The Effect of the Within-speaker Sample Size on the Performance of Likelihood Ratio Based Forensic Voice Comparison: Monte Carlo Simulations

The Effect of the Within-speaker Sample Size on the Performance of Likelihood Ratio Based Forensic Voice Comparison: Monte Carlo Simulations Shunichi Ishihara Department of Linguistics Australian National University shunichi.ishihara@anu.edu.au Abstract This study is an investigation into the effect of sample size on a likelihood ratio (LR) based forensic voice comparison (FVC) system. In particular, we looked into how the offender and suspect sample size (or the within-speaker sample size) would affect the performance of the FVC system, using spectral feature vectors extracted from spontaneous Japanese speech. For this purpose, we repeatedly conducted Monte Carlo method based experiments with different sample size, using the statistics ob- tained from these feature vectors. LRs were estimated using the multivariate kernel density LR formula developed by Aitken and Lucy (2004). The derived LRs were calibrated using the logistic-regression calibration technique proposed by Brümmer and du Preez (2006). The performance of the FVC system was as- sessed in terms of the log-likelihood-ratio cost (Cllr) and the 95% credible interval (CI), which are the metrics of validity and reliability, re- spectively. We will demonstrate in this paper that 1) the validity of the system notably im- proves when up to six tokens are included in modelling a speaker session, and 2) the system performance converges with the relative small token number (four) in the background data- base, regardless of the token numbers in the test and development databases. 1 Introduction It is well known and accepted that statistical ac- curacy relies on having a sufficient amount of data. However, in typical forensic voice compar- ison (FVC) casework, the crime scene recording is often short and contains background noise, which limits the choice of segments that experts can use for the comparison. For example, the word yes is one of the most commonly used segments in FVC. However, the number of yes tokens we can extract from the offender sample to build his/her model really depends on the re- cording condition, something that forensic case- workers cannot control. Thus, we need to know how the performance of an FVC system is influ- enced by sample size. The current study employs the Likelihood Ra- tio (LR) framework, which has been advocated as the logically and legally correct way of ana- lysing and presenting forensic evidence, in the major textbooks on the evaluation of forensic evidence (e.g. Robertson & Vignaux 1995), and by forensic statisticians (e.g. Aitken & Stoney 1991, Aitken & Taroni 2004), and is the standard framework in DNA comparison science. Emulat- ing DNA forensic science, many fields of foren- sic sciences, such as fingerprint (Neumann et al. 2007), handwriting (Bozza et al. 2008), voice (Morrison 2009) and so on, started adopting the LR framework to quantify evidential strength (= LR). In order to calculate an LR, we need three sets of speech samples: a set of questioned samples (offender’s samples); a set of known samples (suspect’s samples); and the background or ref- erence samples. This is because an LR is a ratio of similarity to typicality, …

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