Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.

Statistical classification of road pavements using near field vehicle rolling noise measurements

Low noise surfaces have been increasingly considered as a viable and cost-effective alternative to acoustical barriers. However, road planners and administrators frequently lack information on the correlation between the type of road surface and the resulting noise emission profile. To address this problem, a method to identify and classify different types of road pavements was developed, whereby near field road noise is analyzed using statistical learning methods. The vehicle rolling sound signal near the tires and close to the road surface was acquired by two microphones in a special arrangement which implements the Close-Proximity method. A set of features, characterizing the properties of the road pavement, was extracted from the corresponding sound profiles. A feature selection method was used to automatically select those that are most relevant in predicting the type of pavement, while reducing the computational cost. A set of different types of road pavement segments were tested and the performance of the classifier was evaluated. Results of pavement classification performed during a road journey are presented on a map, together with geographical data. This procedure leads to a considerable improvement in the quality of road pavement noise data, thereby increasing the accuracy of road traffic noise prediction models.

Determination of the radiochemical purity of 99mTc-Tetrofosmin: comparision between five methods

GOAL: The manufacturing and distribution of strips of instant thin - layer chromatography with silica gel (ITLC - SG) (reference method) is currently discontinued so there is a need for an alternative method f or the determination of radiochemical purity (RCP) of 99m Tc - tetrofosmin. This study aims to compare five alternative methods proposed by the producer to determine the RCP of 99m Tc - tetrofosmin. METHODS: Nineteen vials of tetrofosmin were radiolabelled with 99m Tc and the percentages of the RCP were determined. Five different methods were compared with the standard RCP testing method (ITLC - SG, 2x20 cm): Whatman 3MM (1x10 cm) with acetone and dichloro - methane (method 1); Whatman 3MM (1x1 0 cm) with ethyl acetate (method 2); aluminum oxide - coated plastic thin - layer chromatography (TLC) plate (1x10 cm) and ethanol (method 3); Whatman 3MM (2x20 cm) with acetone and dichloro - methane (method 4); solid - phase extraction method C18 cartridge (meth od 5). RESULTS: The average values of RCP were 95,30% ± 1,28% (method 1), 93,95 ± 0,61% (method 2), 96,85% ± 0,93% (method 3), 92,94% ± 0,99% (method 4) and 96,25% ± 2,57% (method 5) (n=12 each), and 93,15% ± 1,13% for the standard method (n=19). There we re statistical significant differences in the values obtained for methods 1 (P=0,001), 3 (P=0,000) and 5 (P=0,004), and there were no statistical significant differences in the values obtained for methods 2 (P=0,113) and 4 (P=0,327). CONCLUSION: From the results obtained, methods 2 and 4 showed a higher correlation with the standard method. Unlike method 4, method 2 is less time - consuming than the reference method and can overcome the problems associated with the solvent toxicity. The remaining methods (1, 3 and 5) tended to overestimate RCP value compared to the standard method.

Practical Quality Control: Comparision of Methods on the Quantification of Stationary Phases in Paper and Thin-Layer Chromatographic Systems

