Parsimonious Higher-Order Hidden Markov Models for Improved Array-CGH Analysis with Applications to Arabidopsis thaliana
Figure 4
Identification of deletions and sequence deviations in the Arabidopsis Array-CGH data set by parsimonious HMMs.
Curves of mean true-positive-rates (TPRs) for the identification of candidate regions of deletions or sequence deviations at a fixed false-positive-rate (FPR) of 1% (a)) and of 2.5% (b)) obtained by parsimonious HMMs of order of different model complexities across twenty different initializations. The rightmost point of each curve of parsimonious HMMs of order
(PHMM(
)) represents the corresponding higher-order HMM of order
with highest model complexity of
leaf nodes in the state-context tree underlying the transition matrix
. The rightmost point of the black curve represents the standard first-order HMM. Standard deviations of the mean TPRs are shown in Figure S4 in Text S1. At both levels of FPRs, parsimonious higher-order HMMs are clearly better than parsimonious HMMs of order one including the standard first-order HMM. At the level of 1% FPR, parsimonious higher-order HMMs with a mean model complexity in the range of 3 up to 9 also identify deletions or sequence deviations better than higher-order HMMs. At 2.5% FPR, clearly reduced model complexities are sufficient to reach identifications of deletions or sequence deviations by parsimonious higher-order HMMs comparable or slightly better than corresponding higher-order HMMs.