I'm enjoying learning about Fisher's distinction between probability and
likelihood, but it seems to me that since language is alive, "modern"
definitions of likelihood and probability should also be discussed.
In economics, for example, in 1921, Frank Knight came up with a distinction
between "risk" and "uncertainty." Risk occurs when an outcome is unknown,
but the probabilty distribution is exactly known, e.g., (said Knight) as is
the case of insurance. With uncertainity, neither the outcome nor the
probabilities of events are known (here he gave starting a new business as
an example). (Hmmm, maybe it goes Fisher : probability : risk :: Knight :
likelihood : uncertainty?)
Now Knight was a big name and a great economist, but almost no economist
uses the words risk and uncertainty in the Knightian way. These words are
essentially perfect synonyms today. In fact, the terms "Knightian risk"
and "Knightian uncertainty" pop up when historians of economic thought chat
about risk and uncertainty.
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?
Yours in Fisherian likelihood and Knightian uncertainty,
Bert
***********************
Humberto Barreto
Department of Economics
Wabash College
Crawfordsville, IN 47933
Phone: 765-361-6315
FAX: 765-361-6277
Email: [EMAIL PROTECTED]
WWW: http://www.wabash.edu/depart/economic/barretoh/barretoh.html
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