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Credible Interval
An interval within which an unknown parameter lies with a specified posterior probability, analogous to the frequentist confidence interval but with a direct probabilistic interpretation.
Bayesian Null Hypothesis
A specific model often defined by a point value for a parameter (e.g., null effect), against which an alternative hypothesis is compared via a Bayes factor.
Spike-and-Slab Model
A variable selection approach using a mixture prior distribution, with a point mass at zero (the spike) and a continuous distribution (the slab) for non-zero coefficients.
Sequential Bayesian Hypothesis Test
A method where data is analyzed as it is collected, allowing for an early decision based on the evolution of the Bayes factor or the posterior probability.
Likelihood Principle
The principle that all the information about the parameters contained in the data is provided by the likelihood function, fundamental to Bayesian inference.
Lindley's Paradox
A phenomenon where a frequentist hypothesis test may reject the null hypothesis while a Bayesian test, based on the Bayes factor, strongly supports this same hypothesis, often due to large sample sizes.
Jeffreys' Scale
A heuristic interpretative scale for the values of the Bayes factor, providing qualitative thresholds (weak, moderate, strong) to assess the weight of evidence in favor of a hypothesis.
Jeffreys Prior
A non-informative prior distribution, designed to be invariant under reparameterization and proportional to the square root of the determinant of the Fisher information.
ABC Method (Approximate Bayesian Computation)
A Bayesian inference technique used when the likelihood is intractable, approximating the likelihood by simulating data from candidate parameters and comparing them to the observed data.
Predictive Information Loss (Predictive Information Criterion)
A Bayesian model selection criterion that evaluates a model's predictive ability by penalizing complexity through the Kullback-Leibler divergence between the predictive distribution and the true data distribution.
Reference Prior
A prior distribution designed to have minimal impact on posterior inference, often used in hypothesis testing to ensure the Bayes factor is not unduly influenced by the choice of prior.