Introduction: Paper and thin layer chromatography methods are frequently used in Classic Nuclear Medicine for the determination of radiochemical purity (RCP) on radiopharmaceutical preparations. An aliquot of the radiopharmaceutical to be tested is spotted at the origin of a chromatographic strip (stationary phase), which in turn is placed in a chromatographic chamber in order to separate and quantify radiochemical species present in the radiopharmaceutical preparation. There are several methods for the RCP measurement, based on the use of equipment as dose calibrators, well scintillation counters, radiochromatografic scanners and gamma cameras. The purpose of this study was to compare these quantification methods for the determination of RCP. Material and Methods: 99mTc-Tetrofosmin and 99mTc-HDP are the radiopharmaceuticals chosen to serve as the basis for this study. For the determination of RCP of 99mTc-Tetrofosmin we used ITLC-SG (2.5 x 10 cm) and 2-butanone (99mTc-tetrofosmin Rf = 0.55, 99mTcO4- Rf = 1.0, other labeled impurities 99mTc-RH RF = 0.0). For the determination of RCP of 99mTc-HDP, Whatman 31ET and acetone was used (99mTc-HDP Rf = 0.0, 99mTcO4- Rf = 1.0, other labeled impurities RF = 0.0). After the development of the solvent front, the strips were allowed to dry and then imaged on the gamma camera (256x256 matrix; zoom 2; LEHR parallel-hole collimator; 5-minute image) and on the radiochromatogram scanner. Then, strips were cut in Rf 0.8 in the case of 99mTc-tetrofosmin and Rf 0.5 in the case of 99mTc-HDP. The resultant pieces were smashed in an assay tube (to minimize the effect of counting geometry) and counted in the dose calibrator and in the well scintillation counter (during 1 minute). The RCP was calculated using the formula: % 99mTc-Complex = [(99mTc-Complex) / (Total amount of 99mTc-labeled species)] x 100. Statistical analysis was done using the test of hypotheses for the difference between means in independent samples. Results:The gamma camera based method demonstrated higher operator-dependency (especially concerning the drawing of the ROIs) and the measures obtained using the dose calibrator are very sensitive to the amount of activity spotted in the chromatographic strip, so the use of a minimum of 3.7 MBq activity is essential to minimize quantification errors. Radiochromatographic scanner and well scintillation counter showed concordant results and demonstrated the higher level of precision. Conclusions: Radiochromatographic scanners and well scintillation counters based methods demonstrate to be the most accurate and less operator-dependant methods.

Arrow plot and CA maps on microarray preprocessing methods

Microarray allow to monitoring simultaneously thousands of genes, where the abundance of the transcripts under a same experimental condition at the same time can be quantified. Among various available array technologies, double channel cDNA microarray experiments have arisen in numerous technical protocols associated to genomic studies, which is the focus of this work. Microarray experiments involve many steps and each one can affect the quality of raw data. Background correction and normalization are preprocessing techniques to clean and correct the raw data when undesirable fluctuations arise from technical factors. Several recent studies showed that there is no preprocessing strategy that outperforms others in all circumstances and thus it seems difficult to provide general recommendations. In this work, it is proposed to use exploratory techniques to visualize the effects of preprocessing methods on statistical analysis of cancer two-channel microarray data sets, where the cancer types (classes) are known. For selecting differential expressed genes the arrow plot was used and the graph of profiles resultant from the correspondence analysis for visualizing the results. It was used 6 background methods and 6 normalization methods, performing 36 pre-processing methods and it was analyzed in a published cDNA microarray database (Liver) available at http://genome-www5.stanford.edu/ which microarrays were already classified by cancer type. All statistical analyses were performed using the R statistical software.

Evaluation of distinct input methods of an intelligent wheelchair in simulated and real environments: a performance and usability study

This paper focuses on evaluating the usability of an Intelligent Wheelchair (IW) in both real and simulated environments. The wheelchair is controlled at a high-level by a flexible multimodal interface, using voice commands, facial expressions, head movements and joystick as its main inputs. A Quasi-experimental design was applied including a deterministic sample with a questionnaire that enabled to apply the System Usability Scale. The subjects were divided in two independent samples: 46 individuals performing the experiment with an Intelligent Wheelchair in a simulated environment (28 using different commands in a sequential way and 18 with the liberty to choose the command); 12 individuals performing the experiment with a real IW. The main conclusion achieved by this study is that the usability of the Intelligent Wheelchair in a real environment is higher than in the simulated environment. However there were not statistical evidences to affirm that there are differences between the real and simulated wheelchairs in terms of safety and control. Also, most of users considered the multimodal way of driving the wheelchair very practical and satisfactory. Thus, it may be concluded that the multimodal interfaces enables very easy and safe control of the IW both in simulated and real environments.

Automatic learning for the classification of chemical reactions and in statistical thermodynamics

