## Category Archives: Statistics

### Review Comments on the "IPCC Test"

In a recent post, I’ve indicated that IPCC authors seems to have invented a “test” for long-term persistence that is nowhere attested in any statistical literature and, if I’ve interpreted what they’ve done correctly, appears to be a useless test. Jean S and I have made a few references to the Review Comments on the […]

### The New “IPCC Test” for Long-Term Persistence

In browsing AR4 chapter 3, I encountered something that seems very strange in Table 3.2 which reports trends and trend significance for a variety of prominent temperature series (HAdCRU, HadSST, CRUTem). The caption states: The Durbin Watson D-statistic (not shown) for the residuals, after allowing for first-order serial correlation, never indicates significant positive serial correlation. […]

### Mannomatic Smoothing and Pinned End-points

We’ve had a couple of discussions of dealing with end-points for smoothing. Here’s a little note about smoothing algorithms, which I think is pretty funny. It’s hard to imagine a note about smoothing algorithms being funny, but see what you think.

### Mann's New Divergence "Theory": A Smoothing Artifact

Over at realclimate, Mann has advocated a new “explanation” of the Divergence Problem raised by one of their readers in connection with IPCC AR4 Figure 6.10. Mann says that there is no Divergence Problem; he blames the reader for failing understand boundary constraints in smoothed series. Raising the Divergence Problem at realclimate was so blasphemous […]

### Inversions from Partial Correlation Coefficients

Willis raised an interesting point about trying to invert series based on partial correlation coefficients with monthly temperatures. His post, together with UC’s response are collected here.

### More on "Naturally Orthogonal"

I realize that not all CA readers are interested in multivariate methods and that dendroclimatologists want to “forget the math”, but I find it interesting to try to relate dendro and paleoclimate recipes to known statistical methodologies that you can read about in texts. I commented the other day on the form of Principal Components […]

### Nature's Style: "Naturally Orthogonal"?

Wilson and Luckman 2003 observe: The first PCs from the RW and MXD PCA are naturally orthogonal (r = —0.006) over the 1900—1991 period suggesting the in’?fluence of different forcing mechanisms upon these parameters. They move on without pausing here, but this point should not be left without a commentary. The issue here is one […]

### Regression and Varimax Rotation

I’ve been reading through some articles on altitudinal reconstructions by Rob Wilson and other Luckman students. The studies all follow a similar strategy as Wilson et al 2007 – principal components analysis; truncation to eigenvalues 1, varimax rotation and regression. It’s pretty obvious that these operations are all linear and if the linear algebra were […]

### Bürger Review

Here is what Reviewer #3 submitted in his review of the Bürger CPD submission (I’ve taken down the draft review.) He regrets agreeing to do the review (for reasons that will become clear). Even though Reviewer #3 has much goodwill towards Bürger, he is rather a stickler for detail and it seems rather unfair that […]

### Varimax Rotation and the AMM

While I was reading about rotated varimax PCA in connection with Rob Wilson’s article, I came across R.W. Houghton and Y.M. Tourre, 1992, Characteristics of Low-Frequency Sea Surface Temperature Fluctuations in the Tropical Atlantic, Journal of Climate Volume 5, Issue 7 (July 1992) pp. 765—772 url. They observed that a PC analysis applied to Atlantic […]