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What does theta subscript imply in e.g. this case: $$ P_\theta(T(x)=t) = 0 $$

Silverfish
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Alex
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    It means that the probability is evaluated with $\theta$ as the parameter of the distribution. – JohnK Apr 13 '16 at 23:27
  • I'm convinced this is a duplicate of an earlier question but I can't seem to find it. – Silverfish Apr 13 '16 at 23:47
  • It could mean several things. For instance, one alternate explanation is that under the probability distribution parameterized by $\theta$, $P(T(x)=t) = 0$. By parameterized I just mean the parameters of this distribution come from the vector $\theta$ – information_interchange Oct 23 '19 at 21:34

1 Answers1

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It means under the distribution $\theta$, the probability of that statistic $T(x)$ being equal to $t$ is zero. Another way you can write it is:

$Pr(T(x) = t | \Theta = \theta) = 0$.

user1357015
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    I would rather phrase it as the distribution indexed by $\theta$, in the sense of facing a collection of distributions indexed or parameterised by a parameter $\theta$. And the conditioning representation only applies in a Bayesian framework so I would also avoid it. – Xi'an Apr 14 '16 at 08:25