As a result of recombination or rate variation, a DNA sequence alignment may have a mosaic structure, where different segments correspond to different evolutionary histories. While several methods have been developed to predict DNA mosaic structures, they do not properly address the question of whether the predicted segmentation itself is statistically significant, or whether it is significantly better than an alternative mosaic structure predicted with another method. The objective of the present article is to devise an approximate Bayesian hypothesis test to discriminate between alternative candidate mosaic structures.