I'll suppose that you don't really want to have a
discussion about probability, but are really
asking about 'likelihood.'
The definition of likelihood today, except that it
may be more abstract than Fisher indented, is the
same as that given by Fisher. In particular the
likelihood of a hypothesis H, given data D, L(H|D)
is proportional to the probability of D given H,
P(D|H), with the constant of proportionality being
arbitrary.
Fisher had in mind a few simple distributions
often involving only a single parameter, and for
these, things work well. It can lead to unwieldy
data summarization's when there are multiple
parameters, but it requires special pleading to
argue in favor of a hypothesis which does not
maximize the likelihood.
Humberto Barreto wrote:
>
>
>
> So, my question to the stat gurus listening in is: how are probability and
> likelihood defined *today*?
>
> If the definitions have changed, then another question would be: how did we
> get from point A, Fisher's definitions, to point B, today's definitions?
> Maybe Fisher's defintions were never accepted? Not earth shattering
> questions, but kinda interesting, don't you think?
>
==================
--
Bob Wheeler --- (Reply to: [EMAIL PROTECTED])
ECHIP, Inc.
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