Sortostat/Optimal sorting cutoffs
What is the optimal cut-off percentile for choosing a chamber to be sorted if you have N sorts (trials) remaining until you must take the sort to preserve a constant dilution rate?
Definition of variables
expected value of the optimal percentage that can be returned from N trials
random variable representing the percentile returned from the ith trial
- all trials are assumed to be independent therefore , for all i
the cut-off percentile for the ith trial.
Since can be factored out of every term after the first above, the solution can be simplified and solved recursively:
- e.g., if you have only 1 trial then you expect to get the mean of the distribution for S.
Since our probability skills were pretty sad, we (Alex Mallet) simulated it to confirm our analytical results. MATLAB file can be found here.