This Thesis describes the application of automatic learning methods for a) the classification of organic and metabolic reactions, and b) the mapping of Potential Energy Surfaces(PES). The classification of reactions was approached with two distinct methodologies: a representation of chemical reactions based on NMR data, and a representation of chemical reactions from the reaction equation based on the physico-chemical and topological features of chemical bonds. NMR-based classification of photochemical and enzymatic reactions. Photochemical and metabolic reactions were classified by Kohonen Self-Organizing Maps (Kohonen SOMs) and Random Forests (RFs) taking as input the difference between the 1H NMR spectra of the products and the reactants. The development of such a representation can be applied in automatic analysis of changes in the 1H NMR spectrum of a mixture and their interpretation in terms of the chemical reactions taking place. Examples of possible applications are the monitoring of reaction processes, evaluation of the stability of chemicals, or even the interpretation of metabonomic data. A Kohonen SOM trained with a data set of metabolic reactions catalysed by transferases was able to correctly classify 75% of an independent test set in terms of the EC number subclass. Random Forests improved the correct predictions to 79%. With photochemical reactions classified into 7 groups, an independent test set was classified with 86-93% accuracy. The data set of photochemical reactions was also used to simulate mixtures with two reactions occurring simultaneously. Kohonen SOMs and Feed-Forward Neural Networks (FFNNs) were trained to classify the reactions occurring in a mixture based on the 1H NMR spectra of the products and reactants. Kohonen SOMs allowed the correct assignment of 53-63% of the mixtures (in a test set). Counter-Propagation Neural Networks (CPNNs) gave origin to similar results. The use of supervised learning techniques allowed an improvement in the results. They were improved to 77% of correct assignments when an ensemble of ten FFNNs were used and to 80% when Random Forests were used. This study was performed with NMR data simulated from the molecular structure by the SPINUS program. In the design of one test set, simulated data was combined with experimental data. The results support the proposal of linking databases of chemical reactions to experimental or simulated NMR data for automatic classification of reactions and mixtures of reactions. Genome-scale classification of enzymatic reactions from their reaction equation. The MOLMAP descriptor relies on a Kohonen SOM that defines types of bonds on the basis of their physico-chemical and topological properties. The MOLMAP descriptor of a molecule represents the types of bonds available in that molecule. The MOLMAP descriptor of a reaction is defined as the difference between the MOLMAPs of the products and the reactants, and numerically encodes the pattern of bonds that are broken, changed, and made during a chemical reaction. The automatic perception of chemical similarities between metabolic reactions is required for a variety of applications ranging from the computer validation of classification systems, genome-scale reconstruction (or comparison) of metabolic pathways, to the classification of enzymatic mechanisms. Catalytic functions of proteins are generally described by the EC numbers that are simultaneously employed as identifiers of reactions, enzymes, and enzyme genes, thus linking metabolic and genomic information. Different methods should be available to automatically compare metabolic reactions and for the automatic assignment of EC numbers to reactions still not officially classified. In this study, the genome-scale data set of enzymatic reactions available in the KEGG database was encoded by the MOLMAP descriptors, and was submitted to Kohonen SOMs to compare the resulting map with the official EC number classification, to explore the possibility of predicting EC numbers from the reaction equation, and to assess the internal consistency of the EC classification at the class level. A general agreement with the EC classification was observed, i.e. a relationship between the similarity of MOLMAPs and the similarity of EC numbers. At the same time, MOLMAPs were able to discriminate between EC sub-subclasses. EC numbers could be assigned at the class, subclass, and sub-subclass levels with accuracies up to 92%, 80%, and 70% for independent test sets. The correspondence between chemical similarity of metabolic reactions and their MOLMAP descriptors was applied to the identification of a number of reactions mapped into the same neuron but belonging to different EC classes, which demonstrated the ability of the MOLMAP/SOM approach to verify the internal consistency of classifications in databases of metabolic reactions. RFs were also used to assign the four levels of the EC hierarchy from the reaction equation. EC numbers were correctly assigned in 95%, 90%, 85% and 86% of the cases (for independent test sets) at the class, subclass, sub-subclass and full EC number level,respectively. Experiments for the classification of reactions from the main reactants and products were performed with RFs - EC numbers were assigned at the class, subclass and sub-subclass level with accuracies of 78%, 74% and 63%, respectively. In the course of the experiments with metabolic reactions we suggested that the MOLMAP / SOM concept could be extended to the representation of other levels of metabolic information such as metabolic pathways. Following the MOLMAP idea, the pattern of neurons activated by the reactions of a metabolic pathway is a representation of the reactions involved in that pathway - a descriptor of the metabolic pathway. This reasoning enabled the comparison of different pathways, the automatic classification of pathways, and a classification of organisms based on their biochemical machinery. The three levels of classification (from bonds to metabolic pathways) allowed to map and perceive chemical similarities between metabolic pathways even for pathways of different types of metabolism and pathways that do not share similarities in terms of EC numbers. Mapping of PES by neural networks (NNs). In a first series of experiments, ensembles of Feed-Forward NNs (EnsFFNNs) and Associative Neural Networks (ASNNs) were trained to reproduce PES represented by the Lennard-Jones (LJ) analytical potential function. The accuracy of the method was assessed by comparing the results of molecular dynamics simulations (thermal, structural, and dynamic properties) obtained from the NNs-PES and from the LJ function. The results indicated that for LJ-type potentials, NNs can be trained to generate accurate PES to be used in molecular simulations. EnsFFNNs and ASNNs gave better results than single FFNNs. A remarkable ability of the NNs models to interpolate between distant curves and accurately reproduce potentials to be used in molecular simulations is shown. The purpose of the first study was to systematically analyse the accuracy of different NNs. Our main motivation, however, is reflected in the next study: the mapping of multidimensional PES by NNs to simulate, by Molecular Dynamics or Monte Carlo, the adsorption and self-assembly of solvated organic molecules on noble-metal electrodes. Indeed, for such complex and heterogeneous systems the development of suitable analytical functions that fit quantum mechanical interaction energies is a non-trivial or even impossible task. The data consisted of energy values, from Density Functional Theory (DFT) calculations, at different distances, for several molecular orientations and three electrode adsorption sites. The results indicate that NNs require a data set large enough to cover well the diversity of possible interaction sites, distances, and orientations. NNs trained with such data sets can perform equally well or even better than analytical functions. Therefore, they can be used in molecular simulations, particularly for the ethanol/Au (111) interface which is the case studied in the present Thesis. Once properly trained, the networks are able to produce, as output, any required number of energy points for accurate interpolations.

