Bayesian Calculations for Frequentist Higher-Order Expansions: An Expository Treatment of the Shrinkage Argument

Xander Spruce

doi:10.5281/zenodo.20579636

June 6, 2026Open Access

Bayesian Calculations for Frequentist Higher-Order Expansions: An Expository Treatment of the Shrinkage Argument

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Key Points

The aim is to provide a clear treatment of the shrinkage argument in Bayesian-frequentist higher-order asymptotics.
Explored the scalar independent and identically distributed (i.i.d.) case.
Defined explicit parameter regions and good events.
Reconstructed posterior Laplace remainders and employed the Bayes-Fubini shrinkage identity.
Clarified the relationship between Bayesian and frequentist approaches in higher-order asymptotics.
Highlighted the conditions under which the shrinkage argument holds.
Demonstrated the implications of the Bayes-Fubini identity in the context of parameter estimation.

Implication

Expository draft reconstructs shrinkage argument in Bayesian-frequentist asymptotics, highlighting implications.

Abstract

An expository draft on the shrinkage argument in Bayesian–frequentist higher-order asymptotics. The manuscript reconstructs the scalar i.i.d. case with explicit parameter regions, good events, posterior Laplace remainders, and the Bayes–Fubini shrinkage identity.

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Cite This Study

Xander Spruce (2026) studied this question.

synapsesocial.com/papers/6a27add2a963992e16267eaf https://doi.org/10.5281/zenodo.20579636

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Bayesian Calculations for Frequentist Higher-Order Expansions: An Expository Treatment of the Shrinkage Argument

Key Points

Implication

Abstract

Discussion

Cite This Study

Bayesian Calculations for Frequentist Higher-Order Expansions: An Expository Treatment of the Shrinkage Argument

Key Points

Implication

Abstract

Discussion

Cite This Study

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