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Re: [Phys-L] conditional probability and statistical inference



Somehow this fits into some kind of statistics/probability discussion. (perhaps)

It is thought (by some) that currently the earth's population is greater than 5% of the total number of 'humans' that have ever been born.

Therefor fewer than .05 of humans have ever died.

So inevitability of death is not significant to the .05 level of significance.

??


On Nov 20, 2012, at 4:53 PM, John Denker wrote:

Hi --

I am continuing to write up my notes on probability and put them on
the web. I recent put up two new sections:

Joint, Marginal, and Conditional Probabilities:
http://www.av8n.com/physics/probability-intro.htm#sec-joint-marginal-conditional

Statistical Inference:
http://www.av8n.com/physics/probability-intro.htm#sec-inference

This thing is now 37 pages long, including 58 figures. The spreadsheets used to
compute many of the figures are readily available.

One conclusion of the Statistical Inference section is this:

Maximum-likelihood methods are very widely used ... and very wildly abused.
For example, practically all “least squares” regression and curve-fitting
routines are maximum likelihood methods, and people are all-too-often
taught to use them in situations where they are not appropriate. In some
cases you can get away with using maximum likelihood methods, especially
if the prior probability is reasonably flat and/or you have huge amounts
of data ... but in other cases maximum likelihood can lead to seriously
wrong inferences.

Suppose there is some rare disease that is carried by one person out of
a million. Carriers are asymptomatic at first, but before long develop
sudden, very serious problems. Now suppose a test for this disease has
been developed, and the test is 99% reliable. Specifically, the test has
a 1% chance of indicating that the disease is present when it is not. If
you take the test and it comes back positive, that emphatically does not
mean that you have a 99% chance of carrying the disease. That’s because
when we take the prior probability into account, your chance of having
the disease only went up from 1 chance in a million to 100 chances in a
million. Even though the test is in some sense 99% accurate, it is still
overwhelmingly likely that you do not carry the disease.

===

That's just a teaser, not an explanation. For the actual explanations
and diagrams, see
http://www.av8n.com/physics/probability-intro.htm#sec-inference
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