Comments on: More on Bürger et al 2006

By: Multivariate Calibration « Climate Audit

Multivariate Calibration « Climate Audit — Fri, 05 Apr 2013 18:14:20 +0000

[...] with CCE. In the absence of noise, ICE and CCE yield (naturally) the same result. Update: see Gerd’s link and, and also note that ICE is a matrix weighted average between CCE and zero-matrix (Brown82, Eq [...]

By: UC

UC — Fri, 05 Oct 2007 13:02:33 +0000

Gerd, re 8 that's interesting result. So, before Mann rescales RPCs they all have larger variance than the target PCs (calibration period). Variance matching makes the variances equal. And as Mann does not reconstruct all PCs, and RPCs are variance-matched to the target PCs, effectively the variance of reconstruction is always less than variance of target temperature. That's why vS04 thought it is direct regression. And that's why Mann claims that

The CPS approach thus differs from a multivariate regression approach wherein the reconstruction is guaranteed to have less variance than the target series over the calibration interval.

even though INVR itself actually amplifies.

By: Steve McIntyre

Steve McIntyre — Fri, 23 Jun 2006 15:57:44 +0000

Gerd, I don’t mean to be ignoring this, but you will understand that I’ve been otherwise preoccupied with the NAS report. I appreciate the comments here and will take a look some time next week.

By: TCO

TCO — Fri, 23 Jun 2006 15:28:48 +0000

SG H-D Prof:

RE 15: Ok, I think I get it. Thanks

a. Why the PC1 of the instrumental temps? Why not, the value itself?
b. Why looking for a correlation with global vice local temperature? Seems non-physical to me and likely to lead to data mining/overmodeling. If there is a plausible teleconnection, then we should model to the teleconnected variable, no? But just fishing for local measures of a global trend? Seems fishy. Like throwing 20 stats into a bag and picking the one that comes up at 95% confidence level for significance! And at a minimum, hurts the claim that we have built up a global picture from multiple local sources (since they’re not really local if they are globally trained/selected/weighted).
c. What are the units for temp and proxy? Standardized and if so, how? This will influence the slope, no?
d. Question 12-2 remains. Can you explain?
e. I agree that a flat sloped line when replotted as x-y versus y-x is now steep. Why is that interesting? We all know that, no? Is there some further thing with variance or mean or something?

Please excuse my humble questions. I have no mathematical training in stats or linear algebra.

By: John A

John A — Fri, 23 Jun 2006 11:59:50 +0000

I would recommend that people use the [ tex][ /tex] tags, so that Gerd’s last comment should read:

where 1 ' title='\frac{1}{G}>1 ' class='latex' />

By: Gerd

Gerd — Fri, 23 Jun 2006 07:09:27 +0000

Interestingly, the “smaller than” and the second equation didn’t go through – although my preview showed them (maybe conflicting with the tag-syntax). So let me try again: The above equation gives

y(t) = 1/G x(t) with 1/G larger than 1.

By: Gerd

Gerd — Fri, 23 Jun 2006 06:59:58 +0000

t is time, x(t) is a proxy, y(t) is the NHT PC1. Then x is regressed on y,

x(t) = G*y(t) with G 1.

By: TCO

TCO — Thu, 22 Jun 2006 13:50:55 +0000

JeanS:
A. Are you still in the one dimensional land where Gerd was speaking to me?
B. If you say that x is “proxies”, what does that mean? Number of them in the reconstruction?
C. I can’t follow that post, Jean.

By: Jean S

Jean S — Thu, 22 Jun 2006 13:43:56 +0000

re #12: TCO, x is not "years", it's "proxies". Both "proxies" and "temperature PCs" are noisy. Read carefully this post, which IMHO is still the most readable account of MBH98 Calibration-Estimation procedure.

By: TCO

TCO — Thu, 22 Jun 2006 13:02:19 +0000

Gerd (if this is too tedious, don’t bother…I’m not matastute in this field):

1. How are both the x and y noisy? If x is years and y is ring width, I would think that y would be noisy, but x not noisy.

2. If both are equally noisy, I would not expect any particular tendancy for flat or steep best fit lines.

3. If there is a given slope (y=kx), then adding y axis noise in general (imagine doing it multiple times), will have an overall effect of what? A tendancy to make the k value vary? Effect of (on average) of driving k down (like averaging a line with zero slope)? Is the noise, noise from the trend line or noise from “zero”? In other words, what is the average slope of the noise? Are you just averaging in stuff that has a slope of zero on average? And how are the mean of the noise and the mean of the trend line related?

4. I’m not clear what “inverting” means. If we have y=kx, does inverting mean y=(1/k)x? Or y= 1/(kx)? or just somehow “plotting” x=(1/k)y?