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While reading a paper, I encountered the symbol $\gtrless$, which I had not seen before:

I would like to know about the stacked < and > symbols.

Please point me to a reference or tell me what the symbol and associated symbols above and below means.

Ames
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    Hard to answer with more context, but if $H_k$ and $H_0$ are certain exclusive assumptions, I'd say that "$>$ if $H_k$ is true, and $<$ if $H_0$ is true". – Ivo Terek Jun 15 '18 at 16:51
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    I believe $H_0$ and $H_k$ are just referring to the null and one of some $k$ alternative hypothesis. Which means, the null hypothesis is that the expression on the left is less than $1$. Any one of the $k$ alternative hypothesis is that the expression on the left is greater than $1$. – Winter Soldier Jun 15 '18 at 17:51
  • @MichaelMartin Thank you, that makes sense in the context of what I am reading. – Ames Jun 15 '18 at 19:42
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    @IvoTerek Thank you, that is also sensible in the context of what I'm reading. – Ames Jun 15 '18 at 19:43

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I assume you are reading about bayesian decision theory or decision-related content. Whenever I encountered this notation would be in the context that you have $H_{0}$, null hypothesis, and $H_{k}$, k hypothesis, and you need to take an action based on which hypothesis is true.

In this case, if the ration is bigger than 1 then you assume $H_{k}$ and take an action based on this, otherwise you assume $H_{0}$. Usually the right side is product between the prior probabilities ratio and decision cost-difference ratios.

$\frac{p_{0}}{p_{1}} \frac{C_{10}-C_{00}}{C_{01}-C_{11}}$

where $C_{i,j}$ is the cost of deciding $i$ when $j$ is true.

BelwarDissengulp
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  • Yes, I'm reading a paper on application of multi-hypothesis tests to locating objects in subsampled imagery. The answer you and the others provided is very helpful. It helped me get a better understanding. Thank you. – Ames Jun 16 '18 at 23:30