Assume two datasets: Y, Y that represent the same physical quantity Q. Dataset X contains values of Q after an event A while dataset Y contains values of Q after an event B.
In R X, Y are vectors of the same length, containing effectivelly a number of observations of Q in each state.
Q is a continous variable.
Now, the two datasets should ideally not have any range of overlapping values. That is
max(x) << min (Y)
but that is not the reality of the problem. there are usually overlaps, bigger or smaller.
Now, what I want to do is the following:
Suppose that we choose a value P so that.
Any X <= P is understood as belonging to group X while
any Y > P is understood as belonging to group Y.
now any values of X > P or of Y <= P are wrongly understood as belonging to Y nad X effectively.
Hence we have Xerr -- > Sum( X >P) and Yerror --> Sum(Y<=P).
I want to solve this bivariate optimization problem where I want to at the same time minimize the error of X and Y for a given P. Ultimately the target is to optimize the value of P so that the errors of both X and Y are optimized.
Does any1 have some functions in mind that can help with parts of this problem ? It's not impossible to write the algorithm but it will take time and things like convergence and robustness need to be checked.... !