Dear Serena,
���������� I think that our assignment of probabilities to the outcome of
flipping a fair coin stem from the definition of "fair", and hence are
neither subjective or frequentistic.
�������������������������������������������������� Jay


On 2/19/21 12:35 PM, Serena Doria wrote:
>
> 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@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 Kadane
>>
>>
>>
>> On 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@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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