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16 February 2025 |
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The E-Posterior | | Peter Grünwald
; | | Date: |
3 Jan 2023 | | Abstract: | We develop a representation of a decision maker’s uncertainty based on
e-variables. Like the Bayesian posterior, this *e-posterior* allows for making
predictions against arbitrary loss functions that may not be specified ex ante.
Unlike the Bayesian posterior, it provides risk bounds that have frequentist
validity irrespective of prior adequacy: if the e-collection (which plays a
role analogous to the Bayesian prior) is chosen badly, the bounds get loose
rather than wrong, making *e-posterior minimax* decision rules safer than
Bayesian ones. The resulting *quasi-conditional paradigm* is illustrated by
re-interpreting a previous influential partial Bayes-frequentist unification,
*Kiefer-Berger-Brown-Wolpert conditional frequentist tests*, in terms of
e-posteriors. | | Source: | arXiv, 2301.01335 | | Services: | Forum | Review | PDF | Favorites | |
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