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Bayesian Tests And Model Diagnostics In Conditionally Independent Hierarchical Models
 Journal of the American Statistical Association
, 1994
"... Consider the conditionally independent hierarchical model (CIHM) where observations y i are independently distributed from f(y i j` i ), the parameters ` i are independently distributed from distributions g(`j), and the hyperparameters are distributed according to a distribution h(). The posterior ..."
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Consider the conditionally independent hierarchical model (CIHM) where observations y i are independently distributed from f(y i j` i ), the parameters ` i are independently distributed from distributions g(`j), and the hyperparameters are distributed according to a distribution h(). The posterior distribution of all parameters of the CIHM can be efficiently simulated by Monte Carlo Markov Chain (MCMC) algorithms. Although these simulation algorithms have facilitated the application of CIHM's, they generally have not addressed the problem of computing quantities useful in model selection. This paper explores how MCMC simulation algorithms and other related computational algorithms can be used to compute Bayes factors that are useful in criticizing a particular CIHM. In the case where the CIHM models a belief that the parameters are exchangeable or lie on a regression surface, the Bayes factor can measure the consistency of the data with the structural prior belief. Bayes factors can ...
A MCMC Algorithm to Fit a General Exchangeable Model
 Communications in Statistics  Simulation and Computation
, 1994
"... Consider the exchangeable Bayesian hierarchical model where observations y i are independently distributed from sampling densities with unknown means, the means ¯ i are a random sample from a distribution g, and the parameters of g are assigned a known distribution h. A simple algorithm is presented ..."
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Consider the exchangeable Bayesian hierarchical model where observations y i are independently distributed from sampling densities with unknown means, the means ¯ i are a random sample from a distribution g, and the parameters of g are assigned a known distribution h. A simple algorithm is presented for summarizing the posterior distribution based on Gibbs sampling and the Metropolis algorithm. The software program Matlab is used to implement the algorithm and provide a graphical output analysis. An binomial example is used to illustrate the flexibility of modeling possible using this algorithm. Methods of model checking and extensions to hierarchical regression modeling are discussed.