Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

Geostatistics for constrained variables: positive data, compositions and probabilities. Applications to environmental hazard monitoring

Aquesta tesi estudia com estimar la distribució de les variables regionalitzades l'espai mostral i l'escala de les quals admeten una estructura d'espai Euclidià. Apliquem el principi del treball en coordenades: triem una base ortonormal, fem estadística sobre les coordenades de les dades, i apliquem els output a la base per tal de recuperar un resultat en el mateix espai original. Aplicant-ho a les variables regionalitzades, obtenim una aproximació única consistent, que generalitza les conegudes propietats de les tècniques de kriging a diversos espais mostrals: dades reals, positives o composicionals (vectors de components positives amb suma constant) són tractades com casos particulars. D'aquesta manera, es generalitza la geostadística lineal, i s'ofereix solucions a coneguts problemes de la no-lineal, tot adaptant la mesura i els criteris de representativitat (i.e., mitjanes) a les dades tractades. L'estimador per a dades positives coincideix amb una mitjana geomètrica ponderada, equivalent a l'estimació de la mediana, sense cap dels problemes del clàssic kriging lognormal. El cas composicional ofereix solucions equivalents, però a més permet estimar vectors de probabilitat multinomial. Amb una aproximació bayesiana preliminar, el kriging de composicions esdevé també una alternativa consistent al kriging indicador. Aquesta tècnica s'empra per estimar funcions de probabilitat de variables qualsevol, malgrat que sovint ofereix estimacions negatives, cosa que s'evita amb l'alternativa proposada. La utilitat d'aquest conjunt de tècniques es comprova estudiant la contaminació per amoníac a una estació de control automàtic de la qualitat de l'aigua de la conca de la Tordera, i es conclou que només fent servir les tècniques proposades hom pot detectar en quins instants l'amoni es transforma en amoníac en una concentració superior a la legalment permesa.

Semivariogram models for estimating fig fly population density throughout the year

The objective of this work was to select semivariogram models to estimate the population density of fig fly (Zaprionus indianus; Diptera: Drosophilidae) throughout the year, using ordinary kriging. Nineteen monitoring sites were demarcated in an area of 8,200 m2, cropped with six fruit tree species: persimmon, citrus, fig, guava, apple, and peach. During a 24 month period, 106 weekly evaluations were done in these sites. The average number of adult fig flies captured weekly per trap, during each month, was subjected to the circular, spherical, pentaspherical, exponential, Gaussian, rational quadratic, hole effect, K-Bessel, J-Bessel, and stable semivariogram models, using ordinary kriging interpolation. The models with the best fit were selected by cross-validation. Each data set (months) has a particular spatial dependence structure, which makes it necessary to define specific models of semivariograms in order to enhance the adjustment to the experimental semivariogram. Therefore, it was not possible to determine a standard semivariogram model; instead, six theoretical models were selected: circular, Gaussian, hole effect, K-Bessel, J-Bessel, and stable.

Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.

Dental caries and the nutritional status of preschool children: a spatial analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Environmental variables and multivariate seabed classification maps via k means clustering of Potter Cove, Antarctica, link to input and result files in GeoTIFF format

This study subdivides the Potter Cove, King George Island, Antarctica, into seafloor regions using multivariate statistical methods. These regions are categories used for comparing, contrasting and quantifying biogeochemical processes and biodiversity between ocean regions geographically but also regions under development within the scope of global change. The division obtained is characterized by the dominating components and interpreted in terms of ruling environmental conditions. The analysis includes in total 42 different environmental variables, interpolated based on samples taken during Australian summer seasons 2010/2011 and 2011/2012. The statistical errors of several interpolation methods (e.g. IDW, Indicator, Ordinary and Co-Kriging) with changing settings have been compared and the most reasonable method has been applied. The multivariate mathematical procedures used are regionalized classification via k means cluster analysis, canonical-correlation analysis and multidimensional scaling. Canonical-correlation analysis identifies the influencing factors in the different parts of the cove. Several methods for the identification of the optimum number of clusters have been tested and 4, 7, 10 as well as 12 were identified as reasonable numbers for clustering the Potter Cove. Especially the results of 10 and 12 clusters identify marine-influenced regions which can be clearly separated from those determined by the geological catchment area and the ones dominated by river discharge.

[impact Variables On The Decline In Infant Mortality In The State Of São Paulo, Brazil: 1998-2008].

