In article <66b61316.0108121325.77eb8bdb@posting.google.com>, S. F. Thomas <sfrthomas@yahoo.com> wrote:> hrubin@odds.stat.purdue.edu (Herman Rubin) wrote in message news:<9l4kv0$2evu@odds.stat.purdue.edu>... >> In article <66b61316.0108091708.7d6b9958@posting.google.com>, >> S. F. Thomas <sfrthomas@yahoo.com> wrote: >>> robert@localhost.localdomain (Robert Dodier) wrote in message >>> news:<9kt895$rs$1@localhost.localdomain>... >>>> In the interest of brevity, I've indulged in wanton snippage, >>>> but I hope what's left yields something comprehensible.
>>>> S. F. Thomas <sfrthomas@yahoo.com> wrote:
>>>>> Robert Dodier wrote:
..............>>> Goodness, no. What I do argue however is that the semantics of >>> likelihood do not just fall neatly out from the semantics of >>> probability. Probability provides some of the underpinning, but not >>> all. Otherwise Fisher would not have been led up a blind alley by >>> asserting that the "likelihood of a or b is like the income of Peter >>> or Paul, we don't know what it is until we know which is meant."
>> I am by no means convinced that Fisher understood this, but >> I can see no way that the likelihood of "a or b" makes any >> sense at all.
> That has precisely been the problem for all the generations of > statisticians since Fisher. I presume you to refer to the original > probability model from which likelihood derives, f(x;w) where x ranges > over sample space, and w ranges over parameter space and f is the > density function for the random variable in question.
There is no problem with this, as long as it is recognized that this is a mathematical function, and NOT a probability. The rest of the argument (deleted) assumes that it is a probability, or at least close to it; Fisher even fell somewhat into that trap. But few mathematical statisticians did so, and the use of the likelihood function goes back at least to the 18th century. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558