Bayesian Statistics

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9 domain-specific abstractions whose origin domain is Bayesian Statistics.

• Bayesian linear regression — A linear conditional model that combines a likelihood for outcomes with prior distributions over coefficients and noise parameters to obtain posterior inference and prediction.
• Bayesian model reduction — A method deriving evidence and posterior parameters for models with altered priors from a previously fitted full Bayesian model.
• Hierarchical Dirichlet process — A Bayesian nonparametric prior for grouped data in which group-specific discrete distributions share a global random set of mixture components while retaining different group weights.
• Jeffreys prior — A Bayesian prior measure proportional to the square root of the Fisher-information determinant, constructed to remain invariant under smooth reparameterization.
• Marginal likelihood — The probability density of observed data under a Bayesian model after integrating the likelihood over the prior distribution of its parameters.
• Normal-inverse-gamma distribution — A four-parameter joint distribution in which a variance has an inverse-gamma law and a mean conditional on that variance is normal, conjugate for a normal model with unknown mean and variance.
• Posterior probability — The probability distribution for an uncertain hypothesis or parameter after combining a prior distribution with observed-data likelihood through Bayes' rule.
• Probability of direction — Summarize a posterior effect's sign certainty as the larger of Pr(θ>0) and Pr(θ<0), ranging from one-half to one for continuous posteriors while deliberately not measuring magnitude or practical importance.
• Widely applicable information criterion — A Bayesian predictive-fit criterion combining log pointwise posterior predictive density with a variance-based effective-complexity penalty.