Math 101 - Filtering Theory http://signals.auditblogs.com Everyone knows how to average Thu, 17 Jul 2008 10:32:50 +0000 http://wordpress.org/?v=2.3.1 en Hockeystick for Matlab http://signals.auditblogs.com/2008/07/01/hockeystick-for-matlab/ http://signals.auditblogs.com/2008/07/01/hockeystick-for-matlab/#comments Tue, 01 Jul 2008 21:54:46 +0000 uced http://signals.auditblogs.com/2008/07/01/hockeystick-for-matlab/ Here’s the version 1.1: hockeystick1.txt

Some notes:

  • Download to empty folder and rename to hockeystick.m
  • Program downloads necessary data from the web (once), uses urlwrite.m (newish Matlab needed)
  • It’s a script
  • Shows what PC1_fixed does
  • Only one file is downloaded from CA (AD1000 proxies), sorry RC, but I don’t know where to find morc014 elsewhere..
  • Pl. tell me if it works or not, uc_edit at yahoo.com !

Updated to Ver 1.1, added cooling trends:

fig1.1.png

]]> http://signals.auditblogs.com/2008/07/01/hockeystick-for-matlab/feed/ Some Interesting Figures http://signals.auditblogs.com/2008/01/03/some-interesting-figures/ http://signals.auditblogs.com/2008/01/03/some-interesting-figures/#comments Thu, 03 Jan 2008 14:23:02 +0000 uced http://signals.auditblogs.com/2008/01/03/some-interesting-figures/ While discussing at CA, I’ve made some figures that are spread around CA posts. Here’s a collection of the interesting ones, along with link to CA post in question. All those seem to be related to Dr. Mann’s work. I wonder why..

  1. Re-scaling the Mann and Jones 2003 PC1

    2. (more…)

    ]]> http://signals.auditblogs.com/2008/01/03/some-interesting-figures/feed/ Multivariate Calibration (II) http://signals.auditblogs.com/2007/07/09/multivariate-calibration-ii/ http://signals.auditblogs.com/2007/07/09/multivariate-calibration-ii/#comments Mon, 09 Jul 2007 10:00:00 +0000 uced http://signals.auditblogs.com/2007/07/09/multivariate-calibration-ii/ In the previous post, I mentioned that Juckes et al INVR is essentially CCE. In addition, it was noted that CCE is not ML estimator and that Brown82 shows how to really compute confidence region in multivariate calibration problems. As Dr. Juckes made a good job of archiving his results, we can now compare his CCE (S=I) and ML estimator results Brown’s confidence region (with central point as point estimate) .

    (more…)

    ]]>     http://signals.auditblogs.com/2007/07/09/multivariate-calibration-ii/feed/     Multivariate Calibration http://signals.auditblogs.com/2007/07/05/multivariate-calibration/ http://signals.auditblogs.com/2007/07/05/multivariate-calibration/#comments Thu, 05 Jul 2007 10:33:04 +0000 uced http://signals.auditblogs.com/2007/07/05/multivariate-calibration/ In calibration problem we have accurately known data values (X) and a responses to those values (Y). Responses are scaled and contaminated by noise (E), but easier to obtain. Given the calibration data (X,Y), we want to estimate new data values (X’) when we observe response Y’. Using Brown’s (Brown 1982) notation, we have a model

    Y=\textbf{1}\alpha ^T + XB + E (1)

    Y'=\alpha ^T + X'^T B + E' (2)

    where sizes of matrices are Y (nXq), E (nXq), B(pXq), Y’ (1Xq), E’ (1Xq), X (nXp) and X’ (pX1). \textbf{1} is a column vector of ones (nX1). This is a bit less general than Brown’s model (only one response vector for each X’). n is length of the calibration data, q length of the response vector, and p length of the unknown X’. For example, if Y contains proxy responses to global temperature X, p is one and q the number of proxy records.

    In the following, it is assumed that columns of E are zero mean, normally distributed vectors. Furthermore, rows of E are uncorrelated. (This assumption would be contradicted by red proxy noise.) The (qXq) covariance matrix of noise is denoted by G. In addition, columns of X are centered and have average sum of squares one.

    (more…)

    ]]>     http://signals.auditblogs.com/2007/07/05/multivariate-calibration/feed/     UC’s Millennium Problems http://signals.auditblogs.com/2007/07/03/ucs-millennium-problems/ http://signals.auditblogs.com/2007/07/03/ucs-millennium-problems/#comments Tue, 03 Jul 2007 20:45:59 +0000 uced http://signals.auditblogs.com/2007/07/03/ucs-millennium-problems/
  2. How are those MBH99 uncertainties estimated?
  3. How many meteorological stations would be needed to beat the uncertainty levels of MBH99?
  4. If you don’t have a prior distribution of the signal, and observe signal+noise (noise independent of the signal), what kind of estimator yields a reconstruction that has a smaller sample variance than the true signal?
  5. How to define / measure natural variability ?
  6. Where do we need evolving multivariate regression ?
  7. Calibration: ICE, CCE or maybe even CVM. Why Kendall’s ATS claims that once the model is clearly stated, the choice of estimator follows directly ?
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