Meaning of $\gtrless$ in the context of multiple hypothesis testing

Question

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

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

Answer 1

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.