  In this paper we study the probabilistic properties of the posteriors in a
speech recognition system that uses a deep neural network (DNN) for acoustic
modeling. We do this by reducing Kaldi's DNN shared pdf-id posteriors to phone
likelihoods, and using test set forced alignments to evaluate these using a
calibration sensitive metric. Individual frame posteriors are in principle
well-calibrated, because the DNN is trained using cross entropy as the
objective function, which is a proper scoring rule. When entire phones are
assessed, we observe that it is best to average the log likelihoods over the
duration of the phone. Further scaling of the average log likelihoods by the
logarithm of the duration slightly improves the calibration, and this
improvement is retained when tested on independent test data.
