Non-contemporaneous speech samples from 27 male speakers of Australian English were compared in a forensic likelihood-ratio framework. Parametric curves (polynomials and discrete cosine transforms) were fitted to the formant trajectories of the diphthongs /a/I, /eI/, /o[see text]/, /a[see text]/, and open /[see text]I/. The estimated coefficient values from the parametric curves were used as input to a generative multivariate-kernel-density formula for calculating likelihood ratios expressing the probability of obtaining the observed difference between two speech samples under the hypothesis that the samples were produced by the same speaker versus under the hypothesis that they were produced by different speakers. Cross-validated likelihood-ratio results from systems based on different parametric curves were calibrated and evaluated using the log-likelihood-ratio cost function (C(llr)). The cross-validated likelihood ratios from the best-performing system for each vowel phoneme were fused using logistic regression. The resulting fused system had a very low error rate, thus meeting one of the requirements for admissibility in court.

Logistic-regression calibration and fusion are potential steps in the calculation of forensic likelihood ratios. The present paper provides a tutorial on logisticregression calibration and fusion at a practical conceptual level with minimal mathematical complexity. A score is log-likelihood-ratio like in that it indicates the degree of similarity of a pair of samples while taking into consideration their typicality with respect to a model of the relevant population. A higher-valued score provides more support for the same-origin hypothesis over the differentorigin hypothesis than does a lower-valued score; however, the absolute values of scores are not interpretable as log likelihood ratios. Logistic-regression calibration is a procedure for converting scores to log likelihood ratios, and logistic-regression fusion is a procedure for converting parallel sets of scores from multiple forensic-comparison systems to log likelihood ratios. Logisticregression calibration and fusion were developed for automatic speaker recognition and are popular in forensic voice comparison. They can also be applied in other branches of forensic science, a fingerprint/finger-mark example is provided.

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