Re: Meaning of Zero and All, Application to archaeology

From: Philip Deitiker (Donevenask_at_worlnet.att.net)
Date: 01/21/05 

Date: Fri, 21 Jan 2005 07:22:57 GMT

Eric Stevens <eric.stevens@sum.co.nz> says in
news:r711v0d9pqm1p8b1eb0g475ul0k8d3uub7@4ax.com:

> You can only say the evidence does not exist when you have
> evidence that it does not exist. Consider the Higgs boson. They
> have been searching for it for more than 30 years and so far,
> nothing. Yet they still keep looking. It's like a treasure hunt.
> You have to have faith that the treasure exists somewhere. That
> you eventually loose faith and give up does not mean that the
> treasure is not out there somewhere in the garden.

Let me repeat myself and make it clear. Without some trend out side
the survey area that something should be in the survey area, there
are an infinite number of things that could be in a survey area.
However if one takes a look at the bpd and then the survey there is
limited open area in the low end of the distribution. If you can have
an infinite number of things, they compete for probability in the low
frequency range, and therefore the probability is infinitely low.
People search in survey areas because some trend or information
suggests that something exists. Simply because a trend says it can
exist does not mean it does. There are cryptic probabilities all
around us, trends we don't see. But ever so frequently something that
is improbable to the reasoning of 1/infinity pops up.

> Yet, although the eventual find proved you correct, had you gone
> hunting for an example on a random basis you almost certainly
> would never have found it.

You've discovered my strategy. lol. There is so much improperly
analyzed data out there that anyone with a good understanding of
statistics and computers could be pumping out a manuscript every
month. If I ever have free time I might do a few write ups. We assume
that every bit of data published has been analyzed for all its
connotations, with the HLA data and X-linked data, very little
analysis has been done. Thus it is rather easy to predict beyond
published claims.

> Yet quite clearly the continuing
> absence of evidence (for your prediction) would not mean there
> was no evidence. All it would have meant was that you had not
> yet found it.

I expect there will be other finds like floriensis. What has happened
since the mtDNA stuff was published is there is great competition for
ideas and for proofs. As a result the old guard of PA is giving way
to new scientist who are surveying places well outside of the favored
places of the old guys. There is a statistical logic in play. If they
were biasing the opinions based on biased surveys, then if you want
to show their bias, you need to survey differently.

>> The other essential fact is that not finding something and
>>expecting something is occasionally also wrong because the trend
>>lines are not defined accurately enough by the data.
>>
>>There are occasion when new finds create shock waves, however
>>just as in the above, careful examination of old data reveals
>>that what is 'unexpected' is sometimes expected. The people who
>>were shocked about floriensis were looking for evidence of
>>something else, not of radiant hominids. If they had been
>>looking for radiant hominids based on the
>>molecular/morphological evidence they would not have been
>>shocked they would have been varifying and expectation.
>>
>>> Of course this opens up the argument of whether or not there
>>is any to
>>> find. You cannot strictly apply your binomial analysis until
>>you know
>>> something about the larger distribution. i.e. - does it exist?
>>
>>
>>Actually that is not true. Statistics is a process based on
>>assumptions but that assumptions are bounded by data. If the
>>sample size is 1 then the variation in distribution is not
>>known, however if the trend in population size to 1 is known,
>>known well enough to define the smallest range which contains
>>68.3 % of values per unit time and if that range overlies the
>>range of 1 then one can do binomial analysis.
>
> But now you are hypothesising that the data set is 1. In the
> real world you cannot know that.

The sample data is what you have relative to your survey. I am not
hypothesizing I am premising the argument, your data set is one, so
what does one mean?

>>possible to the y = 0 axis. An infinite number of zero measured
>>events would have the same probability.
>
> No, I'm not going to folow you there. I'm getting a headache.
> :-)

But that is the point, an infinite number of very low frequency
probabilities can exist and not be demonstrable in the survey.
However, very few of these will ever be found in the survey. And very
few of these occurred as to be found. 

-- 
Philip
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