Introduced in this paper is a family of statistics, G, that can be used as a measure of spatial association in a number of circumstances. The basic statistic is derived, its properties are identified, and its advantages explained. Several of the G statistics make it possible to evaluate the spatial association of a variable within a specified distance of a single point. A comparison is made between a general G statistic and Moran’s I for similar hypothetical and empirical conditions. The empirical work includes studies of sudden infant death syndrome by county in North Carolina and dwelling unit prices in metropolitan San Diego by zip-code districts. Results indicate that G statistics should be used in conjunction with I in order to identify characteristics of patterns not revealed by the I statistic alone and, specifically, the G i and G i ∗ statistics enable us to detect local “pockets” of dependence that may not show up when using global statistics.

http://archive.nefmc.org/tech/cte_mtg_docs/130516/CATT%20Report/Getis-Ord%20statistic.pdf

The Analysis of Spatial Association by Use of Distance Statistics

An overview of model-based geostatistics.- Gaussian models for geostatistical data.- Generalized linear models for geostatistical data.- Classical parameter estimation.- Spatial prediction.- Bayesian inference.- Geostatistical design.

/pdf/model-based-geostatistics-3h5fgto422.pdf

Model-based Geostatistics

Feature selection, as a data preprocessing strategy, has been proven to be effective and efficient in preparing data (especially high-dimensional data) for various data-mining and machine-learning problems. The objectives of feature selection include building simpler and more comprehensible models, improving data-mining performance, and preparing clean, understandable data. The recent proliferation of big data has presented some substantial challenges and opportunities to feature selection. In this survey, we provide a comprehensive and structured overview of recent advances in feature selection research. Motivated by current challenges and opportunities in the era of big data, we revisit feature selection research from a data perspective and review representative feature selection algorithms for conventional data, structured data, heterogeneous data and streaming data. Methodologically, to emphasize the differences and similarities of most existing feature selection algorithms for conventional data, we categorize them into four main groups: similarity-based, information-theoretical-based, sparse-learning-based, and statistical-based methods. To facilitate and promote the research in this community, we also present an open source feature selection repository that consists of most of the popular feature selection algorithms (http://featureselection.asu.edu/). Also, we use it as an example to show how to evaluate feature selection algorithms. At the end of the survey, we present a discussion about some open problems and challenges that require more attention in future research.

https://dl.acm.org/doi/pdf/10.1145/3136625

Feature Selection: A Data Perspective

Sandstones of the Paleozoic turbidite sequences of eastern Australia show a large variation in their major element geochemistry, reflecting the distinct sedimentary provenance and tectonic setting ...

Plate Tectonics and Geochemical Composition of Sandstones

A gridding method commonly called minimum curvature is widely used in the earth sciences. The method interpolates the data to be gridded with a surface having continuous second derivatives and minimal total squared curvature. The minimum-curvature surface has an analogy in elastic plate flexure and approximates the shape adopted by a thin plate flexed to pass through the data points. Minimum-curvature surfaces may have large oscillations and extraneous inflection points which make them unsuitable for gridding in many of the applications where they are commonly used. These extraneous inflection points can be eliminated by adding tension to the elastic-plate flexure equation. It is straightforward to generalize minimum-curvature gridding algorithms to include a tension parameter; the same system of equations must be solved in either case and only the relative weights of the coefficients change. Therefore, solutions under tension require no more computational effort than minimum-curvature solutions, and any algorithm which can solve the minimum-curvature equations can solve the more general system. We give common geologic examples where minimum-curvature gridding produces erroneous results but gridding with tension yields a good solution. We also outline how to improve the convergence of an iterative method of solution for the gridding equations.

/pdf/gridding-with-continuous-curvature-splines-in-tension-40d6kiojd4.pdf

I. L. Gibson

Papers

Statistics and Data Analysis in Geology