Geostatistics for Compositional Data with R

Table of Contents

1. Frontmatter

2. Chapter 1. Introduction

   Raimon Tolosana-Delgado, Ute Mueller

   Abstract

   This chapter provides the framework for the contents of this book. This includes a brief introduction to the problem of geospatial analysis of compositional data and approaches to the solution. Additionally, the data sets and the R packages used throughout the book are presented.

3. Chapter 2. A Review of Compositional Data Analysis

   Raimon Tolosana-Delgado, Ute Mueller

   Abstract

   This chapter provides the concepts from compositional data analysis required to prepare compositional data for geostatistical treatment. Specifically we define the term closure, its rationale and caveats, and the various ways of escaping from its curse, i.e. the various forms of log-ratio transformation.

4. Chapter 3. Exploratory Data Analysis

   Raimon Tolosana-Delgado, Ute Mueller

   Abstract

   In this chapter we will introduce several tools for the exploratory analysis of compositional data, including plots, compositional measures of centre and spread, and compositional principal components to characterise regionalised compositions.

5. Chapter 4. Exploratory Spatial Analysis

   Raimon Tolosana-Delgado, Ute Mueller

   Abstract

   In this chapter the tools for spatial exploratory analysis are provided. These include data postings, swathplots and experimental variograms.

6. Chapter 5. Variogram Models

   Raimon Tolosana-Delgado, Ute Mueller

   Abstract

   Here we look at model fitting. The structural functions mainly used for model fitting are introduced. The main tool for model fitting is the linear model of coregionalisation, but the application of the MAF transformation to build a linear model of coregionalisation is also demonstrated.

7. Chapter 6. Geostatistical Estimation

   Raimon Tolosana-Delgado, Ute Mueller

   Abstract

   In this chapter we consider the main geostatistical estimation methods adapted to regionalised compositions.

8. Chapter 7. Cross-Validation

   Raimon Tolosana-Delgado, Ute Mueller

   Abstract

   Cross-validation is a technique devised to provide a quality assessment of the estimates derived from cokriging and allows appraising different modelling approaches in terms of the choice of variograms and search neighbourhoods.

9. Chapter 8. Multivariate Normal Score Transformation

   K. Gerald van den Boogaart, Ute Mueller, Raimon Tolosana-Delgado

   Abstract

   For the geostatistical simulation of a compositional random function via a Gaussian simulation algorithm, it is often necessary to transform the log-ratio scores of a given composition to multivariate Gaussian variables. In order for the results to be independent of the choice of log-ratio transform, the multivariate normal score transformation needs to be affine equivariant. In this chapter we introduce one such transformation, namely the Gaussian flow anamorphosis and briefly describe its properties.

10. Chapter 9. Simulation

    Raimon Tolosana-Delgado, Ute Mueller

    Abstract

    In this chapter we look at the geostatistical simulation of compositional data. The workflow typically consists of first applying a log-ratio transformation, then testing the transformed data for multivariate normality, applying an affine equivariant multivariate normal score transformation, if necessary, modelling the spatial continuity of the normal scores, followed by simulation and back-transformation. Several algorithms are available for simulating Gaussian random functions. These include LU decomposition simulation, sequential Gaussian simulation and turning bands simulation, which will be introduced briefly.

11. Chapter 10. Compositional Direct Sampling Simulation

    Hassan Talebi, Ute Mueller, Raimon Tolosana-Delgado

    Abstract

    In many instances it is desirable to capture more than the first two moments of the data when exploring their variability. In this chapter direct sampling simulation for compositional data is introduced, which explicitly incorporates multiple-point statistics in the simulation.

12. Chapter 11. Evaluation and Postprocessing of Results

    Raimon Tolosana-Delgado, Ute Mueller

    Abstract

    In this chapter tools for the evaluation of results from estimation and simulation are considered. We include QQ-plots, PP-plots, variogram swarms and misclassification analysis to assess how well the output data reflect the inputs. In addition we consider upscaling of simulation results and different approaches for this.

13. Backmatter