Bayesian tools for zero counts in compositional data

The log-ratio methodology makes available powerful tools for analyzing compositional data. Nevertheless, the use of this methodology is only possible for those data sets without null values. Consequently, in those data sets where the zeros are present, a previous treatment becomes necessary. Last advances in the treatment of compositional zeros have been centered especially in the zeros of structural nature and in the rounded zeros. These tools do not contemplate the particular case of count compositional data sets with null values. In this work we deal with \count zeros" and we introduce a treatment based on a mixed Bayesian-multiplicative estimation. We use the Dirichlet probability distribution as a prior and we estimate the posterior probabilities. Then we apply a multiplicative modi¯cation for the non-zero values. We present a case study where this new methodology is applied. Key words: count data, multiplicative replacement, composition, log-ratio analysis

Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocks based on compositional statistics is introduced. It improves and generalizes the common joins-count statistics known from map analysis in geographic information systems. Assigning phases independently to objects in RD is modelled by a single-trial multinomial random function Z(x), where the probabilities of phases add to one and are explicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistencies of the tests based on the conventional joins{count statistics and their possibly contradictory interpretations are avoided. In practical applications we assume that the probabilities of phases do not depend on the location but are identical everywhere in the domain of de nition. Thus, the model involves the sum of r independent identical multinomial distributed 1-trial random variables which is an r-trial multinomial distributed random variable. The probabilities of the distribution of the r counts can be considered as a composition in the Q-part simplex SQ. They span the so called Hardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This is a generalisation of the well-known Hardy-Weinberg law of genetics. If the assignment of phases accounts for some kind of spatial dependence, then the r-trial probabilities do not remain on H. This suggests the use of the Aitchison distance between observed probabilities to H to test dependence. Moreover, when there is a spatial uctuation of the multinomial probabilities, the observed r-trial probabilities move on H. This shift can be used as to check for these uctuations. A practical procedure and an algorithm to perform the test have been developed. Some cases applied to simulated and real data are presented. Key words: Spatial distribution of crystals in rocks, spatial distribution of phases, joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinberg manifold, Aitchison geometry

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel density estimation techniques in the context of compositional data analysis. Indeed, they gave two options for the choice of the kernel to be used in the kernel estimator. One of these kernels is based on the use the alr transformation on the simplex SD jointly with the normal distribution on RD-1. However, these authors themselves recognized that this method has some deficiencies. A method for overcoming these dificulties based on recent developments for compositional data analysis and multivariate kernel estimation theory, combining the ilr transformation with the use of the normal density with a full bandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu- Figueras (2006). Here we present an extensive simulation study that compares both methods in practice, thus exploring the finite-sample behaviour of both estimators

A new distribution on the simplex containing the Dirichlet family

The Dirichlet family owes its privileged status within simplex distributions to easyness of interpretation and good mathematical properties. In particular, we recall fundamental properties for the analysis of compositional data such as closure under amalgamation and subcomposition. From a probabilistic point of view, it is characterised (uniquely) by a variety of independence relationships which makes it indisputably the reference model for expressing the non trivial idea of substantial independence for compositions. Indeed, its well known inadequacy as a general model for compositional data stems from such an independence structure together with the poorness of its parametrisation. In this paper a new class of distributions (called Flexible Dirichlet) capable of handling various dependence structures and containing the Dirichlet as a special case is presented. The new model exhibits a considerably richer parametrisation which, for example, allows to model the means and (part of) the variance-covariance matrix separately. Moreover, such a model preserves some good mathematical properties of the Dirichlet, i.e. closure under amalgamation and subcomposition with new parameters simply related to the parent composition parameters. Furthermore, the joint and conditional distributions of subcompositions and relative totals can be expressed as simple mixtures of two Flexible Dirichlet distributions. The basis generating the Flexible Dirichlet, though keeping compositional invariance, shows a dependence structure which allows various forms of partitional dependence to be contemplated by the model (e.g. non-neutrality, subcompositional dependence and subcompositional non-invariance), independence cases being identified by suitable parameter configurations. In particular, within this model substantial independence among subsets of components of the composition naturally occurs when the subsets have a Dirichlet distribution

CODAMAT: a modern analogue techinque for compositional data

The quantitative estimation of Sea Surface Temperatures from fossils assemblages is a fundamental issue in palaeoclimatic and paleooceanographic investigations. The Modern Analogue Technique, a widely adopted method based on direct comparison of fossil assemblages with modern coretop samples, was revised with the aim of conforming it to compositional data analysis. The new CODAMAT method was developed by adopting the Aitchison metric as distance measure. Modern coretop datasets are characterised by a large amount of zeros. The zero replacement was carried out by adopting a Bayesian approach to the zero replacement, based on a posterior estimation of the parameter of the multinomial distribution. The number of modern analogues from which reconstructing the SST was determined by means of a multiple approach by considering the Proxies correlation matrix, Standardized Residual Sum of Squares and Mean Squared Distance. This new CODAMAT method was applied to the planktonic foraminiferal assemblages of a core recovered in the Tyrrhenian Sea. Kew words: Modern analogues, Aitchison distance, Proxies correlation matrix, Standardized Residual Sum of Squares

