Dear Professor Kadane and dear all,
thank you, all comments were for me very interesting and stimulating!
From a mathematical point of view, it seems to me that the crucial
point, in the probabilistic field, is not the different role and
meaning of the words "objective" and "subjective" but between the
procedures used in the subjectivist approach (based on the notion of
coherent bet) and in the axiomatic approach (based on Kolmogorov
axioms). In both cases we assign 1/2 head and 1/2 cross in the toss
of a fair coin.
One of the differences could be that in the subjectivist approach such
assignment can be interpreted as that of a person betting on the given
event in a coherent bet.
Another important difference could be that a "coherent" person who
knows the result \omega of a random experiment assess probability 1
to any event containing \omega and 0 to any event which does not
contain \omega.
Best regards, Serena
Jay Kadane <kadane(a)andrew.cmu.edu> ha scritto:
Dear Serena, Thank you for this clarification of de Finetti's cultural
surroundings. I've heard it said that the data are the data, and
everything else we made up. (Sometimes it turns out that what one
thought were data , turn out not be the data, but that's another
issue). We may have better or worse reasons for the model, prior,
etc. used in an analysis, and to be persuasive, it is necessary to
explain the thought process behind the choices made. Sometimes the
word "objective" is used to try to intimidate people from
challenging the choices made. All the best, Jay KadaneOn 2/18/21 3:36 AM, Serena Doria wrote:
Dear all
the term "subjective" for probability was introduced by Bruno de Finetti, and to understand the motivation it is necessary to understand the
cultural environment in Italy in that period. In 1934 Luigi
Pirandello received the Nobel Prize in Literature and his vision of
life and knowledge affirmed that there was no 'single truth' but
reality was what the individual subject perceived. And this is also
evident from some of the best-known titles of his plays ( Cosi e'
se vi pare, Uno nessuno centomila). de Finetti grows in this cultural context but gives to the term
"subjective" a value more rigorous and "objective" through the
concept of coherent betting.Personally, I do not believe that the term subjective is to be
understood in a negative way because it highlights how the
knowledge an individual has about a phenomenon depends on the
information the subject has.For this reason, in the subjectivist approach to probability, the
concept of conditional probability and conditioning events are
fundamental to represent respectively partial knowledge and
different information that individuals have.Best regards,
Serena Doria
"Kreinovich, Vladik" <vladik(a)utep.edu> ha scritto:
Dear Friends,
We often talk and write about objective and subjective
probabilities, about objective and subjective measures of
uncertainty. However, at a recent conference on uncertainty, Yakov
Ben-Haim made an important observation -- based on his experience
of working on applications with colleagues from many different
areas.His experience is that in many application areas, the word
"subjective" has a negative connotation: it means unjustified
estimates based on gut feeling only, prone to bias and wild
variations.Such gut-feeling-based estimations sometimes happen, but mostly,
when we talk about "subjective", we mean judgmental estimates,
estimates which are not just coming out of gut feeling, but which
can be usually provided with some justification. For example, if
we estimate to what extent someone is young (one of Zadeh's
original examples) we can usually explain the degree we assign to
"youngness" of an individual by referring to features which are
present and which are typical young age - and features of this
individual which are more typical for mature-age folks.For example, subjective probability often means simply probability
that is not coming from the analysis of frequency, but from expert
estimates.Yakov's recommendations is to use words like "judgmental" (or
"expert-based") instead of "subjective" in such situations,
especially when working on applications - and applications are the
main goal of uncertainty studies in the first place.
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