# Tag Info

Accepted

### 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 ...

### 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 ...
• 41.8k
Accepted

### 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 ...
• 107k
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 ...
• 9,407
1 vote
Accepted

### 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\...
• 9,407

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