A quality-based cost distribution charging scheme for QoS multicast networks

This paper presents a new charging scheme for cost distribution along a point-to-multipoint connection when destination nodes are responsible for the cost. The scheme focus on QoS considerations and a complete range of choices is presented. These choices go from a safe scheme for the network operator to a fair scheme to the customer. The in-between cases are also covered. Specific and general problems, like the incidence of users disconnecting dynamically is also discussed. The aim of this scheme is to encourage the users to disperse the resource demand instead of having a large number of direct connections to the source of the data, which would result in a higher than necessary bandwidth use from the source. This would benefit the overall performance of the network. The implementation of this task must balance between the necessity to offer a competitive service and the risk of not recovering such service cost for the network operator. Throughout this paper reference to multicast charging is made without making any reference to any specific category of service. The proposed scheme is also evaluated with the criteria set proposed in the European ATM charging project CANCAN

Application for fault location in electrical power distribution systems

Fault location has been studied deeply for transmission lines due to its importance in power systems. Nowadays the problem of fault location on distribution systems is receiving special attention mainly because of the power quality regulations. In this context, this paper presents an application software developed in Matlabtrade that automatically calculates the location of a fault in a distribution power system, starting from voltages and currents measured at the line terminal and the model of the distribution power system data. The application is based on a N-ary tree structure, which is suitable to be used in this application due to the highly branched and the non- homogeneity nature of the distribution systems, and has been developed for single-phase, two-phase, two-phase-to-ground, and three-phase faults. The implemented application is tested by using fault data in a real electrical distribution power system

Visual management of sags and incidents gathered in distribution substations for power quality management

Monitor a distribution network implies working with a huge amount of data coining from the different elements that interact in the network. This paper presents a visualization tool that simplifies the task of searching the database for useful information applicable to fault management or preventive maintenance of the network

Plasmodium vivax lineages: geographical distribution, tandem repeat polymorphism, and phylogenetic relationship

Background: Multi-drug resistance and severe/ complicated cases are the emerging phenotypes of vivax malaria, which may deteriorate current anti-malarial control measures. The emergence of these phenotypes could be associated with either of the two Plasmodium vivax lineages. The two lineages had been categorized as Old World and New World, based on geographical sub-division and genetic and phenotypical markers. This study revisited the lineage hypothesis of P. vivax by typing the distribution of lineages among global isolates and evaluated their genetic relatedness using a panel of new mini-satellite markers. Methods: 18S SSU rRNA S-type gene was amplified from 420 Plasmodium vivax field isolates collected from different geographical regions of India, Thailand and Colombia as well as four strains each of P. vivax originating from Nicaragua, Panama, Thailand (Pak Chang), and Vietnam (ONG). A mini-satellite marker panel was then developed to understand the population genetic parameters and tested on a sample subset of both lineages. Results: 18S SSU rRNA S-type gene typing revealed the distribution of both lineages (Old World and New World) in all geographical regions. However, distribution of Plasmodium vivax lineages was highly variable in every geographical region. The lack of geographical sub-division between lineages suggests that both lineages are globally distributed. Ten mini-satellites were scanned from the P. vivax genome sequence; these tandem repeats were located in eight of the chromosomes. Mini-satellites revealed substantial allelic diversity (7-21, AE = 14.6 +/- 2.0) and heterozygosity (He = 0.697-0.924, AE = 0.857 +/- 0.033) per locus. Mini-satellite comparison between the two lineages revealed high but similar pattern of genetic diversity, allele frequency, and high degree of allele sharing. A Neighbour-Joining phylogenetic tree derived from genetic distance data obtained from ten mini-satellites also placed both lineages together in every cluster. Conclusions: The global lineage distribution, lack of genetic distance, similar pattern of genetic diversity, and allele sharing strongly suggested that both lineages are a single species and thus new emerging phenotypes associated with vivax malaria could not be clearly classified as belonging to a particular lineage on basis of their geographical origin.

Distribution patterns of infection with multiple types of human papillomaviruses and their association with risk factors

Background: Infection with multiple types of human papillomavirus (HPV) is one of the main risk factors associated with the development of cervical lesions. In this study, cervical samples collected from 1,810 women with diverse sociocultural backgrounds, who attended to their cervical screening program in different geographical regions of Colombia, were examined for the presence of cervical lesions and HPV by Papanicolau testing and DNA PCR detection, respectively. Principal Findings: The negative binomial distribution model used in this study showed differences between the observed and expected values within some risk factor categories analyzed. Particularly in the case of single infection and coinfection with more than 4 HPV types, observed frequencies were smaller than expected, while the number of women infected with 2 to 4 viral types were higher than expected. Data analysis according to a negative binomial regression showed an increase in the risk of acquiring more HPV types in women who were of indigenous ethnicity (+37.8%), while this risk decreased in women who had given birth more than 4 times (-31.1%), or were of mestizo (-24.6%) or black (-40.9%) ethnicity. Conclusions: According to a theoretical probability distribution, the observed number of women having either a single infection or more than 4 viral types was smaller than expected, while for those infected with 2-4 HPV types it was larger than expected. Taking into account that this study showed a higher HPV coinfection rate in the indigenous ethnicity, the role of underlying factors should be assessed in detail in future studies.

