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From: hardy@como.stat.umn.edu (Michael Hardy)
Subject: Re: Fuzzy theory or probability theory?
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Date: Wed, 7 Dec 1994 02:06:05 GMT
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In article <3btr7d$r89@usenet.srv.cis.pitt.edu>,
		Bogdan Kosanovic <bogdan@neuronet.pitt.edu> wrote:



>>  Math departments have lots of probabilists
>> who know nothing about estimation, confidence intervals, hypothesis testing,
>> sufficiency, regression, design of experiments, sampling, the whole frequent-
>> ist versus Bayesian controversy, etc.  Every statistician knows about all of
>> these things; many probabilists do not.
>
>
>That's neither my problem (coming from an "engineering" department ;-) nor
>the point I was trying to make. (probability distribution DOES NOT equal
>statistical distribution, even when BOTH are epistemic)


	I wasn't writing about departments.  I'm saying that there already is
a conventional distinction between "statistics" and "probability" that you are
plainly unaware of, and it would behoove you to find out about before critic-
izing conventional practice.  The reason why probabilists don't know these
things is that they belong to statistics and not to probability theory.  You
are uninformed on your topic.


>> 	As a Bayesian I regard "probabilities" as epistemic and not intrinsic.
>> Just what you mean by "statistical distribution" is impossible to tell from
>> your vague statement.


>    2. statistical distribution (SD):
>
>       a density function that is obtained either empiricly _OR_ is
>       "epistemic". No matter how "obtained", SD describes how the quality is
>       distributed, e.g. how the height is distributed in some "space" or
>       "environment".
>
>       If SD is "given from God" than it is called epistemic.  Otherwise it
>       represents a factual truth based on experience.


	That is _not_ what epistemic means.  Epistemic means pertaining to
knowledge.  Epistemic probabilities _are_ based on experience.  It looks as if
you are construing the word to mean something like the opposite of what it
really means.


>    3. probability distribution (PD):
>
>       a density function that is used in _PREDICTION_ through performance
>       of a "random" experiment. ("Random" in a sense that we do not know
>       the result of experiment in advance. Otherwise we wouldn't use the word
>       "probability".)  Namely, using SD (either empirical or epistemic)
>       one can try to "predict" the value (or range of values) of a
>       "distributed quality" that is most likely to occur as a result of the
>       experiment. Hence, the SD becomes a PD ;-)


	Probabilities are not only used in prediction, even when we are
dealing with "random experiments".  We can speak of the probability that the
Big Bang happened, the conditional probability that a die is loaded given its
past observed behavior, or the probability that Aristotle was born on a Tues-
day.


>I hope the above "definitions" are clear enough and sufficient for the
>purpose of discussion in this group.


	They are not sufficient, since they are wrong.


>I wanted to say that, IMHO, there is no point in using word "probability"
>unless we want to infer and quantify (i.e. measure) how PROBABLE or LIKELY is
>something to happen. I used the word _random_ in that sense only.


	We can also speak of how probable it is that something _has_ happened
or how probable it is that a proposition is true.


>[digression: It should be noted that the "knowledge" about an outcome
>    in real-world experiments always has (at least) two components:
>
>      1. "stochastic" or "random" or "probabilistic" - relates to the
>         uncertainty as to the _future_ "state of the system"
>         (this it the way I used word "random")


	Look, we can speak of P(A|B) or of P(B|A), when A is an event that
happened in 1860 if it happened at all and B is an event that will happend in
2060, if indeed it will happen.


>It should be noted that "statistics" is _static_ since all data IS available.
>(i.e. "statistical distribution" IS available)


	Statisticians never work with _all_ available data.  If _all_ data
were available, there would be no need for statistical analysis.


>I was reffering to whether or not the SD is available. In _that_ sense I
>consider "statistics" as being _static_.


	Statisticians _estimate_ what you call "SD"s based on incomplete data.
They never actually know what you call the SD.  You are very badly uninformed
about what statisticians do.


>"All data" OBVIOUSLY stands for the SD in above quote. If I wanted to refer
>to "all facts" I would use a different choice of words instead.  Since I knew
>that some people,  may confuse "all data" with "all facts", I intentionally
>added the i.e.-part to avoid such problems. (I'm sorry to learn that it
>didn't help)


	It didn't help not because you were unclear but because you were
wrong.  Statisticians do not have the "SD" available --- probabilists do.


>Moreover, whenever a "statistician" starts to "predict" he/she becomes a
>"probabilist".


	Not so.  Standard frequentist prediction intervals are _not_
probability intervals.  Frequentist statisticians refuse to assign make assert-
ions like "there is a 90% probability that the outcome of this experiment will
be between 20 and 25" but they still assign "90%" prediction intervals that
neither they nor anyone else considers probability intervals.


	Mike Hardy

Michael Hardy			"Free will is located in or near
School of Statistics		 the anterior cingulate sulcus."
University of Minnesota
hardy@stat.umn.edu				- Francis Crick
