nonBayesian

Non-Bayesian refers to statistical or learning methods that do not use Bayesian probability as the formal framework for inference. Instead they rely on alternative philosophies such as frequentist statistics, fiducial inference, or decision-theoretic principles.

In statistics, non-Bayesian methods emphasize point estimates, long-run error rates, and procedures with guarantees under repeated sampling. Common approaches include maximum likelihood estimation, method of moments, least squares, hypothesis testing with p-values, confidence intervals, and bootstrapping within a frequentist interpretation. They may also include minimax or other decision rules that do not require prior distributions.

In data science and machine learning, non-Bayesian approaches typically optimize a defined loss function over data, using empirical risk minimization, regularization, and cross-validation to select models. Probabilistic interpretations, such as posterior distributions, are not central to the method, though probabilistic outputs may be produced post hoc. Examples include linear regression with least squares, support vector machines, gradient-boosted trees, and many unsupervised methods.

The term is often used in contrast to Bayesian methods, which incorporate prior beliefs and update them with data via Bayes' rule to produce posterior distributions. Debates around non-Bayesian versus Bayesian approaches concern prior influence, interpretability, robustness, and computational considerations.

In practice, many applications blend ideas, using non-Bayesian estimation with Bayesian ideas, or using Bayesian methods for some components and non-Bayesian for others. The label non-Bayesian thus describes a broad set of methods unified mainly by the absence of formal Bayesian probabilistic updating.