Handling random errors and biases in methods used for short-term dietary assessment

Epidemiological studies have shown the effect of diet on the incidence of chronic diseases; however, proper planning, designing, and statistical modeling are necessary to obtain precise and accurate food consumption data. Evaluation methods used for short-term assessment of food consumption of a population, such as tracking of food intake over 24h or food diaries, can be affected by random errors or biases inherent to the method. Statistical modeling is used to handle random errors, whereas proper designing and sampling are essential for controlling biases. The present study aimed to analyze potential biases and random errors and determine how they affect the results. We also aimed to identify ways to prevent them and/or to use statistical approaches in epidemiological studies involving dietary assessments.

Assessing and comparing the total antioxidant capacity of commercial beverages: application to beers, wines, waters and soft drinks using TRAP, TEAC and FRAP methods.

This work measures and tries to compare the Antioxidant Capacity (AC) of 50 commercial beverages of different kinds: 6 wines, 12 beers, 18 soft drinks and 14 flavoured waters. Because there is no reference procedure established for this purpose, three different optical methods were used to analyse these samples: Total Radical trapping Antioxidant Parameter (TRAP), Trolox Equivalent Antioxidant Capacity (TEAC) and Ferric ion Reducing Antioxidant Parameter (FRAP). These methods differ on the chemical background and nature of redox system. The TRAP method involves the transfer of hydrogen atoms while TEAC and FRAP involves electron transfer reactions. The AC was also assessed against three antioxidants of reference, Ascorbic acid (AA), Gallic acid (GA) and 6-hydroxy-2,5,7,8-tetramethyl- 2-carboxylic acid (Trolox). The results obtained were analyzed statistically. Anova one-way tests were applied to all results and suggested that methods and standards exhibited significant statistical differences. The possible effect of sample features in the AC, such as gas, flavours, food colouring, sweeteners, acidity regulators, preservatives, stabilizers, vitamins, juice percentage, alcohol percentage, antioxidants and the colour was also investigated. The AC levels seemed to change with brand, kind of antioxidants added, and kind of flavour, depending on the sample. In general, higher ACs were obtained for FRAP as method, and beer for kind of sample, and the standard expressing the smaller AC values was GA.

