In article <[EMAIL PROTECTED]>,
Alan Mclean <[EMAIL PROTECTED]> wrote:
>Herman Rubin wrote:
>> In article <[EMAIL PROTECTED]>,
>> Alan McLean <[EMAIL PROTECTED]> wrote:
>> >I am sure there is a multitude of possible answers to this one.
>> >One way I would answer it is to say that probability is only applicable
>> >to *observable* events - that is, the occurrence of something which is
>> >in some way directly measurable. The existence of God is not observable
>> >in this sense, so probability is irrelevant to any discussion about the
>> >existence of God.
>> This would exclude the application of probability to such
>> things as nuclear physics. While we have to use
>> observations to draw inferences, the probabilities of
>> interest are not those about the observations, but about
>> the underlying process.
>Not really. The probability models that constitute nuclear physics provide
>probabilities for events which can be measured - and thus provide a test of the
>models. (I know this is oversimplified.)
The probability models do provide these, and this is how
they are verified and the parameters estimated. But it is
very often the case that these probabilities come from
probabilities of events which cannot be observed, using a
fairly complicated model. The basic theory does not deal
directly with probabilities of the observations, but leads
to this.
In fact, in many cases, the events are not even observed,
but there are enough to use the law of large numbers directly.
While modern theory deals with the behavior of gas particles,
these are translated into pressure and temperature, and the
probabilistic models are tested by this macroscopic data.
>> >Another, related way to express this is to say that belief in the
>> >existence of God is a *model* for the universe. Within that model
>> >probability questions can be asked, but one cannot talk meaningfully of
>> >the existence of the model. (The same comment applies, for example,
>> >about general relativity as a theory which models the universe.)
>> However, we use probability methods (actually statistical)
>> to draw inferences not just within a model, but between
>> models. One mistake, however, is to treat composite
>> hypotheses or models as simple, as is the case here.
>A statistical model is a probability model. I actually goofed a bit here - I
>meant to say "...but one cannot talk meaningfully of **the probability of** the
>existence of the model." And whether the model is 'composite' or 'simple' does
>not change this.
It makes a difference, and this is much misunderstood. If
one has simple hypotheses, one can proceed with only the
posterior probabilities of the hypotheses. On the other
hand, for composite hypotheses, it is necessary to use also
the distribution of the simple hypotheses within them. It
is very easy to give examples where ignoring this leads to
quite substantial errors.
The difference between probability and statistics is that
in probability one starts with the distribution, while in
statistics, the major problem is that the distribution is
not assumed.
>> >Repeatability is certainly (oops! - with high probability) not a
>> >prerequisite for probability to make sense.
>> This is very definitely the case.
>Good!
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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