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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 ..."
Abstract

Cited by 16 (1 self)
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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 ...
Assessment of Spatial Variation of Risks in Small Populations
"... Often environmental hazards are assessed by examining the spatial variation of diseasespecific mortality or morbidity rates. These rates, when estimated for small local populations, can have a high degree of random variation or uncertainty associated with them. If those rate estimates are used to p ..."
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Cited by 1 (0 self)
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Often environmental hazards are assessed by examining the spatial variation of diseasespecific mortality or morbidity rates. These rates, when estimated for small local populations, can have a high degree of random variation or uncertainty associated with them. If those rate estimates are used to prioritize environmental cleanup actions or to allocate resources, then those decisions may be influenced by this high degree ofuncertainty. Unfortunately, the effect of this uncertainty is not to add "random noise " into the decsionmaking process, but to systematicaily bias action toward the smaIlest populations where uncertainty is greatest and where extreme high and low rate deviations are most likely to be manifest by chance. We present a statistical procedure for adjusting rate estimates for differences in variability due to differentials in local area population sizes. Such adjustments produce rate estimates for areas that have better properties than the unadjusted rates for use in making statistically based decisions about the entire set of areas. Examples are provided for county variation in bladder, stomach, and lung cancer mortality rates for U.S white males for the period 1970 to 1979.