Upper Arm Measurements of Healthy Neonates Comparing Ultrasonography and Anthropometric Methods

Objective: To compare measurements of the upper arm cross-sectional areas (total arm area,arm muscle area, and arm fat area of healthy neonates) as calculated using anthropometry with the values obtained by ultrasonography. Materials and methods: This study was performed on 60 consecutively born healthy neonates: gestational age (mean6SD) 39.661.2 weeks, birth weight 3287.16307.7 g, 27 males (45%) and 33 females (55%). Mid-arm circumference and tricipital skinfold thickness measurements were taken on the left upper mid-arm according to the conventional anthropometric method to calculate total arm area, arm muscle area and arm fat area. The ultrasound evaluation was performed at the same arm location using a Toshiba sonolayer SSA-250AÒ, which allows the calculation of the total arm area, arm muscle area and arm fat area by the number of pixels enclosed in the plotted areas. Statistical analysis: whenever appropriate, parametric and non-parametric tests were used in order to compare measurements of paired samples and of groups of samples. Results: No significant differences between males and females were found in any evaluated measurements, estimated either by anthropometry or by ultrasound. Also the median of total arm area did not differ significantly with either method (P50.337). Although there is evidence of concordance of the total arm area measurements (r50.68, 95% CI: 0.55–0.77) the two methods of measurement differed for arm muscle area and arm fat area. The estimated median of measurements by ultrasound for arm muscle area were significantly lower than those estimated by the anthropometric method, which differed by as much as 111% (P,0.001). The estimated median ultrasound measurement of the arm fat was higher than the anthropometric arm fat area by as much as 31% (P,0.001). Conclusion: Compared with ultrasound measurements using skinfold measurements and mid-arm circumference without further correction may lead to overestimation of the cross-sectional area of muscle and underestimation of the cross-sectional fat area. The correlation between the two methods could be interpreted as an indication for further search of correction factors in the equations.

EVALUATION OF METHODS IN DETECTING VANCOMYCIN MIC AMONG MRSA ISOLATES AND THE CHANGES IN ACCURACY RELATED TO DIFFERENT MIC VALUES

INTRODUCTION: Methicillin-Resistant Staphylococcus aureus (MRSA) presenting reduced susceptibility to vancomycin has been associated to therapeutic failure. Some methods used by clinical laboratories may not be sufficiently accurate to detect this phenotype, compromising results and the outcome of the patient. OBJECTIVES: To evaluate the performance of methods in the detection of vancomycin MIC values among clinical isolates of MRSA. MATERIAL AND METHODS: The Vancomycin Minimal Inhibitory Concentration was determined for 75 MRSA isolates from inpatients of Mãe de Deus Hospital, Porto Alegre, Brazil. The broth microdilution (BM) was used as the gold-standard technique, as well as the following methods: E-test® strips (BioMérieux), M.I.C.E® strips (Oxoid), PROBAC® commercial panel and the automated system MicroScan® (Siemens). Besides, the agar screening test was carried out with 3 µg/mL of vancomycin. RESULTS: All isolates presented MIC ≤ 2 µg/mL for BM. E-test® had higher concordance (40%) in terms of global agreement with the gold standard, and there was not statistical difference among E-test® and broth microdilution results. PROBAC® panels presented MICs, in general, lower than the gold-standard panels (58.66% major errors), while M.I.C.E.® MICs were higher (67.99% minor errors). CONCLUSIONS: For the population of MRSA in question, E-test® presented the best performance, although with a heterogeneous accuracy, depending on MIC values.

Numerical methods and tangible interfaces for pollutant dispersion simulation

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia do Ambiente, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Estimation of statistical cure from cancer using population-based data

Dissertação de mestrado em Estatística

Correlations Between the Collagen Content of the Human Left Ventricular Myocardium, Measured by Biochemical and Morphometric Methods

OBJECTIVE: To assess, in myocardium specimens obtained from necropsies, the correlation between the concentration of hydroxyproline, measured with the photocolorimetric method, and the intensity of fibrosis, determined with the morphometric method. METHODS: Left ventricle myocardium samples were obtained from 45 patients who had undergone necropsy, some of them with a variety of cardiopathies and others without any heart disease. The concentrations of hydroxyproline were determined with the photocolorimetric method. In the histologic sections from each heart, the myocardial fibrosis was quantified by using a light microscope with an integrating ocular lens. RESULTS: A median of, respectively, 4.5 and 4.3 mug of hydroxyproline/mg of dry weight was found in fixed and nonfixed left ventricle myocardium fragments. A positive correlation occurred between the hydroxyproline concentrations and the intensity of fibrosis, both in the fixed (Sr=+0.25; p=0.099) and in the nonfixed (Sr=+0.32; p=0.03) specimens. CONCLUSION: The biochemical methodology was proven to be adequate, and manual morphometry was shown to have limitations that may interfere with the statistical significance of correlations for the estimate of fibrosis intensity in the human myocardium.

