  This paper introduces a novel method for quantifying vowel overlap. There is
a tension in previous work between using multivariate measures, such as those
derived from empirical distributions, and the ability to control for unbalanced
data and extraneous factors, as is possible when using fitted model parameters.
The method presented here resolves this tension by jointly modelling all
acoustic dimensions of interest and by simulating distributions from the model
to compute a measure of vowel overlap. An additional benefit of this method is
that computation of uncertainty becomes straightforward. We evaluate this
method on corpus speech data targeting the PIN-PEN merger in four dialects of
English and find that using modelled distributions to calculate Bhattacharyya
affinity substantially improves results compared to empirical distributions,
while the difference between multivariate and univariate modelling is subtle.
