We propose a new approach to the problem of uncertainty modeling in text-dependent speaker verification where speaker factors are used as the feature representation. The state-of-the-art backend in this situation consists in using point estimates of speaker factors to model the joint distribution of pairs of enrollment and test feature vectors under the same-speaker hypothesis. We develop a version of this backend that works with Baum-Welch statistics instead of point estimates. The likelihood ratio calculations for speaker verification turn out to be formally equivalent to evidence calculations with i-vector extractors having non-standard normal priors. Experiments show that this i-vector backend performs well on Part III of the RSR2015 dataset.