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{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/1247195","sourcedb":"PMC","sourceid":"1247195","source_url":"https://www.ncbi.nlm.nih.gov/pmc/1247195","text":"Bayesian inference is based on the joint posterior distribution of all parameters given the data. In our case this joint distribution is mathematically intractable and is simulated using the framework of Markov chain Monte Carlo techniques now commonly used in Bayesian analyses (Gilks et al. 1996). All parameters involved in the models described above, for example, the variances σ2 or τ2 or the interaction parameter ψ, are given prior distributions at a third level of the hierarchy. Implementation of the BYM and L1-BYM was carried out using the free software WinBUGS (Spiegelhalter et al. 2002). Implementation of the MIX model was carried out using a purpose-built Fortran code.","tracks":[]}