0000000001217893
AUTHOR
Juan Ferrándiz
Sparse Sampling and Maximum Likelihood Estimation for Boolean Models
A condition for practical independence of contact distribution functions in Boolean models is obtained. This result allows the authors to use maximum likelihcod methods, via sparse sampling, for estimating unknown parameters of an isotropic Boolean model. The second part of this paper is devoted to a simulation study of the proposed method. AMS classification: 60D05
Spatial Interaction between Neighbouring Counties: Cancer Mortality Data in Valencia (Spain)
The statistical analysis of geographical mortality data has usually been approached via regression models that include appropriate covariates. These models assume stochastic independence of mortality counts for neighbouring sites, a questionable assumption that spatial automodels (Besag, 1974, Journal of the Royal Statistical Society, Series B 36, 192-236) make unnecessary. This paper presents the use of the autopoisson distribution in order to detect spatial interaction between neighbouring sites. If this interaction results in being nonsignificant, the auto-Poisson distribution reduces to a usual Poisson regression model, a particular case of generalized linear models (McCullagh and Nelde…
Statistical inference and Monte Carlo algorithms
This review article looks at a small part of the picture of the interrelationship between statistical theory and computational algorithms, especially the Gibbs sampler and the Accept-Reject algorithm. We pay particular attention to how the methodologies affect and complement each other.
Potential approach in marginalizing Gibbs models
Abstract Given an undirected graph G or hypergraph potential H model for a given set of variables V , we introduce two marginalization operators for obtaining the undirected graph G A or hypergraph H A associated with a given subset A ⊂ V such that the marginal distribution of A factorizes according to G A or H A , respectively. Finally, we illustrate the method by its application to some practical examples. With them we show that potential approach allow defining a finer factorization or performing a more precise conditional independence analysis than undirected graph models. Finally, we explain connections with related works.
Simulation in the Simple Linear Regression Model
Summary This article presents an activity which simulates the linear regression model in order to verify the probabilistic behaviour of the resulting least-squares statistics in practice.
Procesos puntuales como herramienta para el análisis de posibles fuentes de contaminación
El análisis de un patrón puntual engloba una serie de técnicas que permiten estudiar la distribución de un conjunto de eventos ocurridos sobre una región del plano. Este problema surge en epidemiología cuando se investiga una potencial fuente de contaminación ambiental alrededor de la cual se sospecha que surgen casos de una determinada enfermedad. En el presente trabajo, se explica brevemente en qué consiste el análisis de un patrón puntual y se ilustra con una aplicación a la determinación del origen medioambiental y al estudio de las zonas de mayor riesgo de incidencia en un brote de neumonía por Legionella ocurrido entre mediados de septiembre y principios de octubre en la ciudad de Alc…
Spatial analysis of the relationship between mortality from cardiovascular and cerebrovascular disease and drinking water hardness
Journal Article; Research Support, Non-U.S. Gov't; Reproduced with permission from Environmental Health Perspectives. Previously published scientific papers have reported a negative correlation between drinking water hardness and cardiovascular mortality. Some ecologic and case-control studies suggest the protective effect of calcium and magnesium concentration in drinking water. In this article we present an analysis of this protective relationship in 538 municipalities of Comunidad Valenciana (Spain) from 1991-1998. We used the Spanish version of the Rapid Inquiry Facility (RIF) developed under the European Environment and Health Information System (EUROHEIS) research project. The strateg…
The foundations of decision theory: An intuitive, operational approach with mathematical extensions
A new axiomatic basis for the foundations of decision theory is introduced and its mathematical development outlined. The system combines direct intuitive operational appeal with considerable structural flexibility in the resulting mathematical framework.
Geographical Distribution of Cardiovascular Mortality in Comunidad Valenciana (Spain)
Comunidad Valenciana is one of the seventeen autonomous regions into which Spain is divided. It is located on the east coast of Spain, next to the Mediterranean sea, with an area of 23,255 km2 and with 4,009,329 inhabitants in 1996. From an administrative point of view there are three levels of aggregation: provinces (3 units), health areas (20 units) and municipalities (541 units).
Statistical relationship between hardness of drinking water and cerebrovascular mortality in Valencia: a comparison of spatiotemporal models
The statistical detection of environmental risk factors in public health studies is usually difficult due to the weakness of their effects and their confounding with other covariates. Small area geographical data bring the opportunity of observing health response in a wide variety of exposure values. Temporal sequences of these geographical datasets are crucial to gaining statistical power in detecting factors. The spatiotemporal models required to perform the statistical analysis have to allow for spatial and temporal correlations, which are more easily modelled via hierarchical structures of hidden random factors. These models have produced important research activity during the last deca…
Temporal aggregation in chain graph models
The dependence structure of an observed process induced by temporal aggregation of a time evolving hidden spatial phenomenon is addressed. Data are described by means of chain graph models and an algorithm to compute the chain graph resulting from the temporal aggregation of a directed acyclic graph is provided. This chain graph is the best graph which covers the independencies of the resulting process within the chain graph class. A sufficient condition that produces a memory loss of the observed process with respect to its hidden origin is analyzed. Some examples are used for illustrating algorithms and results.
Boolean Models: Maximum Likelihood Estimation from Circular Clumps
This paper deals with the problem of making inferences on the maximum radius and the intensity of the Poisson point process associated to a Boolean Model of circular primary grains with uniformly distributed random radii. The only sample information used is observed radii of circular clumps (DUPAC, 1980). The behaviour of maximum likelihood estimation has been evaluated by means of Monte Carlo methods.
Marginalizing in Undirected Graph and Hypergraph Models
Given an undirected graph G or hypergraph X model for a given set of variables V, we introduce two marginalization operators for obtaining the undirected graph GA or hypergraph HA associated with a given subset A c V such that the marginal distribution of A factorizes according to GA or HA, respectively. Finally, we illustrate the method by its application to some practical examples. With them we show that hypergraph models allow defining a finer factorization or performing a more precise conditional independence analysis than undirected graph models.