Hybrid Model: Combine two Classifiers built on different Populations / datasets

Question

I have two classifier (A & B) built upon two distinct datasets (a & b), classifying a binary outcome (0,1). The two datasets (a & b) contain exactly the same variables, but strongly differ in the number of observations (e.g. n of a = 50, n of b = 400) Note that the two datasets cannot be combined due to methodological reasons!

I want to apply each classifier to make probabilistic predictions on new data. So each classifier gets the same new input data and makes its own probabilistic estimates (e.g. A: 0.4 and B: 0.55). I could now take the mean of those predictions (0.475) and be happy with it. However I am looking for methods that weight those predictions based on some criteria such as the number of observations each classifier was built on.

Alternatively, I would also be happy with a combined classifier C, that results for example from weighting model coefficients from both classifiers A & B.

(I learned about Ensemble methods but as far i understand it, those methods combine predictions from various models - but those models are built upon the same populations, which is not what I need)

Answer 1

I am not experienced in this area. Perhaps you need a mixture model with an additional parameter p that indicates the probability of the response being in distribution A. The probability of being in distribution B would be (1-p). But this is only suitable if you have a mixture of two different distributions. In your case, I am not sure. It sounds like the same endpoint being measured in two samples of different sizes.