My data points can be expressed in a vector form as:
$X = [x(1), x(2), x(3), ..........,x(N)]$
Each element of $X$ has two criteria/characteristics, $P$ and $H$. $P$ is the posterior probability (probability of choosing any elements of $X$, calculated based on some input data) and $H$ is a scalar value (also calculated from the input data). In my system, a larger value of $P$ and a smaller value of $H$ is preferred for the best selection of data point. I want to combine $P$ and $H$ using any mathematical model such that I can have a good data point selection and have a good theoretical explanation.
What kind of mathematical model or filter can I use in my case?
Thank you in advance.
You need to think about the relative importance of $H$ and $P$. You could select the highest $P$ and use $H$ to break ties. You could select the lowest $H$ and use $P$ to break ties. You could compute $aP-bH$ and use that for ranking for some selection of positive number $a,b$. There are more complicated things you can do as well. Once you decide what your priorities are (assuming they are consistent), there will be a formula for it, but we can't guess what formula fits your priorities.