Publications by Marc in the box
Propagation of error
At the onset, this was strictly an excercise of my own curiosity and I didn't imagine writing this down in any form at all. As someone who has done some modelling work in the past, I'm embarrassed to say that I had never fully grasped how one can gauge the error of a model output without having to do some sort of Monte Carlo simulation w...
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Empirical Orthogonal Function (EOF) Analysis for gappy data
The following is a function for the calculation of Empirical Orthogonal Functions (EOF). For those coming from a more biologically-oriented background and are familiar with Principal Component Analysis (PCA), the methods are similar. In the climate sciences the method is usually used for the decomposition of a data field into dominant spatial-tem...
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Define intermediate color steps for colorRampPalette
The following function, color.palette(), is a wrapper for colorRampPalette() and allows some increased flexibility in defining the spacing between main color levels. One defines both the main color levels (as with colorRampPalette) and an optional vector containing the number of color levels that should be put in between at equal distances. ...
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Another aspect of speeding up loops in R
Any frequent reader of R-bloggers will have come across several posts concerning the optimization of code – in particular, the avoidance of loops.Here's another aspect of the same issue. If you have experience programming in other languages besides R, this is probably a no-brainer, but for laymen, like myself, the following example was a total ...
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Maximum Covariance Analysis (MCA)
Maximum Covariance Analysis (MCA) (Mode 1; scaled) of Sea Level Pressure (SLP) and Sea Surface Temperature (SST) monthly anomalies for the region between -180 °W to -70 °W and +30 °N to -30 °S. MCA coefficients (scaled) are below. The mode represents 94% of the squared covariance fraction (SCF).Maximum Correlation Analysis (MCA) is similar ...
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Maximal Information Coefficient (MIC)
Pearson r correlation coefficients for various distributions of paired data (Credit: Denis Boigelot, Wikimedia Commons)A paper published this week in Science outlines a new statistic called the maximal information coefficient (MIC), which is able to equally describe the correlation between paired variables regardless of linear or nonlinear relati...
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XYZ geographic data interpolation, part 2
Having recently received a comment on a post regarding geographic xyz data interpolation, I decided to return to my original “xyz.map” function and open it up for easier interpretation. This should make the method easier to adapt and follow.The above graph shows the distance to Mecca as interpolated from 1000 randomly generated lat/lon data u...
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XYZ geographic data interpolation, part 3
This will be probably be a final posting on interpolation of xyz data as I believe I have come to some conclusions to my original issues. I show three methods of xyz interpolation:1. The quick and dirty method of interpolating projected xyz points (bi-linear)2. Interpolation using Cartesian coordinates (bi-linear)3. Interpolation using spherical ...
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A ridiculous proof of concept: xyz interpolation
Ridiculous OrbThis is really the last one on this theme for a while… I had alluded to a combination of methods regarding xyz interpolation at the end of my last post and wanted to demonstrate this in a final example.The ridiculousness that you see above involved two interpolation steps. First, a thin plate spline interpolation (“Tps” functi...
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Exponentiation of a matrix (including pseudoinverse)
The following function “exp.mat” allows for the exponentiation of a matrix (i.e. calculation of a matrix to a given power). The function follows three steps:1) Singular Value Decomposition (SVD) of the matrix2) Exponentiation of the singular values3) Re-calculation of the matrix with the new singular valuesThe most common case where the metho...
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