  Speech utterances recorded under differing conditions exhibit varying degrees
of confidence in their embedding estimates, i.e., uncertainty, even if they are
extracted using the same neural network. This paper aims to incorporate the
uncertainty estimate produced in the xi-vector network front-end with a
probabilistic linear discriminant analysis (PLDA) back-end scoring for speaker
verification. To achieve this we derive a posterior covariance matrix, which
measures the uncertainty, from the frame-wise precisions to the embedding
space. We propose a log-likelihood ratio function for the PLDA scoring with the
uncertainty propagation. We also propose to replace the length normalization
pre-processing technique with a length scaling technique for the application of
uncertainty propagation in the back-end. Experimental results on the
VoxCeleb-1, SITW test sets as well as a domain-mismatched CNCeleb1-E set show
the effectiveness of the proposed techniques with 14.5%-41.3% EER reductions
and 4.6%-25.3% minDCF reductions.
