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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?

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I have now found a helpful piece of literature which basically answers my question. In case others are interested, here is a publication that I found very useful:

M. Saerens, P. Latinne, and C. Decaestecker. Adjusting the outputs of a classifier to new a priori probabilities: a simple procedure. Neural computation , 14(1):21–41, 2002

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