Hierarchical Bayesian models

J Uncertainty Analysis Using Classical and Bayesian Hierarchical Models... 

Case Study Example of Bayesian Hierarchical Modeling... 

A Bayesian hierarchical modeling framework was used to evaluate the effects data for each species and test endpoint (Figure 7.4). Hierarchical models reduce the effect of incomplete data sets, small numbers of tests, inconsistent information on effects among species, and other issues that lend uncertainty to the risk characterization results. 

To summarize, let 9 be the parameters Rq, Wq, a, and 3 and n be a probability density function. The distribution n describes the variability of the model parameters. The objective of a Bayesian hierarchical model is to generate the distributions of these parameters, based on all available information. 

Bayesian Hierarchical Modeling with Markov Chain Monte Carlo Methods... 

BAYESIAN HIERARCHICAL MODELING WITH MARKOV CHAIN MONTE CARLO METHODS... 

One implementation of Bayesian hierarchical modeling can be found in Wang (2008) where differential expression patterns are compared in the pathway and the rest of the genes. The model is one for the gene expression values ... 

In summary, the fiexible framework of Bayesian hierarchical modeling will likely be exploited more often in future pathway analysis. The method is computationally expensive, but its benefits (allowing the quantification of all aspects of uncertainty in the problem and incorporating physical models and expert opinions) far outweigh this cost. 

Xia HA, Ma H, Carlin BP. 2011. Bayesian hierarchical modeling for detecting safety signals in clinical trials. Journal of Biopharmaceutical Statistics 21(5) 1006-1029. 

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