nonposterior

Nonposterior is a term used, sometimes informally, to refer to quantities, methods, or analyses that do not produce or rely on a posterior distribution of model parameters in Bayesian statistics. In Bayesian inference, the posterior distribution combines a prior belief with the observed data through Bayes' theorem. Nonposterior approaches, by contrast, do not generate a distribution over parameters after observing the data.

Common nonposterior methods include frequentist techniques such as maximum likelihood estimation, which uses only the likelihood function to obtain point estimates of parameters. Hypothesis testing with p-values, and confidence intervals derived from sampling distributions, are also nonposterior in the sense that they do not require a prior. Likelihood-based methods and tests, including likelihood ratio tests, can be used without forming a full posterior. Model comparison in nonposterior frameworks often relies on information criteria like AIC or BIC rather than Bayes factors.

In practice, nonposterior methods are favored when objective procedures are desired, when prior information is weak or controversial, or when computational simplicity is important. They provide probabilistic statements about data or parameters within a non-Bayesian paradigm, but do not yield a probabilistic assessment of parameters themselves in the Bayesian sense.

Limitations include potential underutilization of prior information and varying interpretations across paradigms. The term nonposterior is not widely standardized; readers should rely on context to distinguish between Bayesian posterior-based analyses and non-Bayesian or likelihood-based approaches. See also Bayesian inference, posterior distribution, prior, likelihood, and frequentist methods.