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2 votes
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Birnbaum's Theorem: Strong belief in a model $\implies$ the likelihood function must be used as a data reduction device?

No, a strong belief in a model does not require that we maintain consistency with all these principles. To explain the reason, we need to describe some historical background from around 1962 when ...
Graham Bornholt's user avatar
2 votes

When are Bayes estimators injective as a function of sufficient statistics?

This trivially fails for non-minimal sufficient statistics: eg, $t$ is the whole sample and $t'$ is a different whole sample with the same value of the estimator. It will fail more interestingly when ...
Thomas Lumley's user avatar
2 votes
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Help developing intuition behind sufficient statistics (Casella & Berger)

One can visualize this explanation along a temporal axis The random variable $\mathbf X$ is generated by a distribution $\mathbb P_\theta(\mathbf x)$ with unknown parameter $\theta$ and its observed ...
Xi'an's user avatar
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1 vote

Help developing intuition behind sufficient statistics (Casella & Berger)

What is a sufficient statistic? What is its objective? To understand that, consider a (Polish) measurable space $(\mathscr X,\mathfrak A ) $ let $\mathfrak P$ be a collection of probability measures ...
User1865345's user avatar
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1 vote
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Formal definition of sufficient statistic

I am failing to see any problem. For a collection of probability measures $\mathfrak M:=\{P_\theta,\theta\in\Theta\},$ the statistic $T$ is sufficient if there exists a version of $\mathbf E_\theta [1\...
User1865345's user avatar
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