(G(a,b)); perhaps I could use $u()$ but I didn't want to reinvent the wheel2011-05-06