The Bühlmann model, introduced by Hans Bühlmann in the context of actuarial science, is a method for estimating risk or making predictions, particularly in the field of insurance. It is designed to improve the estimation of claims or losses by considering both historical data and additional information, which may help refine predictions.
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Given a latent risk parameter , observations are independent and identically distributed random variables with conditional expectation and conditional variance . The Bühlmann credibility premium estimates by an affine function of past observations under mean squared error. Its population parameters are , expected process variance , and variance of hypothetical means .