A Class-Kriging predictor for Functional Compositions with Application to Particle-Size Curves in Heterogeneous Aquifers

This work addresses the problem of characterizing the spatial field of soil particle-size distributions within a heterogeneous aquifer system. The medium is conceptualized as a composite system, characterized by spatially varying soil textural properties associated with diverse geomaterials. The heterogeneity of the system is modeled through an original hierarchical model for particle-size distributions that are here interpreted as points in the Bayes space of functional compositions. This theoretical framework allows performing spatial prediction of functional compositions through a functional compositional Class-Kriging predictor. To tackle the problem of lack of information arising when the spatial arrangement of soil types is unobserved, a novel clustering method is proposed, allowing to infer a grouping structure from sampled particle-size distributions. The proposed methodology enables one to project the complete information content embedded in the set of heterogeneous particle-size distributions to unsampled locations in the system. These developments are tested on a field application relying on a set of particle-size data observed within an alluvial aquifer in the Neckar river valley, in Germany

Statistical analysis of complex and spatially dependent data: A review of Object Oriented Spatial Statistics

We review recent advances in Object Oriented Spatial Statistics, a system of ideas, algorithms and methods that allows the analysis of high dimensional and complex data when their spatial dependence is an important issue. At the intersection of different disciplines – including mathematics, statistics, computer science and engineering – Object Oriented Spatial Statistics provides the right perspective to address key problems in varied contexts, from Earth and life sciences to urban planning. We illustrate a few paradigmatic methods applied to problems of prediction, classification and smoothing, giving emphasis to the key ideas Object Oriented Spatial Statistics relies upon

Physics-based Residual Kriging for dynamically evolving functional random fields

AbstractWe present a novel approach named Physics-based Residual Kriging for the statistical prediction of spatially dependent functional data. It incorporates a physical model—expressed by a partial differential equation—within a Universal Kriging setting through a geostatistical modelization of the residuals with respect to the physical model. The approach is extended to deal with sequential problems, where samples of functional data become available along consecutive time intervals, in a context where the physical and stochastic processes generating them evolve, as time intervals succeed one another. An incremental modeling is used to account for both these dynamics and the misfit between previous predictions and actual observations. We apply Physics-based Residual Kriging to forecast production rates of wells operating in a mature reservoir according to a given drilling schedule. We evaluate the predictive errors of the method in two different case studies. The first deals with a single-phase reservoir where production is supported by fluid injection, while the second considers again a single-phase reservoir but the production is driven by rock compaction

Profile Monitoring of Probability Density Functions via Simplicial Functional PCA with application to Image Data

The advance of sensor and information technologies is leading to data-rich industrial environments, where large amounts of data are potentially available. This study focuses on industrial applications where image data are used more and more for quality inspection and statistical process monitoring. In many cases of interest, acquired images consist of several and similar features that are randomly distributed within a given region. Examples are pores in parts obtained via casting or additive manufacturing, voids in metal foams and light-weight components, grains in metallographic analysis, etc. The proposed approach summarizes the random occurrences of the observed features via their (empirical) probability density functions (PDFs). In particular, a novel approach for PDF monitoring is proposed. It is based on simplicial functional principal component analysis (SFPCA), which is performed within the space of density functions, that is, the Bayes space B2. A simulation study shows the enhanced monitoring performances provided by SFPCA-based profile monitoring against other competitors proposed in the literature. Finally, a real case study dealing with the quality control of foamed material production is discussed, to highlight a practical use of the proposed methodology. Supplementary materials for the article are available online

Universal kriging of functional data: trace-variography vs cross-variography? Application to forecasting in unconventional shales

In this paper we investigate the practical and methodological use of Universal Kriging of functional data to predict unconventional shale gas production in undrilled locations from known production data. In Universal Kriging of functional data, two approaches are considered: (1) estimation by means of Cokriging of functional components (Universal Cokriging, UCok), requiring cross-variography and (2) estimation by means of trace-variography (Universal Trace-Kriging, UTrK), which avoids cross-variogram modeling. While theoretically, under known variogram structures, such approaches may be quite equivalent, their practical application implies different estimation procedures and modeling efforts. We investigate these differences from the methodological viewpoint and by means of a real field application in the Barnett shale play. An extensive Monte Carlo study inspired from such real field application is employed to support our conclusions

funcharts: Control charts for multivariate functional data in R

Modern statistical process monitoring (SPM) applications focus on profile monitoring, i.e., the monitoring of process quality characteristics that can be modeled as profiles, also known as functional data. Despite the large interest in the profile monitoring literature, there is still a lack of software to facilitate its practical application. This article introduces the funcharts R package that implements recent developments on the SPM of multivariate functional quality characteristics, possibly adjusted by the influence of additional variables, referred to as covariates. The package also implements the real-time version of all control charting procedures to monitor profiles partially observed up to an intermediate domain point. The package is illustrated both through its built-in data generator and a real-case study on the SPM of Ro-Pax ship CO2 emissions during navigation, which is based on the ShipNavigation data provided in the Supplementary Material