Interesting question. If one calibrates 8 independent proxy series to their mean, S-matrix ( see the next thread) will be singular, but not zero matrix. The calibration algorithm sees correlated noise between proxies, even though there was no noise at all. Might cause some trouble.

But if you have the mean of the temperatures available, you also have the individual local temperature records. And calibration locally would make much more sense, as one looses information in the averaging process. If it is assumed that proxies directly respond to global average (*) , then we can use R safely.

(*) sun sensor, CO2 sensor, PC1, for example

w.

Steve: More to come.

The equations don’t display in your linked article. Both in my browser and when I download it.

1. Before calibration can even begin, the physical causality of tree
ring width/maximum densities and ambient temperature (never mind the
magic of detecting the global temperature field from Colorado) must
be established, not simply assumed to be true. There was a recent
report which shows that tree leaves stay at nearly a constant
temperature regardless of the ambient temperature, trashing one of
the most cherished assumptions of dendroclimatologists.

Sure, one should not attempt calibration when one is not confident that ( Brown82 ) . And our ideas on causation must come from outside statistics (any stat book).

2. I missed this in the post above, but how are confidence limits dealt with in datasets with high autocorrelation?

Brown assumes that errors are uncorrelated over time, Brown 87 Eq 2, i is annual time index in tree-ring case. Mann has some tools for redness estimation and correction ( http://www.climateaudit.org/?p=1810 )

Steve: I made the following request above:

Please, I don’t want people piling on with comments about cherrypicking or causality. It’s not like I’m unaware of these issues. Those are valid lines of argument, but please bite your tongues.

I’m going to be pretty strict in what remains in this thread. If you want to post something other than technical or if you want to debate tree rings, then assume that the comment is going to be transient in the record or going to Unthreaded. I’ve already done this with some posts which had transient interest; I’m just going to try to keep a fairly coherent comment thread, that’s all.

I don’t think that should be an absolute rule. It’s probably a useful rule of thumb when small hand-collected datasets meet the data mining capability of modern CPUs. But think what happens when our modern CPUs meet enormous data sets from modern automated instruments. If someone discovers a very strong correlation in terabytes of genomic data or astronomical observations, it’s fairly likely to be something real even if we don’t yet have the foggiest idea why.

(It should be possible to quantify the risk of overfitting, instead of just making a yes/no binary rule of thumb. I’m vaguely aware of two ways to do so. However, I’ve never used either. Thus, to reduce my risk of saying something unusually dumb, I’ll leave constructive suggestions to others.)

The approach taken here differs from the approach taken in UC’s post. UC uses the methods described in Brown 1982 for CIs, while I’ve used the later method in Brown and Sundberg 1987, which looks like an improvement over the earlier method. I’m pretty sure that we can tie things back and forth and we’re definitely making progress!

And yes, this is the sort of thing that I’m inclined to work up for publication in a technical publication. It’s something that I’ve been working at on and off for a long time and only recently got a secure foothold on Brown and Sundberg. The approach that this leads to is clearly fresh and distinctive, and will lead to new perspectives without being argumentative.