I am using a Gaussian Process model for probabilistic classification. My data covers two classes, let's call them "Sick" and "Healthy". For each of these classes, I have 5000 training samples. Although my data is balanced, the prior for being "Healthy" in the real world is around 100 times larger than that for "Sick". I want my model to take that into account when calculating probabilities.
I came up with two different approaches:
1) Give the model imbalanced training data, i.e. repeat the "Healthy" samples 100 times. But this will a) promote overfitting and b) make training and prediction really slow and expensive, so I don't like the approach very much.
2) Leave the Gaussian process model balanced, and adjust the probabilities afterwards, e.g. multiplying them with a prior or something like that - maybe there there is some Bayes-related rules on what to do. I don't know exactly how that should work, though.
Could you give me an opinion on my approaches and/or point me to a fruitfull direction?