Revisiting the Relationship between Income Distribution and Economic Growth

La mayoría de los modelos que exploran la relación entre la desigualdad en la distribución del ingreso y el crecimiento económico, postulan la existencia de una correlación negativa entre las dos que es generada a través de diferentes mecanismos. Paralelamente a los modelos teóricos, un número importante de estudios empíricos han tratado de evaluar esta relación. De este esfuerzo ha surgido un consenso amplio que valida la existencia de dicha relación negativa. No obstante, estudios recientes basados en el uso de datos de panel han producido el resultado contrario, documentando la presencia de una relación positiva entre desigualdad y crecimiento. El examen del debate generado a partir de estos resultados, así como el trabajo empírico adelantado en este estudio, indican que las estimaciones obtenidas en diversos trabajos pueden no ser tan robustas como se creía En consecuencia, se sugiere que la realización de estudios de caso por país puede ser una mejor vía para explorar este tema.

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.

Models to predict the distribution and abundance of breeding ducks in Canada

Detailed knowledge of waterfowl abundance and distribution across Canada is lacking, which limits our ability to effectively conserve and manage their populations. We used 15 years of data from an aerial transect survey to model the abundance of 17 species or species groups of ducks within southern and boreal Canada. We included 78 climatic, hydrological, and landscape variables in Boosted Regression Tree models, allowing flexible response curves and multiway interactions among variables. We assessed predictive performance of the models using four metrics and calculated uncertainty as the coefficient of variation of predictions across 20 replicate models. Maps of predicted relative abundance were generated from resulting models, and they largely match spatial patterns evident in the transect data. We observed two main distribution patterns: a concentrated prairie-parkland distribution and a more dispersed pan-Canadian distribution. These patterns were congruent with the relative importance of predictor variables and model evaluation statistics among the two groups of distributions. Most species had a hydrological variable as the most important predictor, although the specific hydrological variable differed somewhat among species. In some cases, important variables had clear ecological interpretations, but in some instances, e.g., topographic roughness, they may simply reflect chance correlations between species distributions and environmental variables identified by the model-building process. Given the performance of our models, we suggest that the resulting prediction maps can be used in future research and to guide conservation activities, particularly within the bounds of the survey area.

Distribution and statistics of African mesoscale convective weather systems based on the ISCCP Meteosat imagery

This paper provides for the first time an objective short-term (8 yr) climatology of African convective weather systems based on satellite imagery. Eight years of infrared International Satellite Cloud Climatology Project-European Space Agency's Meteorological Satellite (ISCCP-Meteosat) satellite imagery has been analyzed using objective feature identification, tracking, and statistical techniques for the July, August, and September periods and the region of Africa and the adjacent Atlantic ocean. This allows various diagnostics to be computed and used to study the distribution of mesoscale and synoptic-scale convective weather systems from mesoscale cloud clusters and squall lines to tropical cyclones. An 8-yr seasonal climatology (1983-90) and the seasonal cycle of this convective activity are presented and discussed. Also discussed is the dependence of organized convection for this region, on the orography, convective, and potential instability and vertical wind shear using European Centre for Medium-Range Weather Forecasts reanalysis data.

Stochastic modelling of rainfall from satellite data

Satellite-based rainfall monitoring is widely used for climatological studies because of its full global coverage but it is also of great importance for operational purposes especially in areas such as Africa where there is a lack of ground-based rainfall data. Satellite rainfall estimates have enormous potential benefits as input to hydrological and agricultural models because of their real time availability, low cost and full spatial coverage. One issue that needs to be addressed is the uncertainty on these estimates. This is particularly important in assessing the likely errors on the output from non-linear models (rainfall-runoff or crop yield) which make use of the rainfall estimates, aggregated over an area, as input. Correct assessment of the uncertainty on the rainfall is non-trivial as it must take account of • the difference in spatial support of the satellite information and independent data used for calibration • uncertainties on the independent calibration data • the non-Gaussian distribution of rainfall amount • the spatial intermittency of rainfall • the spatial correlation of the rainfall field This paper describes a method for estimating the uncertainty on satellite-based rainfall values taking account of these factors. The method involves firstly a stochastic calibration which completely describes the probability of rainfall occurrence and the pdf of rainfall amount for a given satellite value, and secondly the generation of ensemble of rainfall fields based on the stochastic calibration but with the correct spatial correlation structure within each ensemble member. This is achieved by the use of geostatistical sequential simulation. The ensemble generated in this way may be used to estimate uncertainty at larger spatial scales. A case study of daily rainfall monitoring in the Gambia, west Africa for the purpose of crop yield forecasting is presented to illustrate the method.