Compositional ideas in the bayesian analysis of categorical data with application to dose finding clinical trials

Compositional random vectors are fundamental tools in the Bayesian analysis of categorical data. Many of the issues that are discussed with reference to the statistical analysis of compositional data have a natural counterpart in the construction of a Bayesian statistical model for categorical data. This note builds on the idea of cross-fertilization of the two areas recommended by Aitchison (1986) in his seminal book on compositional data. Particular emphasis is put on the problem of what parameterization to use

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the study of tephrochrology. In this paper, DFA is applied to compositional datasets of two different types of tephras from Mountain Ruapehu in New Zealand and Mountain Rainier in USA. The canonical variables from the analysis are further investigated with a statistical methodology of change-point problems in order to gain a better understanding of the change in compositional pattern over time. Finally, a special case of segmented regression has been proposed to model both the time of change and the change in pattern. This model can be used to estimate the age for the unknown tephras using Bayesian statistical calibration

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

Intrinsic test of independence in contingency tables

A condition needed for testing nested hypotheses from a Bayesian viewpoint is that the prior for the alternative model concentrates mass around the small, or null, model. For testing independence in contingency tables, the intrinsic priors satisfy this requirement. Further, the degree of concentration of the priors is controlled by a discrete parameter m, the training sample size, which plays an important role in the resulting answer regardless of the sample size. In this paper we study robustness of the tests of independence in contingency tables with respect to the intrinsic priors with different degree of concentration around the null, and compare with other “robust” results by Good and Crook. Consistency of the intrinsic Bayesian tests is established. We also discuss conditioning issues and sampling schemes, and argue that conditioning should be on either one margin or the table total, but not on both margins. Examples using real are simulated data are given

A Novel Breast Tissue Density Classification Methodology

It has been shown that the accuracy of mammographic abnormality detection methods is strongly dependent on the breast tissue characteristics, where a dense breast drastically reduces detection sensitivity. In addition, breast tissue density is widely accepted to be an important risk indicator for the development of breast cancer. Here, we describe the development of an automatic breast tissue classification methodology, which can be summarized in a number of distinct steps: 1) the segmentation of the breast area into fatty versus dense mammographic tissue; 2) the extraction of morphological and texture features from the segmented breast areas; and 3) the use of a Bayesian combination of a number of classifiers. The evaluation, based on a large number of cases from two different mammographic data sets, shows a strong correlation ( and 0.67 for the two data sets) between automatic and expert-based Breast Imaging Reporting and Data System mammographic density assessment

Probabilistic models to assist maintenance of multiple instruments

The paper discusses maintenance challenges of organisations with a huge number of devices and proposes the use of probabilistic models to assist monitoring and maintenance planning. The proposal assumes connectivity of instruments to report relevant features for monitoring. Also, the existence of enough historical registers with diagnosed breakdowns is required to make probabilistic models reliable and useful for predictive maintenance strategies based on them. Regular Markov models based on estimated failure and repair rates are proposed to calculate the availability of the instruments and Dynamic Bayesian Networks are proposed to model cause-effect relationships to trigger predictive maintenance services based on the influence between observed features and previously documented diagnostics

Cancer mortality inequalities in urban areas: a Bayesian small area analysis in Spanish cities

Intra-urban inequalities in mortality have been infrequently analysed in European contexts. The aim of the present study was to analyse patterns of cancer mortality and their relationship with socioeconomic deprivation in small areas in 11 Spanish cities

Desigualdades geográficas en mortalidad e incidencia por cáncer de laringe en varones: factores socioeconómicos y ambientales

Diversos estudios sugieren la relación entre menor nivel socioeconómico y factores ambientales con mayor riesgo de cáncer. El objetivo del trabajo es identificar desigualdades geográficas en mortalidad e incidencia por cáncer de laringe (CL) en varones y su asociación con factores de privación y ambientales en el marco del proyecto MEDEA. Métodos: Estudio ecológico cuya población de referencia fueron los hombres residentes en el municipio de Zaragoza. El periodo de estudio fue 1996-2003. Las defunciones fueron obtenidas del Registro de Mortalidad de Aragón, los casos incidentes del Registro Poblacional de Cáncer de Zaragoza y los datos socioeconómicos del Censo de 2001. Se utilizó la base de datos del Registro Europeo de Emisiones Contaminantes en la localización de posibles industrias contaminantes. Para cada sección censal (SC) se obtuvo un índice de privación mediante análisis de componentes principales. Se obtuvieron las Razones de Mortalidad e Incidencia Estandarizadas suavizadas aplicando metodología bayesiana. Resultados: Se analizaron 211 defunciones y 569 casos incidentes, con SC conocida, que correspondieron al 95% del total de casos registrados de mortalidad y el 97,8% de incidencia. Las SC que se encontraban en el cuartil superior, mayor índice de privación, tuvieron significativamente mayor riesgo, tanto de mortalidad (2,74 veces) como de incidencia (1,66 veces). Sin embargo no se encontró asociación estadísticamente significativa con los indicadores ambientales utilizados. Conclusiones: Las SC con menor nivel económico presentan mayor riesgo de mortalidad e incidencia por CL. La posible exposición a focos industriales contaminantes no explica la variabilidad geográfica observada

Cancer mortality inequalities in urban areas: a Bayesian small area analysis in Spanish cities [correcció]

After publication of this work in 'International Journal of Health Geographics' on 13 january 2011 was wrong. The map of Barcelona in Figure two (figure 1 here) was reversed. The final correct Figure is presented here

Filogenia y genética poblacional del género Androcymbium (Colchiceae)

En este trabajo se ha estudiado el género Androcymbium (Colchicaceae) a dos niveles: macro- y micro- evolutivo. A nivel microevolutivo se ha obtenido que para las especies de Sudáfrica oriental la componente interpoblacional es muy importante para explicar la distribución de la variabilidad genética, igual que en Sudáfrica occidental. Para las especies de Namibia, la componente mas importante es la intrapoblacional, igual que en el norte de África. A nivel macroevolutivo se ha obtenido que el origen del género se sitúa en Sudáfrica occidental, datándose en 11,22 ma. Este género ha resultado ser parafilético, dada la aparición conjunta en un mismo clado de especies de Androcymbium y Colchicum, y las especies del norte de África derivan de un taxa de Namibia que llegó a la cuenca Mediterránea a principios del Plioceno gracias a la formación de un corredor árido entre las zonas áridas del suroeste y este de África.

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.