DESARROLLO DE APLICACIONES ESTADÍSTICAS PARA LA AGRICULTURA DE PRECISIÓN. STATISTICAL APPLICATIONS FOR PRECISION AGRICULTURE

A partir de las últimas décadas se ha impulsado el desarrollo y la utilización de los Sistemas de Información Geográficos (SIG) y los Sistemas de Posicionamiento Satelital (GPS) orientados a mejorar la eficiencia productiva de distintos sistemas de cultivos extensivos en términos agronómicos, económicos y ambientales. Estas nuevas tecnologías permiten medir variabilidad espacial de propiedades del sitio como conductividad eléctrica aparente y otros atributos del terreno así como el efecto de las mismas sobre la distribución espacial de los rendimientos. Luego, es posible aplicar el manejo sitio-específico en los lotes para mejorar la eficiencia en el uso de los insumos agroquímicos, la protección del medio ambiente y la sustentabilidad de la vida rural. En la actualidad, existe una oferta amplia de recursos tecnológicos propios de la agricultura de precisión para capturar variación espacial a través de los sitios dentro del terreno. El óptimo uso del gran volumen de datos derivado de maquinarias de agricultura de precisión depende fuertemente de las capacidades para explorar la información relativa a las complejas interacciones que subyacen los resultados productivos. La covariación espacial de las propiedades del sitio y el rendimiento de los cultivos ha sido estudiada a través de modelos geoestadísticos clásicos que se basan en la teoría de variables regionalizadas. Nuevos desarrollos de modelos estadísticos contemporáneos, entre los que se destacan los modelos lineales mixtos, constituyen herramientas prometedoras para el tratamiento de datos correlacionados espacialmente. Más aún, debido a la naturaleza multivariada de las múltiples variables registradas en cada sitio, las técnicas de análisis multivariado podrían aportar valiosa información para la visualización y explotación de datos georreferenciados. La comprensión de las bases agronómicas de las complejas interacciones que se producen a la escala de lotes en producción, es hoy posible con el uso de éstas nuevas tecnologías. Los objetivos del presente proyecto son: (l) desarrollar estrategias metodológicas basadas en la complementación de técnicas de análisis multivariados y geoestadísticas, para la clasificación de sitios intralotes y el estudio de interdependencias entre variables de sitio y rendimiento; (ll) proponer modelos mixtos alternativos, basados en funciones de correlación espacial de los términos de error que permitan explorar patrones de correlación espacial de los rendimientos intralotes y las propiedades del suelo en los sitios delimitados. From the last decades the use and development of Geographical Information Systems (GIS) and Satellite Positioning Systems (GPS) is highly promoted in cropping systems. Such technologies allow measuring spatial variability of site properties including electrical conductivity and others soil features as well as their impact on the spatial variability of yields. Therefore, site-specific management could be applied to improve the efficiency in the use of agrochemicals, the environmental protection, and the sustainability of the rural life. Currently, there is a wide offer of technological resources to capture spatial variation across sites within field. However, the optimum use of data coming from the precision agriculture machineries strongly depends on the capabilities to explore the information about the complex interactions underlying the productive outputs. The covariation between spatial soil properties and yields from georeferenced data has been treated in a graphical manner or with standard geostatistical approaches. New statistical modeling capabilities from the Mixed Linear Model framework are promising to deal with correlated data such those produced by the precision agriculture. Moreover, rescuing the multivariate nature of the multiple data collected at each site, several multivariate statistical approaches could be crucial tools for data analysis with georeferenced data. Understanding the basis of complex interactions at the scale of production field is now within reach the use of these new techniques. Our main objectives are: (1) to develop new statistical strategies, based on the complementarities of geostatistics and multivariate methods, useful to classify sites within field grown with grain crops and analyze the interrelationships of several soil and yield variables, (2) to propose mixed linear models to predict yield according spatial soil variability and to build contour maps to promote a more sustainable agriculture.