optimalstop

This program is used in order to solve the optimal stop problem labeled here:

https://en.wikipedia.org/wiki/Optimal_stopping

This is the original correspondence between myself and the author of the program:

"Here is my HACK of a python program to test my method for the optimal stopping problem. Effectively the method does the following:

1. Assume the skills of the secretary or "fitness" for the job is distributed normally & score each applicant during their interview.
2. Starting at interview #2 calculate each of the following after each interview
   1. The mean of all applicants interviewed
   2. The standard deviation of all applicants interviewed
   3. Bernards estimate of rank (percentile) for the number of applicants left - AND the Bernard's estimate for the number of applicants left minus 1.

Since the Nth Bernard's of N things is an estimate of the percentile of the highest percentile thing, that implies there is a 50% chance of finding the Nth Bernards rank of N things. Similarly, since the Bernard's rank of the (N-1)th thing of N things is the ESTIMATE of the 2nd highest thing, I calculate what is half way between the Nth Bernards of N things (estimate of highest percentile thing) and the Bernards rank of the penultimate thing (Nth-1) of N things (estimate of the 2nd highest percentile thing). This average sets my "stopping criteria" halfway between the EXPECTED highest percentile thing (Nth of N) and the 2nd highest EXPECTED thing ([N-1]th of N ). Some simple algebra of [(N-0.3)/(N+0.4) + ((N-1)-0.3)/(N+0.4)] / 2 gives me (N2-0.9N-0.17)/(N2-0.2N-0.24). That becomes my selection criteria. Note I use the number of applicants LEFT to interview to calculate my maximum EXPECTED percentile - so as the interview process goes on my percentile selection criterion drops. That can be observed in the plots attached (each color is a separate random dataset)"

"I would preface it with the method is rather brute force, and it was a solution that was proposed based on zero research of the problem."

"I would also include that I used the problem as a learning opportunity for Python so I’m sure the code is PURE HACK since it was my first attempt at a Python Program."

My Personal Story:

As I was reading Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian and Tom Griffiths, I came across the optimal stopping problem and challenged my girlfriend's dad to the problem. He took this opportunity to learn the python programming language. I want to submit this github link for review.

Best Wishes!