Propose a probabilistic framework or alternative approach that can represent degrees of belief in non-repeatable events like patient diagnoses, and discuss its advantages over traditional probability theory.

Use Bayesian neural networks (BNNs) to model expert knowledge as prior distributions. Update these priors using likelihood estimates from diagnostic tests to capture uncertainty and context-dependent evidence. This approach can better represent human degrees of belief in rare conditions than traditional probability theory, but requires careful tuning of hyperparameters.