Bayesianlike

Bayesianlike is a term used in statistics, machine learning, and cognitive science to describe methods and models that are inspired by Bayesian reasoning but do not constitute formal Bayesian inference. These approaches typically aim to incorporate prior information and update beliefs in light of data, yet rely on approximations or alternative update mechanisms that prevent a genuine posterior distribution from being computed. As a result, they are sometimes described as Bayesian-like rather than truly Bayesian.

Common examples include variational inference and empirical Bayes, which are rooted in Bayesian theory but rely on tractable approximations or hyperparameter estimation that deviate from exact Bayesian updating. Other practices, such as ensemble methods or certain probabilistic neural networks with dropout, are used to obtain uncertainty estimates in a Bayesian-like fashion without claiming full Bayesian validity.

In applied research, Bayesianlike models are used to capture uncertainty and prior knowledge while maintaining computational practicality. They appear in cognitive modeling to explain belief revision and in machine learning for risk assessment and decision making under uncertainty. Critics note that the label can be vague and emphasize the need to specify the inferential rules and priors involved.

See also: Bayesian inference, variational inference, empirical Bayes, approximate Bayesian computation, uncertainty quantification.