This is an ecological, analytical and retrospective study comprising the 645 municipalities in the State of São Paulo, the scope of which was to determine the relationship between socioeconomic, demographic variables and the model of care in relation to infant mortality rates in the period from 1998 to 2008. The ratio of average annual change for each indicator per stratum coverage was calculated. Infant mortality was analyzed according to the model for repeated measures over time, adjusted for the following correction variables: the city's population, proportion of Family Health Programs (PSFs) deployed, proportion of Growth Acceleration Programs (PACs) deployed, per capita GDP and SPSRI (São Paulo social responsibility index). The analysis was performed by generalized linear models, considering the gamma distribution. Multiple comparisons were performed with the likelihood ratio with chi-square approximate distribution, considering a significance level of 5%. There was a decrease in infant mortality over the years (p < 0.05), with no significant difference from 2004 to 2008 (p > 0.05). The proportion of PSFs deployed (p < 0.0001) and per capita GDP (p < 0.0001) were significant in the model. The decline of infant mortality in this period was influenced by the growth of per capita GDP and PSFs.

Variables Associated With The Performance Of Centers For Dental Specialties In Brazil.

The aim of this study was to evaluate the performance of the Centers for Dental Specialties (CDS) in the country and associations with sociodemographic indicators of the municipalities, structural variables of services and primary health care organization in the years 2004-2009. The study used secondary data from procedures performed in the CDS to the specialties of periodontics, endodontics, surgery and primary care. Bivariate analysis by χ2 test was used to test the association between the dependent variable (performance of the CDS) with the independents. Then, Poisson regression analysis was performed. With regard to the overall achievement of targets, it was observed that the majority of CDS (69.25%) performance was considered poor/regular. The independent factors associated with poor/regular performance of CDS were: municipalities belonging to the Northeast, South and Southeast regions, with lower Human Development Index (HDI), lower population density, and reduced time to deployment. HDI and population density are important for the performance of the CDS in Brazil. Similarly, the peculiarities related to less populated areas as well as regional location and time of service implementation CDS should be taken into account in the planning of these services.

Sexual dysfunction in epilepsy: identifying the psychological variables

In order to evaluate the psychological variables that affect sexual dysfunction (SD) in epilepsy, where compared 60 epileptics (Group 1) with 60 healthy individuals (Group 2), through the State-Trait Anxiety Inventory (Spielberger et al., 1970), Beck Depression Inventory (Beck, 1974) and Sexual Behavior Interview (Souza, 1995). Sexual dysfunction (SD), anxiety and depression were found more frequently in Group 1 than in Group 2 and were not related to sex. Variables such as the onset duration and frequency of seizures as well as the use to medication were not associated with SD. Temporal lobe epilepsy was related to SD (p = 0.035) but not to anxiety or depression. Anxiety and depression were related to SD in both groups. Perception in controlling the seizures was closely related to anxiety (p = 0) and depression (p = 0.009). We conclude that psychological factors play an important role in the alteration of sexual behavior in epileptics and that suitable attention must be given to the control of these variables.

Identification of family variables in parents' groups of children with epilepsy

OBJECTIVE: To verify the effectiveness of the support group in the identification of family variables linked to epilepsy. METHOD: Pre-test were applied to parents of 21 children with benign epilepsy of childhood recently diagnosed, from 5 to 15 years, who participated in the groups at HC/Unicamp. There was a presentation of an educational video, discussion and application of the post-test 1. After six months, the post-test 2 was applied. RESULTS: The beliefs were: fear of swallowing the tongue during the seizures (76.19%) and of a future mental disease (66.67%). Facing the epilepsy, fear and sadness appeared. 76.19% of the parents presented overprotection and 90.48%, expected a new seizure. In the post-test 1, the parents affirmed that the information offered had modified the beliefs. In the post-test 2, 80.95% didn't report great doubts about epilepsy and 90.48% considered their relationship with their children better. CONCLUSIONS: The demystification of beliefs supplied from the groups influenced the family positively, prevented behavior alterations and guaranteed effective care in the attendance to the child with epilepsy.

