Analysing Spatial Data in R: Worked examples: (Bayesian ...

Analysing Spatial Data in R: Worked examples:( bayesian ) disease mapping IIVirgilio G omez-RubioDepartment of Epidemiology and Public HeathImperial College LondonLondon, UK31 August 2007 bayesian Disease mappingIBayesian Estimation in Disease Mapping has been one of theleading topics in Spatial statistics in the last 20 yearsIBayesian Hierarchical Models can be used to model complexdata structuresIThe bayesian approach offers an easy approach to theestimation of complex models via Markov Chain Monte CarloISpatial analysis of routinoulsy collected health data isstandard practise nowadaysISpatio-temporal models can be usedIWaller & Gotway (2004) and Banerjee et al. (2003) accountfor a comprehensive summary on Spatial modelsBayesian InferenceIBayesian inference is based on estimating the probabilitydensity of the parameters in the modelafterobserving thedata, , their posterior distributions:p( |y)Ip( |y) is usually difficult to derive:p( |y) =p(y| )p( ) p(y| )p( ) p(y| )p( )Ip(y| ) is the likelihood of the model, which reflects therelationship between the data and the par

Benefits of Bayesian Inference I Suitable framework to deal with a large number of problems I Priors can be used to account for initial information (for example, spatial dependence) I If no prior information is available, vague (or non-informative) priors can be used so that the posterior distribution will only depend on the data and the model.

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  Inference, Bayesian, Bayesian inference

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