Cho and Lee (2004) proposed a Bayesian hierarchical error model (HEM) to account for heterogeneous error variability in oligo-nucleotide microarray experiments. They estimated the parameters of their model using Markov Chain Monte Carlo (MCMC) and proposed an F-like summary statistic to identify differentially expressed genes under multiple conditions. Their HEM is one of the emerging Bayesian hierarchical modeling tools that have been developed for the analysis of multiple-level data structures and variation in microarray gene expression data (Broet et al., 2002; Tadesse and Ibrahim, 2004; Cho and Lee, 2004). In this letter, we first discuss the significance of the HEM developed by Cho and Lee. Then, we re-derive the fully conditional distributions for gene and conditional effects, since we think that these two fully conditional distributions were not presented properly in their paper. Finally, we expand the HEM to deal with biological or/and experimental correlations in gene expression data. A FORTRAN 90 program was developed to implement our extended method and it is available from the authors upon request.
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