An Extension to the Scale Mixture of Normals for Bayesian Small-Area Estimation

• Main Authors: FRANCISCO J. TORRES-AVILÉS, GLORIA ICAZA, REINALDO B. ARELLANO-VALLE
• Format: Article
• Language: English
• Published: Universidad Nacional de Colombia 2012-06-01
• Series: Revista Colombiana de Estadística
• Subjects: Disease mapping; Markov random field; Hierarchical model; Incidence rate; Relative risk
• Online Access: http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512012000200001&lng=en&tlng=en

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.