Estimation of graphical models whose conditional independence graphs are interval graphs and its application to modelling linkage disequilibrium

Estimation of graphical models whose conditional independence graph comes from the general class of decomposable graphs is compared with estimation under the more restrictive assumption that the graphs are interval graphs. This restriction is shown to improve the mixing of the Markov chain Monte Carlo search to find an optimal model with little effect on the haplotype frequencies implied by the estimates. A further restriction requiring intervals to cover specified points is also considered and shown to be appropriate for modelling associations between alleles at genetic loci. As well as usefully describing the patterns of associations, these estimates can also be used to model population haplotype frequencies in statistical gene mapping methods such as linkage analysis and association studies.