Kernel Analyses of Volcanic Vent Distribution: How Accurate and Complete are the Objective Bandwidth Selectors?

Abstract

Kernel Density Estimation is a powerful tool that can be used to extract information about the underlying plumbing system in zones of distributed volcanism. Different approaches concerning the form in which this tool should be applied, however, exist on the literature. One of those approaches sustains that an unbiased selection of a parameter known as the bandwidth is preferable to other alternatives because it reduces biases on the analysis. Nevertheless, there are more than 30 different forms in which a bandwidth can be “objectively” selected, therefore questioning the meaning of “objectivity” on the selection of a method used for its calculation. Furthermore, as shown in this work, the range of allowed “objective” choices of the bandwidth is not much different from a typical range that could be selected subjectively. Consequently, instead of focusing on the question of “what is the best method?” it is shown here that a more informative approach is to focus on the questions of “what are the special values of different methods, and what are their several advantageous applicabilities?”. The benefits of this shift in approach are illustrated with application to three locations of volcanic interest that have a previously well-constrained volcanic structure.

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“…In this work I provide an overview of the uses and limitations of several methods used for the study of the spatial distribution of volcanic vents, making emphasis on the assumptions embedded in those methods. Several of these issues have been addressed to different degrees elsewhere (Cañón-Tapia, 2016;Cañón-Tapia, 2020;Cañón-Tapia, 2021a;Cañón-Tapia, 2022). Nevertheless, it seems convenient to make an abridged revision of the most important concepts in a single place to facilitate the appreciation of the utility of this type of studies.…”