| { | |
| "paper_id": "U13-1005", | |
| "header": { | |
| "generated_with": "S2ORC 1.0.0", | |
| "date_generated": "2023-01-19T03:10:19.206245Z" | |
| }, | |
| "title": "The Effect of the Within-speaker Sample Size on the Performance of Likelihood Ratio Based Forensic Voice Comparison: Monte Carlo Simulations", | |
| "authors": [ | |
| { | |
| "first": "Shunichi", | |
| "middle": [], | |
| "last": "Ishihara", | |
| "suffix": "", | |
| "affiliation": { | |
| "laboratory": "", | |
| "institution": "Australian National University", | |
| "location": {} | |
| }, | |
| "email": "[email protected]" | |
| } | |
| ], | |
| "year": "", | |
| "venue": null, | |
| "identifiers": {}, | |
| "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 obtained 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 Br\u00fcmmer and du Preez (2006). The performance of the FVC system was assessed in terms of the log-likelihood-ratio cost (C llr) and the 95% credible interval (CI), which are the metrics of validity and reliability, respectively. We will demonstrate in this paper that 1) the validity of the system notably improves 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 database, regardless of the token numbers in the test and development databases.", | |
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| "paper_id": "U13-1005", | |
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| "abstract": [ | |
| { | |
| "text": "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 obtained 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 Br\u00fcmmer and du Preez (2006). The performance of the FVC system was assessed in terms of the log-likelihood-ratio cost (C llr) and the 95% credible interval (CI), which are the metrics of validity and reliability, respectively. We will demonstrate in this paper that 1) the validity of the system notably improves 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 database, regardless of the token numbers in the test and development databases.", | |
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| "section": "Abstract", | |
| "sec_num": null | |
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| "text": "It is well known and accepted that statistical accuracy relies on having a sufficient amount of data. However, in typical forensic voice comparison (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 recording condition, something that forensic caseworkers cannot control. Thus, we need to know how the performance of an FVC system is influenced by sample size.", | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "The current study employs the Likelihood Ratio (LR) framework, which has been advocated as the logically and legally correct way of analysing 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. Emulating DNA forensic science, many fields of forensic 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).", | |
| "cite_spans": [ | |
| { | |
| "start": 244, | |
| "end": 269, | |
| "text": "Robertson & Vignaux 1995)", | |
| "ref_id": "BIBREF20" | |
| }, | |
| { | |
| "start": 308, | |
| "end": 328, | |
| "text": "Aitken & Stoney 1991", | |
| "ref_id": "BIBREF1" | |
| }, | |
| { | |
| "start": 329, | |
| "end": 351, | |
| "text": ", Aitken & Taroni 2004", | |
| "ref_id": "BIBREF3" | |
| }, | |
| { | |
| "start": 497, | |
| "end": 518, | |
| "text": "(Neumann et al. 2007)", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 533, | |
| "end": 552, | |
| "text": "(Bozza et al. 2008)", | |
| "ref_id": "BIBREF4" | |
| }, | |
| { | |
| "start": 561, | |
| "end": 576, | |
| "text": "(Morrison 2009)", | |
| "ref_id": "BIBREF14" | |
| } | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
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| { | |
| "text": "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 reference samples. This is because an LR is a ratio of similarity to typicality, which quantifies how similar/different the questioned and the known samples are, and then evaluates that similarity/difference in terms of typicality/atypicality against the relevant background population (i.e. reference samples). Some investigations have been made on how factors such as the size and linguistic compatibility of the background population data can influence LR-based FVC (Kinoshita & Norris 2010 , Ishihara & Kinoshita 2008 , Kinoshita et al. 2009 . Ishihara and Ki-noshita (2008) , for example, investigated how many speakers are ideally required in the background population data in order to reliably evaluate speech evidence in FVC.", | |
| "cite_spans": [ | |
| { | |
| "start": 652, | |
| "end": 676, | |
| "text": "(Kinoshita & Norris 2010", | |
| "ref_id": "BIBREF12" | |
| }, | |
| { | |
| "start": 677, | |
| "end": 704, | |
| "text": ", Ishihara & Kinoshita 2008", | |
| "ref_id": "BIBREF8" | |
| }, | |
| { | |
| "start": 705, | |
| "end": 728, | |
| "text": ", Kinoshita et al. 2009", | |
| "ref_id": "BIBREF11" | |
| }, | |
| { | |
| "start": 731, | |
| "end": 761, | |
| "text": "Ishihara and Ki-noshita (2008)", | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
