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pcs in obscure supplementary information he vehemently and repeatedly asserted that he had used two north american pcs in the ad1400 because that was the correct number to use under application of the standard selection rules it was a preoccupation at the opening of realclimate in december 2014 when mann was attempting block publication of our submission to grl for example the very first article scroll through 2004 archives to page 9 link in the entire realclimate archive dated november 22 2004 almost three weeks before realclimate opened to the public on december 10 2004 is entitled pca details pca of the 70 north american itrdb tree ring proxy series used by mann et al 1998 mann stated that two north american pcs were used in the ad1400 network based on application of the standard selection rules applied to short centered data realclimate opened on december 10 2004 link and on opening featured two attacks on us by mann link link entitled false claims by mcintyre and mckitrick regarding the mann et al 1998 reconstruction and myth vs fact regarding the hockey stick both were dated december 4 2004 mann cited our nature submission as the target of his animus in these earliest realclimate articles link link mann vehemently asserted linking back to the pca details article that they had used two pc series in the mbh98 ad1400 network by application of preisendorfer s rule n to principal components calculated using mbh98 centering i e mann s incorrect short centering the mbh98 reconstruction is indeed almost completely insensitive to whether the centering convention of mbh98 data centered over 1902 1980 calibration interval or mm data centered over the 1400 1971 interval is used claims by mm to the contrary are based on their failure to apply standard selection rules used to determine how many principal component pc series should be retained in the analysis application of the standard selection rule preisendorfer s rule n used by mbh98 selects 2 pc series using the mbh98 centering convention but a larger number 5 pc series using the mm centering convention in an early climate audit article link i tested every mbh98 tree ring and step using preisendorfer s rule n and was unable to replicate the numbers of retained pcs reported in the si using that rule soderqvist s discovery that mbh98 used six north american pcs not only refutes mann s claim that he used two north american pcs but refutes his claim that he used preisendorfer s rule n to select two pcs soderqvist s discovery raises a new question how did mann decide to retain six north american pcs in the ad1400 it obviously wasn t preisendorfer s rule n so what was the procedure mann has never revealed it subsequent to the original controversy i ve written many climate audit posts on properties of principal components calculations including some of what i regard as the most interesting climate audit posts on chaldni patterns arising from principal components applied to spatially autocorrelated tree ring series the takeaway is that for a large scale temperature reconstruction one should not use any pcs below the pc1 the reason is blindingly obvious once stated the pc2 and lower pcs contain negative signs for approximately half the locations i e they flip the proxies upside down if the tree ring data are indeed temperature proxies they should be used in the correct orientation thus no need for lower order pcs in many important cases the pc1 is similar to a simple average of the series lower order pcs tend to be contrasts between regional groupings in the north american network southeastern us cypress form a grouping that is identifiable in the pc5 centered and needless to say the stripbark bristlecones form another distinct grouping he then observed that under mm05 correct centering the hockey stick pattern appeared in the pc4 for the subsequent inverse regression step of mbh98 methodology it didn t matter whether the hockey stick pattern appeared in the pc1 inclusion even as a pc4 was sufficient to impart a hockey stick shape to the resulting reconstruction although not disclosed by mm04 precisely the same hockey stick pc pattern appears using their convention albeit lower down in the eigenvalue spectrum pc 4 figure 1a if the correct 5 pc indicators are used rather than incorrectly truncating at 2 pcs as mm04 have done a reconstruction similar to mbh98 is obtained being a distinct regional pattern does not prove that the pattern is a temperature proxy significance under rule n is according to preisendorfer himself merely a attention getter a ringing bell a signal to look deeper to test further see our discussion of preisendorfer here the null hypothesis of a dominant variance selection rule such as rule n says that z is generated by a random process of some specified form for example a random process that generates equal eigenvalues of the associated scatter covariance matrix s one may only view the rejection of a null hypothesis as an attention getter a ringing bell that says you may have a non random process generating your data set z the rejection is a signal to look deeper to test further our response has always been that the relevant question was not whether the hockey stick pattern of the stripbark bristlecones was a distinctive pattern within the north american tree ring network but whether this pattern was local and specialized as opposed to an overall property and if local to stripbark bristlecones whether the stripbark bristlecones were magic world thermometers the 2006 nas panel recommended that stripbark bristlecones be avoided in temperature reconstructions but their recommendation was totally ignored they continued in use in mann et al 2008 pages2k and many other canonical reconstructions none of which are therefore independent of mann et al 1998 99 while most external attention on mbh98 controversy has focussed on principal component issues when i reviewed the arc of climate audit posts in 2007 2008 prior to climategate they were much more focused on questions pertaining to properties of the inverse regression step subsequent to the principal components calculation and in particular to overfitting issues arising from inverse regression our work on these issues got sidetracked by climategate but there is a great deal of interesting material that deserves to be followed up on by stephen mcintyre posted in uncategorized tagged mbh98 preisendorfer soderqvist comments 52 mbh98 confidence intervals nov 10 2023 10 55 am continued from here the dirty laundry residual datasets for ad1000 ad1400 and ad1600 were each calculated using mann s sparse instrumental dataset but the resultant sigmas and re calibration statistics don t match reported values in contrast the dirty laundry residual dataset for the ad1820 step which was calculated by tim osborn of cru because mann couldn t find his copy of the ad1820 residual data used a different mbh98 target instrumental dataset the dense instrumental series question is it possible that mann had two versions of the residual data sparse and dense and that he chose the dense version for mbh98 statistics sigma re_calibration because it yielded better statistics but inadvertently sent the sparse version with worse values to osborn this appears to be exactly what happened if one uses the dirty laundry values for the reconstruction in 1902 1980 versus the mbh98 dense temperature series one gets an exact replication of reported mbh98 calibration re and sigma standard error of residuals for the ad1400 and ad1600 step and reported mbh99 calibration re for the ad1000 step conclusion we know that mbh98 calculated residual series using the sparse target because they were sent to osborn in the dirty laundry email and shown in the mbh99 submission figure 1a we know that mbh98 calculated residual series using the dense target because of the reported re_calibration and sigma values in mbh98 the corollary is that mbh98 calculated two sets of residual series and then selected the better values for display without disclosing the worse values or the selection operation mbh99 confidence intervals are related to mbh98 confidence intervals but different they were a longstanding mystery during the heyday of climate audit blog in next post i ll review mbh99 confidence intervals we re a bit closer to a solution and maybe a reader will be able to figure out the balance over and above this particular issue is another even more fundamental issue the use of calibration period residuals to estimate confidence intervals when there is a massive failure of verification period r 2 values prior to climategate i had written several posts and comments in which i had raised the issue and problem of massive overfitting in the calibration period through a little discussed mbh98 99 step involving a form of inverse regression closer to pls regression than to ols regression some intuitions of ols practitioners have to be set aside there are some very interesting issues and problems arising from this observation and even some points of potential mathematical interest i ll try to elaborate on this in a future post postscript there is a substantial and surprisingly large difference between the two mbh98 target instrumental series see diagram below the sparse series according to mbh98 is the subset of the gridded data m 219 grid points for which independent values are available from 1854 to 1901 the dense series is calculated for 1902 1980 from 1082 gridcells in the 19802 1980 mbh calibration period there is considerably more variability in the sparse series by stephen mcintyre posted in uncategorized tagged confidence interval dirty laundry mbh98 re comments 6 older posts tip jar the tip jar is working again via a temporary location pages about blog rules and road map ca assistant ca blog setup contact steve mc econometric references faq 2005 gridded data high resolution ocean sediments hockey stick studies proxy data station data statistics and r subscribe 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