Coherent frequentism

Abstract

By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior distribution. The closure of the set of expected losses corresponding to the dual frequentist posteriors constrains decisions without arbitrarily forcing optimization under all circumstances. This decision theory reduces to those that maximize expected utility when the pair of frequentist posteriors is induced by an exact or approximate confidence set estimator or when an automatic reduction rule is applied to the pair. In such cases, the resulting frequentist posterior is coherent in the sense that, as a probability distribution of the parameter of interest, it satisfies the axioms of the decision-theoretic and logic-theoretic systems typically cited in support of the Bayesian posterior. Unlike the p-value, the confidence level of an interval hypothesis derived from such a measure is suitable as an estimator of the indicator of hypothesis truth since it converges in sample-space probability to 1 if the hypothesis is true or to 0 otherwise under general conditions.

The confidence-measure theory of inference and decision is explicitly extended to vector parameters of interest. The derivation of upper and lower confidence levels from valid and nonconservative set estimators is formalized

References in corpus (6)

• Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory
• Combining information from independent sources through confidence distributions
• Confidence distribution (CD) -- distribution estimator of a parameter
• Statistical inference optimized with respect to the observed sample for single or multiple comparisons
• Estimating the null distribution for conditional inference and genome-scale screening
• A frequentist framework of inductive reasoning

Cited by in corpus (5)

• Resolving conflicts between statistical methods by probability combination: Application to empirical Bayes analyses of genomic data
• Large-scale interval and point estimates from an empirical Bayes extension of confidence posteriors
• Controlling the degree of caution in statistical inference with the Bayesian and frequentist approaches as opposite extremes
• A frequentist framework of inductive reasoning
• Blending Bayesian and frequentist methods according to the precision of prior information with an application to hypothesis testing