When we predict probabilities, what do we predict?

When we predict probabilities, what do we predict?

I was interviewed a long time ago, and the subject of the interview made me think again.

Interviewer: Did you know Logistic is coming back? Me: Of course I know, very often. Interviewer: So how do you think the probability of Logistic's regression prediction is to be explained? Me: Certainly not. The individual probability cannot be estimated if there is only one observation. It should be explained as, given N individuals with the same characteristics, the success rate is equal to the estimated probability.

Well, the interviewer couldn't say no, and of course the final result was that I was expelled (probably because of my background in economics and not statistics or computers).

You may find what I said above a bit contradictory or hard to understand, but when we estimated Logistic's return, we estimated:

Shouldn't it be explained as the probability of individual success?

• I think there is something wrong with that statement.

  When we talk about the probability of success of a single person, it should be the average number of times the same person succeeds in 100 repetitions under the same conditions. If we remember t as the number of times someone tries, then our ideal model (data generation process) should look like this:

  

  Alternatively, however, the actual data generation process might look something like this: