Spatial Point Pattern Analysis of the Unidentified Aerial Phenomena in France

We model the unidentified aerial phenomena observed in France during the last 60 years as a spatial point pattern. We use some public information such as population density, rate of moisture or presence of airports to model the intensity of the unidentified aerial phenomena. Spatial exploratory data analysis is a first approach to appreciate the link between the intensity of the unidentified aerial phenomena and the covariates. We then fit an inhomogeneous spatial Poisson process model with covariates. We find that the significant variables are the population density, the presence of the factories with a nuclear risk and contaminated land, and the rate of moisture. The analysis of the residuals shows that some parts of France (the Belgian border, the tip of Britany, some parts in the SouthEast , the Picardie and Haute-Normandie regions, the Loiret and Corr eze departments) present a high value of local intensity which are not explained by our model

Accuracy of areal interpolation methods for count data

The combination of several socio-economic data bases originating from different administrative sources collected on several different partitions of a geographic zone of interest into administrative units induces the so called areal interpolation problem. This problem is that of allocating the data from a set of source spatial units to a set of target spatial units. A particular case of that problem is the re-allocation to a single target partition which is a regular grid. At the European level for example, the EU directive 'INSPIRE', or INfrastructure for SPatial InfoRmation, encourages the states to provide socio-economic data on a common grid to facilitate economic studies across states. In the literature, there are three main types of such techniques: proportional weighting schemes, smoothing techniques and regression based interpolation. We propose a stochastic model based on Poisson point patterns to study the statistical accuracy of these techniques for regular grid targets in the case of count data. The error depends on the nature of the target variable and its correlation with the auxiliary variable. For simplicity, we restrict attention to proportional weighting schemes and Poisson regression based methods. Our conclusion is that there is no technique which always dominates

Exploratory spatial data analysis with GEOXP

GEOX is a computer package of Splus and Matlab routines implementing interactive graphics methods for exploring spatial data. We analyse a large data basis from the regional public health insurance agency concerning physicians'' activity in the Midi-Pyrénées region. We evaluate in particular heterogeneity and outliers in the density of physicians, their prescriptions per patient, salaries, number of visits per patient, etc.. We examine spatial dependencies of the main variables and thus locate spatial clusters. We attempt to explain the patterns of the prescription by some characteristics of the physicians together with the socio-economic characteristics of the counties using a spatial regression model with autocorrelated errors involving a hierarchical structure since these two sets of variables are known at a different level: physician level or county level.

Covariates impacts in compositional models and simplicial derivatives

In the framework of Compositional Data Analysis, vectors carrying relative information, also called compositional vectors, can appear in regression models either as dependent or as explanatory variables. In some situations, they can be on both sides of the regression equation. Measuring the marginal impacts of covariates in these types of models is not straightforward since a change in one component of a closed composition automatically affects the rest of the composition. J. Morais, C. Thomas-Agnan and M. Simioni [Austrian Journal of Statistics, 47(5), 1-25, 2018] have shown how to measure, compute and interpret these marginal impacts in the case of linear regression models with compositions on both sides of the equation. The resulting natural interpretation is in terms of an elasticity, a quantity commonly used in econometrics and marketing applications. They also demonstrate the link between these elasticities and simplicial derivatives. The aim of this contribution is to extend these results to other situations, namely when the compositional vector is on a single side of the regression equation. In these cases, the marginal impact is related to a semi-elasticity and also linked to some simplicial derivative. Moreover we consider the possibility that a total variable is used as an explanatory variable, with several possible interpretations of this total and we derive the elasticity formulas in that case

Measuring and testing spatial mass concentration with micro-geographic data

We address the question of measuring and testing industrial spatial concentration based on micro-geographic data with distance based methods. We discuss the basic requirements for such measures and we propose four additional requirements. We also discuss the null assumptions classically used for testing aggregation of a particular sector and propose an alternative point of view. Our general index measure involves a cumulative and a non-cumulative version. This allows us to propose an alternative version of the Duranton Overman index with a proper baseline as well as a cumulative version of this same index. We illustrate the approach with some simulated data

Measuring and testing spatial mass concentration with micro-geographic data

We address the question of measuring and testing industrial spatial concentration based on micro-geographic data with distance based methods. We discuss the basic requirements for such measures and we propose four additional requirements. We also discuss the null assumptions classically used for testing aggregation of a particular sector and propose an alternative point of view. Our general index measure involves a cumulative and a non-cumulative version. This allows us to propose an alternative version of the Duranton Overman index with a proper baseline as well as a cumulative version of this same index. We illustrate the approach with some simulated data

Origin and distribution of rare earth elements in various lichen and moss species over the last century in France

Rare earth elements (REE) are known to be powerful environmental tracers in natural biogeochemical compartments. In this study, the atmospheric deposition of REE was investigated using various lichens and mosses as well as herbarium samples from 1870 to 1998 from six major forested areas in France. The comparison between the REE distribution patterns in organisms and bedrocks showed a regional uniformity influence from dust particles originating from the bedrock and/or soil weathering that were entrapped by lichens and mosses. These lithological signatures were consistent over the last century. The REE patterns of different organism species allowed minor influence of the species to be highlighted compared to the regional lithology. This was even true where the morphological features played a role in the bioaccumulation levels, which were related to the variable efficiency in trapping atmospheric dust particles. A comparison between REE profiles in the organisms and bark indicated a lack of influence of the substrate on lichen REE content. Lichens and mosses appear to be robust passive monitors of REE atmospheric deposition over decades because the mineral data was preserved in herbarium samples despite organic degradation being shown by carbon isotopes and SEM observations. To overcome the bias of REE concentration that resulted from organic degradation, the use of a normalized method is recommended to interpret the historical samples

About predictions in spatial autoregressive models

We address the problem of prediction in the spatial autoregressive SAR model for areal data which is classically used in spatial econometrics. With the Kriging theory, prediction using Best Linear Unbiased Predictors is at the heart of the geostatistical literature. From the methodological point of view, we explore the limits of the extension of BLUP formulas in the context of the spatial autoregressive SAR models for out-of-sample prediction simultaneously at several sites. We propose a more tractable \almost best" alternative and clarify the relationship between the BLUP and a proper EM-algorithm predictor. From an empirical perspective, we present data-based simulations to compare the efficiency of the classical formulas with the best and almost best predictions