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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 distri- butions, 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.