Bayesian Neural Network

A Bayesian neural network is a neural network whose weights are treated as probability distributions rather than point estimates, allowing the model to represent epistemic uncertainty — uncertainty about which parameters are correct — alongside the aleatoric uncertainty inherent in the data. The approach replaces the single forward pass with an integration over the posterior weight distribution, typically approximated through variational inference, Monte Carlo dropout, or Laplace approximations. The appeal is both philosophical and practical: philosophically, it promises to move machine learning from pattern matching to genuine probabilistic reasoning; practically, it offers calibrated uncertainty estimates that are essential for decision-making in high-stakes domains. Whether current approximations are sufficient to realize this promise remains a live research question, and the gap between Bayesian ideals and computational reality is where the most interesting work now occurs.