Paper No. 5
Presentation Time: 9:05 AM


VERMEESCH, Pieter, Earth Sciences, University College London, Gower Street, London, WC1E 6BT, United Kingdom,

[1] The Probability Density Plot (PDP) is a visual aid for measurements with variable analytical precision. It is produced by sorting the values from small to large, superimposing a Gaussian ‘bell curve’ on top of each of them, and summing those to form a summary curve.

[2] Any detrital geochronologist (including the author) will have seen and used PDPs. Nowadays, hardly any detrital zircon U-Pb dataset is published without an accompanying PDP. Implicit to their ubiquity is the assumption that they are theoretically sound and robust. Alas, nothing could be further from the truth.

[3] The truth is that the PDP is an ad-hoc invention of geologists which is not used in any other field of science, and whose theoretical basis cannot be found anywhere in the statistics literature. The PDP is seriously flawed, and produces counter-intuitive and nonsensical results when data quantity (sample size) or data quality (analytical precision) is high.

[4] Kernel Density Estimation (KDE) is a superior alternative to the PDP, which does have a sound statistical basis. Just like PDPs, KDEs are also constructed by stacking a number of Gaussian ‘kernels’, whose standard deviation, however, is independent of the analytical uncertainty but is calculated independently, like the number of bins in a histogram.

[5] KDEs are widely used in Physics, Chemistry, and the Biosciences; PDPs are nowhere to be found in these fields of science. There is a Wikipedia page about KDEs; there is no Wikipedia entry about PDPs. Countless statistics textbooks and papers have been written about KDEs; PDPs are not mentioned in the statistics literature even once.

[6] It is easy to shows that the KDE asymptotically approaches the true data distribution as the analytical precision and/or sample size approach infinity. In contrast, the PDP catastrophically breaks down under those same conditions.

[7] For these reasons, it is best that the PDP is abandoned by the Earth Sciences community entirely, in favour of established alternatives such as the KDE.