Analysis of the effects of conical indentation variables on the indentation response of elastic-plastic materials through factorial design of experiment

In this work, the effects of conical indentation variables on the load-depth indentation curves were analyzed using finite element modeling and dimensional analysis. A factorial design 2(6) was used with the aim of quantifying the effects of the mechanical properties of the indented material and of the indenter geometry. Analysis was based on the input variables Y/E, R/h(max), n, theta, E, and h(max). The dimensional variables E and h(max) were used such that each value of dimensionless Y/E was obtained with two different values of E and each value of dimensionless R/h(max) was obtained with two different h(max) values. A set of dimensionless functions was defined to analyze the effect of the input variables: Pi(1) = P(1)/Eh(2), Pi(2) = h(c)/h, Pi(3) = H/Y, Pi(4) = S/Eh(max), Pi(6) = h(max)/h(f) and Pi(7) = W(P)/W(T). These six functions were found to depend only on the dimensionless variables studied (Y/E, R/h(max), n, theta). Another dimension less function, Pi(5) = beta, was not well defined for most of the dimensionless variables and the only variable that provided a significant effect on beta was theta. However, beta showed a strong dependence on the fraction of the data selected to fit the unloading curve, which means that beta is especially Susceptible to the error in the Calculation of the initial unloading slope.

Depressive symptoms in old age: relations among sociodemographic and self-reported health variables

Background: Depression in old age is a complex multifactorial phenomenon that is influenced by several biopsychosocial variables. Depressive symptoms are associated with the presence of chronic diseases, with being female, with low education and low income levels, and with poor perceived health assessment. In impoverished areas, older adults may have more physical disability, as they may have less access to health services. Therefore, they may be more likely to report depressive symptoms. Methods: Population-based cross-sectional research was undertaken using data from the FIBRA study conducted in Ermelino Matarazzo, a poor subdistrict of the city of Sao Paulo, Brazil. The participants comprised 303 elderly people, aged 65 years and over, who attended a single-session data collection effort carried out at community centers. The protocol comprised sociodemographic and self-reported health variables, and the Geriatric Depression Scale. Results: The majority of the subjects reported five or fewer symptoms of depression (79.21%), reported one or two self-reported chronic diseases (56.86%), declared themselves to have one or two self-reported health problems (46.15%), and had good perceived health assessment (40.27%). The presence of depressive symptoms was associated with a higher number of self-reported health problems, poor perceived health assessment, and lower schooling levels, in the total sample and in analyses including men only. For women, depressive symptoms were associated with the number of self-reported health problems and family income. Conclusion: The presence of health problems, such as falls and memory problems, lower perceived health, and low education (and low family income for women) were associated with a higher presence of depressive symptoms among elderly people in this poor area of Sao Paulo.

An exploratory analysis of relationships between socioeconomic, land use, activity participation variables and travel patterns

This paper aims to find relations between the socioeconomic characteristics, activity participation, land use patterns and travel behavior of the residents in the Sao Paulo Metropolitan Area (SPMA) by using Exploratory Multivariate Data Analysis (EMDA) techniques. The variables influencing travel pattern choices are investigated using: (a) Cluster Analysis (CA), grouping and characterizing the Traffic Zones (17), proposing the independent variable called Origin Cluster and, (b) Decision Tree (DT) to find a priori unknown relations among socioeconomic characteristics, land use attributes of the origin TZ and destination choices. The analysis was based on the origin-destination home-interview survey carried out in SPMA in 1997. The DT application revealed the variables of greatest influence on the travel pattern choice. The most important independent variable considered by DT is car ownership, followed by the Use of Transportation ""credits"" for Transit tariff, and, finally, activity participation variables and Origin Cluster. With these results, it was possible to analyze the influence of a family income, car ownership, position of the individual in the family, use of transportation ""credits"" for transit tariff (mainly for travel mode sequence choice), activities participation (activity sequence choice) and Origin Cluster (destination/travel distance choice). (c) 2010 Elsevier Ltd. All rights reserved.

Approximate algorithms for credal networks with binary variables

This paper presents a family of algorithms for approximate inference in credal networks (that is, models based on directed acyclic graphs and set-valued probabilities) that contain only binary variables. Such networks can represent incomplete or vague beliefs, lack of data, and disagreements among experts; they can also encode models based on belief functions and possibilistic measures. All algorithms for approximate inference in this paper rely on exact inferences in credal networks based on polytrees with binary variables, as these inferences have polynomial complexity. We are inspired by approximate algorithms for Bayesian networks; thus the Loopy 2U algorithm resembles Loopy Belief Propagation, while the Iterated Partial Evaluation and Structured Variational 2U algorithms are, respectively, based on Localized Partial Evaluation and variational techniques. (C) 2007 Elsevier Inc. All rights reserved.