• Corpus ID: 251594514

E-Statistics, Group Invariance and Anytime Valid Testing

  title={E-Statistics, Group Invariance and Anytime Valid Testing},
  author={Muriel Felipe P'erez-Ortiz and Tyron Lardy and Rianne de Heide and Peter D. Grunwald},
We study worst-case growth-rate optimal (GROW) e -statistics for hypothesis testing between two group models. If the underlying group G acts freely on the observation space, there exists a maximally invariant statistic of the data. We show that among all e -statistics, invariant or not, the likelihood ratio of the maximally invariant is GROW and that an anytime valid test can be based on this likelihood ratio. By virtue of a representation theorem of Wijsman, it is equivalent to a Bayes factor… 

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The e-posterior

  • P. Grünwald
  • Computer Science
    Philosophical Transactions of the Royal Society A
  • 2023
A representation of a decision maker’s uncertainty based on e-variables that provides risk bounds that have frequentist validity irrespective of prior adequacy, making e-posterior minimax decision rules safer than Bayesian ones.

The E-Posterior

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