¹Universidad de Santiago de Chile, Facultad de Ciencia, Departamento de Matemática y Ciencia de la Computación, Santiago, Chile. Assistant professor. Email: francisco.torres@usach.cl
²Universidad de Talca, Instituto de Matemática y Física, Talca, Chile. Associate professor. Email: gicaza@utalca.cl
³Pontificia Universidad Católica de Chile, Facultad de Matemáticas, Departamento de Estadística, Santiago, Chile. Professor. Email: reivalle@mat.puc.cl

This work considers distributions obtained as scale mixture of normal densities for correlated random variables, in the context of the Markov random field theory, which is applied in Bayesian spatial intrinsically autoregressive random effect models. Conditions are established in order to guarantee the posterior distribution existence when the random field is assumed as scale mixture of normal densities. Lung, trachea and bronchi cancer relative risks and childhood diabetes incidence in Chilean municipal districts are estimated to illustrate the proposed methods. Results are presented using appropriate thematic maps. Inference over unknown parameters is discussed and some extensions are proposed.

Key words: Disease mapping, Markov random field, Hierarchical model, Incidence rate, Relative risk.

Este trabajo aborda las distribuciones obtenidas como mezcla de escala de normales para variables aleatorias correlacionadas, en el contexto de la teoría de los campos markovianos, la cual es aplicada a modelos bayesianos espaciales con efectos aleatorios autoregresivos intrínsecos. Se establecen condiciones para garantizar la existencia de la distribución a posteriori cuando se asume una distribución mezcla de escala de normales para el campo markoviano propuesto. Para ilustrar los métodos propuestos, se estiman los riesgos relativos de cáncer de tráquea, bronquios y pulmón, y tasas de incidencia de diabetes tipo 1 en distritos municipales de Chile. Los resultados son presentados usando mapas temáticos apropiados. Se discute la inferencia sobre los parámetros desconocidos y se proponen algunas extensiones.

Palabras clave: campo aleatorio markoviano, mapeo de enfermedades, modelo jerárquico, riesgo relativo, tasa de incidencia.

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