I encountered the following (to me) weird problem while trying to do some simple sampling.
- I have a system that generates random numbers. Let's for simplicity assume the numbers are 0, 1 and 2 with uniform probability.
- I generated one sample and that obtained sample didn't look random to me. Let's just say it was a 0 (random vector in the real system).
- Because I had some doubts about the randomness of the sample, I decided to test the system a few times (by sampling) to verify that the first sample just looks non-random to me. Turns out it is random.
- Now I want to continue sampling. This is where I'm not sure whether I keep my sample from the beginning (the 0) or if I just start over.
- If I start over isn't it like rejecting a sample conditionally on it's value (which would change the overall probability distribution)? But then again after a certain outcome was received, the chance of getting that outcome is the same as it was before.
Should I reject the first draw or not?
I hope this is not a philosophical issue in the end.