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[Phys-L] pseudo-pundits +- systematic error



Hi --

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 possible.

Action Items:
*) 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.