## Thursday, March 16, 2017

### What's Your Jacoby Number? - 6, 35, 67, 72, 75, 180

Jeff Jacoby has exposed himself to the Skeptical Science in an article that appeared recently in the Boston Globe.  While it's not even a winner in Climate Change Denial Bingo (Trademark Tim Lambert) Eli prefers to simply call out the numbers at Skeptical Science.

Mostly the article simply repeats old nonsense, but there is one new deceptive argument typical of those like Jacoby who know nothing and whose stock in trade is bluster about everything including climate change.  For the sake of argument Eli would like to dissect that

But for the sake of argument, say there are merely 15 variables involved in predicting global climate change, and assume that climatologists have mastered each one to a near-perfect accuracy of 95 percent. What are the odds that a climate model built on a system that simple would be reliable? Less than 50/50. (Multiplying .95 by itself 15 times yields 46.3 percent.) Is it any surprise that climate-change predictions in the real world — where the complexities are exponentially greater and the exactitude of knowledge much less — have such a poor track record?
Eli will call this the Jacoby birthday argument for it's vague relation to the old proposition of how many people do you have to have in a room to get good odds that they have the same birthday.  As everybunny knows you figure this by taking the probability that two people don't have the same birthday, eg. that the second persons birthday is one of the other 364 days and then continuing so the probability is 364/365 x 363/365 x 362/365 etc. and you find that with 23 people it's even odds that two have the same happy day.

When Ms. Not Mr. Bluster says that she knows the value of a parameter to an accuracy of 95%, what she means is that she has evidence that the actual value lies within some range of her estimate of the most likely value.  The most likely value and the range can be set by theory, by observation, by observation, by experience, aka expertise or some combination of the three.

Since at least for climate models the uncertainty in the parameters is two sided, e.g. each parameter estimate is as likely to be too small and too large.  So if you have 15 parameters that you multiply together odds are some will be a little too large and some a little too small, and in the end the result will average out to be just right (or close).

Best sets of parameters can also be inferred from comparison with observations. Climate modelers can create an ensemble of results by systematically or randomly varying the parameters of their model, observing the variation in their results and comparing with observation.

There is even a way out of the one Earth problem, ie that there is only one set of observations which is discussed in Numerical Recipes pp689  Confidence Limits on Estimated Model Parameters describing how uncertainties in parameters can be deduced as well as the best fit parameters.

Matt M said...

John Garland said...
This comment has been removed by the author.
John Garland said...

His calculation has nothing whatever to do with "reliability". I don't know where he learned to think it was.

The product of two or more random variables is a bit complex. But it can be modeled easily in R. This script runs nearly instantaneously even on an i3.

require(matrixStats)
require(psych)
set.seed <- 123456
Exp <- rowProds(matrix(rnorm(1500000,mean=1,sd=.1),nrow=100000,ncol=15,byrow = TRUE))
hist(Exp)
describe(Exp)

If we take 15 variables known to be 1 +/-.1sd and multiply them together, the resulting variable is known to 1 +/-.4sd

neverendingaudit said...

I prefer my Matrix:

https://contrarianmatrix.wordpress.com

Tony Lurker said...