Yes, indeed (sorry for the delay, I am not connected most of the time…)

]]>Nevermind.

I thought that superscripts 1 and 2 in (y¹,y²) were used to discriminate any results of either E¹ or E².

But reading it again I realised that (y¹,y²) refers only to the pair in which the likelihoods are proportional.

]]>I don’t understand the logic of this example.

You say:

“Then it is possible to build a sufficient statistic T that is equal to the data (j,x), except when j=2 and x=y², in which case T(j,x)=(1,y¹).”

How is that possible?

If j=2 and x=y² that means that you did not perform experiment 1, right?

So, if you did not perform experiment 1, how can you know the value of (1,y¹)?

Maybe I’m missing something here.

]]>I need to correct a serious misimpression, unless it is just a very different use of language. Roberts wrote:

xi’an Says:

October 16, 2011 at 5:38 pm

Just an addendum on “the distribution of the inference”: as read today in Error and Inference (page 310), Deborah Mayo uses the sentence “This differs from the sampling distributions of both InfrE’ (y‘*) and InfrE” (y”*). Which seems to indicate she also considers inference has a distribution.

The sampling distribution is the distribution of the (test) statistic. A frequentist has no inference without consideration of the sampling distribution of a (relevant) statistic. That is because without it there are no error probabilities. The sampling distributions I am referring to are the ones associated with the inferences that would be the outputs of these two observed outcomes from the two distinct experiments, E’ and E”, respectively.

]]>I need to correct a serious misimpression, unless it is just a very different use of language. Roberts wrote:

xi’an Says:

October 16, 2011 at 5:38 pm

Just an addendum on “the distribution of the inference”: as read today in Error and Inference (page 310), Deborah Mayo uses the sentence “This differs from the sampling distributions of both InfrE’ (y‘*) and InfrE” (y”*). Which seems to indicate she also considers inference has a distribution.

The sampling distribution is the distribution of the (test) statistic. A frequentist has no inference without consideration of the sampling distribution of a (relevant) statistic. That is because without it there are no error probabilities. The sampling distributions I am referring to are the ones associated with the inferences that would be the outputs of these two observed outcomes from the two distinct experiments, E’ and E”, respectively.

]]>