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| "text": "However, to the best of our knowledge, studies focusing on the sample size of the offender and suspect data are conspicuously sparse. Needless to say, the sample size of the offender and suspect datafor example, the number of yes tokens we can use in order to build the offender's and suspect's modelshas a great affect on the performance of FVC systems.", | |
| "cite_spans": [], | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
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| { | |
| "text": "Thus, this study investigated how the offender and suspect sample sizes (or within-speaker sample size) would influence the performance of an FVC system by employing Monte Carlo simulations (Fishman 1995) . In order to answer this question, two experiments: Experiments 1 and 2, were conducted. Detailed explanations of these two experiments are given \u00a74.4.", | |
| "cite_spans": [ | |
| { | |
| "start": 190, | |
| "end": 204, | |
| "text": "(Fishman 1995)", | |
| "ref_id": "BIBREF6" | |
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| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Introduction", | |
| "sec_num": "1" | |
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| { | |
| "text": "LRs were estimated using Aitken and Lucy's (2004) MVLR formula (see \u00a74.3). The derived LRs were calibrated using the logistic-regression calibration technique proposed by Br\u00fcmmer and du Preez (2006) (see \u00a74.5). The performance of the FVC system was assessed in terms of the loglikelihood-ratio cost (C llr ) (Br\u00fcmmer & du Preez 2006) and the 95% credible interval (CI) (Morrison 2011b ) (see \u00a74.6).", | |
| "cite_spans": [ | |
| { | |
| "start": 25, | |
| "end": 49, | |
| "text": "Aitken and Lucy's (2004)", | |
| "ref_id": "BIBREF0" | |
| }, | |
| { | |
| "start": 171, | |
| "end": 198, | |
| "text": "Br\u00fcmmer and du Preez (2006)", | |
| "ref_id": "BIBREF5" | |
| }, | |
| { | |
| "start": 308, | |
| "end": 333, | |
| "text": "(Br\u00fcmmer & du Preez 2006)", | |
| "ref_id": "BIBREF5" | |
| }, | |
| { | |
| "start": 369, | |
| "end": 384, | |
| "text": "(Morrison 2011b", | |
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| "section": "Introduction", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "The LR is the probability that the evidence would occur if an assertion is true, relative to the probability that the evidence would occur if the assertion is not true (Robertson & Vignaux 1995) . Thus, the LR can be expressed as Equation 1).", | |
| "cite_spans": [ | |
| { | |
| "start": 168, | |
| "end": 194, | |
| "text": "(Robertson & Vignaux 1995)", | |
| "ref_id": "BIBREF20" | |
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| "section": "Likelihood Ratio", | |
| "sec_num": "2" | |
| }, | |
| { | |
| "text": "For FVC, it will be the probability of observing the difference (referred to as the evidence, E) between the offender's and the suspect's speech samples if they had come from the same speaker (H p ) (i.e. if the prosecution hypothesis is true) relative to the probability of observing the same evidence (E) if they had been produced by different speakers (H d ) (i.e. if the defence hypothesis is true). The relative strength of the given evidence with respect to the competing hypotheses (H p vs. H d ) is reflected in the magnitude of the LR. The more the LR deviates from unity (LR = 1; logLR = 0), the greater support for either the prosecution hypothesis (LR > 1; logLR > 0) or the defence hypothesis (LR < 1; logLR < 0).", | |
| "cite_spans": [], | |
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| "section": "Likelihood Ratio", | |
| "sec_num": "2" | |
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| "text": "For example, an LR of 20 means that the evidence (= the difference between the offender and suspect speech samples) is 20 times more likely to occur if the offender and the suspect had been the same individual than if they had been different individuals. Note that an LR value of 20 does NOT mean that the offender and the suspect are 20 times more likely to be the same person than different people, given the evidence.", | |
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| "section": "Likelihood Ratio", | |
| "sec_num": "2" | |
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| "text": "The important point is that the LR is concerned with the probability of the evidence, given the hypothesis (either prosecution or defence), which is the province of forensic scientists, while the trier-of-fact is concerned with the probability of the hypothesis (either prosecution or defence), given the evidence. That is, the ultimate decision as to whether the suspect is guilty or not (e.g. the offender and suspect samples are from the same speaker or not) does not lie with the forensic expert, but with the court. The role of the forensic scientist is to estimate the strength of evidence (= LR) in order to assist the trier-of-fact to make a final decision (Morrison 2009: 229) .", | |
| "cite_spans": [ | |
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| "end": 685, | |
| "text": "(Morrison 2009: 229)", | |
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| "section": "Likelihood Ratio", | |
| "sec_num": "2" | |
