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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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  • $\begingroup$ For 1: tried this? $\endgroup$ – J. M. isn't a mathematician May 6 '11 at 15:53
  • $\begingroup$ @J.M. that gives the analytical form of the mode, but that is not what I want. I have changed my question to focus on notation for mode rather than calculation of the mode of the gamma. $\endgroup$ – David LeBauer May 6 '11 at 16:04
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    $\begingroup$ I was addressing the "Google results are confounded by" portion in #1; that is, use quote marks to tell Google that you meant what you said. $\endgroup$ – J. M. isn't a mathematician May 6 '11 at 16:06
  • $\begingroup$ @J.M. Thanks for the hint. But I am still unsuccessful. $\endgroup$ – David LeBauer May 6 '11 at 16:14
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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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  • $\begingroup$ Note: This can also be written simply as $\operatorname{argmax} f$. $\endgroup$ – user76284 Oct 28 '19 at 1:20
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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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  • $\begingroup$ .. except that I am not using a posterior, I am using data to set the mode of an informed Gamma prior. $\endgroup$ – David LeBauer May 6 '11 at 16:13
  • $\begingroup$ @David: I would just pick a symbol and explain it. $\endgroup$ – Emre May 6 '11 at 16:16
  • $\begingroup$ thanks ... right now I am using mode(G(a,b)); perhaps I could use $u()$ but I didn't want to reinvent the wheel $\endgroup$ – David LeBauer May 6 '11 at 16:21

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