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From: Phys-l [mailto:firstname.lastname@example.org] On Behalf Of John Denker
Sent: Tuesday, November 06, 2012 1:04 PM
Subject: [Phys-L] pseudo-pundits +- systematic error
Lately we have had some discussions that hinge on the notion that a
distribution is not a number, and a number is not a distribution.
In grade-school people learn how to do arithmetic numbers. Later they learn
how to do arithmetic with vectors, such as adding them tip-to-tail. At some
point they ought to learn how to do arithmetic with probability distributions
... which are more like vectors than numbers. You can visualize a vector as
either a little arrow or as contour lines on a topographic map. You can
visualize a probability distribution as a pie chart or as a histogram. There is no
such thing as a random number. If you have a number drawn from a random
distribution, the randomness is in the distribution, not in the number.
Here is a timely real-world application:
This morning I did something I don't normally do: I spent a few minutes
watching the news on TV. It was a powerful reminder as to why I don't
normally do that.
-- One so-called pundit said that if Obama carried Ohio, that would
be the end of the story.
-- Another so-called pundit said that if Obama carried Florida, that
would be the end of the story.
What a load of nonsense! These guys have obviously not the slightest idea
what probability is or how it works.
The word "pundit" come from Sanskrit roots and is supposed to mean a
learned person. I wonder, what is the point of calling yourself a pundit if you
don't actually know what you're talking about.
I don't want to get into partisan politics in this forum, but logic and statistics
seem like fair game. Non-partisan facts include:
*) Elections have consequences
*) This election is a lot closer than the so-called pundits seem to think.
*) A lot more states are in play than the so-called pundits seem to think.
Some of the guys on TV were clever enough to add the disclaimer "unless
the opinion polls are wrong". The problem is, they weren't clever enough to
appreciate that the polls don't have to be off by very much in order to
significantly affect the result.
The so-called "margin of error" quoted in most polls is only the shot noise,
i.e. the sampling error introduced by having only a finite-sized sample. It
does not include any allowance for possible systematic error.
My models indicate that even quite small systematic errors can have a
dramatic effect on the outcome.
Also: It may be that this-or-that so-called pundit "cannot imagine" a path to
victory that does not run through the battleground states.
However, that does not mean that no such path exists. My models indicate
that an astronomical number of such paths exist, so that even though the
probability per path is small, the sum over paths is significant.
My models are not rocket science. Just add up a whole bunch of Gaussians.
I've been doing this for years. I've been doing it for longer than Nate Silver
has. Under plausible assumptions I get the same numbers he does, but the
results are highly sensitive to assumptions about systematic error.
Let's be clear:
I'm not saying I know what is going to happen. Au contraire, I'm saying
nobody knows what is going to happen. A normal-looking result is entirely
possible ... but all sorts of highly abnormal-looking results are also entirely
*) Go vote.
*) Even if you live in a non-battleground state, go vote. There are
lots of scenarios where your vote could matter quite a lot.
*) Cajole your friends to go vote.
I'll not use this forum to tell anybody /how/ to vote. I reckon you can figure
that out for yourself. I do however have opinions on the matter.
If anybody wants to hear my recommendations, you can contact me off-list.
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