Bayesian Markov Chain Monte Carlo and Restricted Maximum Likelihood Study of Gene Expression Patterns Across Time

The performance of Restricted Maximum Likelihood (REML) and Bayesian Markov Chain approaches to study gene expression trends across time were compared. Measurements of performance included the consistent identi cation of cDNAs differentially expressed and not differentially expressed and estimates of changes in cDNA expression across age was investigated. The normalized observations were assumed to have a Gaussian distribution in both approaches and two sets of prior distributions for array and residual variances with different levels of information were considered in the Bayesian approach. One set of prior distributions were non-informative (uniform) while the other set of prior distributions (LogNormal) were more informative and based on the distribution of the variances across multiple (all) cDNAs. The identi cation of differentially expressed cDNAs was based on a combination of maximum fold-change among any pair of ages and P value in the REML approach or Bayesian Factors (BF) in Bayesian approaches. A total of 437 cDNAs were declared differentially expressed based on P value < 10 4 and maximum fold change between ages greater than 2 in the REML approach. Of the 437 cDNAs, 409 and 423 cDNAs had BF > 1800 and 216 (comparable to approximate P value < 10 4 and< 10 , respectively) when non-informative prior distributions were used and 429 and 434 cDNAs had BF> 1800 and 216 respectively, when informative prior distributions were used. There results suggest that for relatively small microarray data sets comparable to that studied here, the use of information from multiple cDNAs improves the ability to detect differential expression. Out of 500 cDNAs not differentially expressed in REML (P values >0.1), 458 had BF <3.8 (comparable to approximate P value >0.1) when non-informative prior distributions were used. The correlations of the maximum fold change estimates from the REML and Bayesian non-informative approaches were 0.995, 0.996 and 0.9956 for the 437, 409 and 423 cDNAs previously characterized. The differences between the REML and Bayesian approach with non-informative prior may be due to the low information contained in the data and impact of the prior distribution on the posterior density estimates.