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| "text": "In this study, we used the monologues from the Corpus of Spontaneous Japanese (CSJ) (Maekawa et al. 2000) . There are two types of monologues in CSJ: Academic Presentation Speech (APS) and Simulated Public Speech (SPS). Both types were used in this study. APS was recorded live at academic presentations, most of them 12-25 minutes long. SPS contains 10-12 minute mock speeches on everyday topics. For this study, we focused on the filler /e:/ and the /e:/ segment of the filler /e:to:/. Fillers are a sound or a word (e.g. um, you know, like in English) which is uttered by a speaker to signal that he/she is thinking or hesitating. We decided to use these fillers because 1) they are two of the most frequently used fillers (thus many monologues contain at least ten of these fillers) (Ishihara 2010) , 2) the vowel /e/ reportedly has the strongest speaker-discriminatory power out of the five Japanese vowels /a, i. u, e, o/ (Kinoshita 2001) , and 3) the segment /e:/ is significantly long so that it is easy to extract stable spectral features from this segment. It is also considered that fillers are uttered unconsciously by the speaker and carry no lexical meaning. They are thus not likely to be affected by the 1) pragmatic focus of the utterance. This is another reason we decided to focus on fillers in this study.", | |
| "cite_spans": [ | |
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| "start": 84, | |
| "end": 105, | |
| "text": "(Maekawa et al. 2000)", | |
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| "start": 787, | |
| "end": 802, | |
| "text": "(Ishihara 2010)", | |
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| "end": 944, | |
| "text": "(Kinoshita 2001)", | |
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| "section": "Database, target segment, and speakers", | |
| "sec_num": "3" | |
| }, | |
| { | |
| "text": "For the experiments, we selected our speakers based on five criteria: 1) availability of two non-contemporaneous recordings per speaker, 2) high spontaneity of the speech (e.g. not reading), 3) speaking entirely in standard modern Japanese, 4) containing at least ten /e:/ segments, and 5) availability of complete annotation of the data. Having real casework in mind, we selected only male speakers. This is because they are more likely to commit a crime than females (Kanazawa & Still 2000) . These criteria resulted in 236 recordings (118 speakers x 2 non-contemporaneous recordings), and they were used in our experiments.", | |
| "cite_spans": [ | |
| { | |
| "start": 469, | |
| "end": 492, | |
| "text": "(Kanazawa & Still 2000)", | |
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| } | |
| ], | |
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| "section": "Database, target segment, and speakers", | |
| "sec_num": "3" | |
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| { | |
| "text": "These 118 speakers (D all ) were divided into three mutually-exclusive sub databases; test database (D test = 40 speakers), the background database (D background = 39 speakers) and the development database (D development = 39 speakers). Each speaker of these databases has two recordings which are non-contemporaneous. The first ten /e:/ segments were annotated in each recording. Thus, for example, there are 800 annotated /e:/ segments in the test database (= 40 speakers x 2 sessions x 10 segments). The statistics which are necessary for conducting Monte Carlo simulations were calculated from these databases.", | |
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| "section": "Database, target segment, and speakers", | |
| "sec_num": "3" | |
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| "text": "The test database was used to assess the performance of the FVC system. The background database was for a background population, and the development database was for obtaining the logistic-regression weight, which was used to calibrate the LRs of the test database (refer to \u00a74.5 for the detailed explanation of calibration).", | |
| "cite_spans": [], | |
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| "section": "Database, target segment, and speakers", | |
| "sec_num": "3" | |
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| { | |
| "text": "We used 16 Mel Frequency Cepstrum Coefficients (MFCC) in the experiments as feature vectors. MFCC is a standard spectral feature which is used in many voice-related applications, including automatic speaker recognition. All original speech samples were downsampled to 16KHz, and then MFCC values were extracted from the mid-duration-point of the target segment /e:/ with a 20 ms wide hamming window. No normalisation procedure (e.g. Cepstrum Mean Normalisation) was employed as all recordings were made using the same equipment in CSJ.", | |
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| "section": "Features", | |
| "sec_num": "4.1" | |
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| "text": "There are two types of tests for FVC: one is the so-called Same Speaker Comparison (SS comparison) where two speech samples produced by the same speaker are expected to receive the desired LR value given the same-origin, whereas the other is, mutatis mutandis, Different Speaker Comparison (DS comparison).", | |
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| "section": "General experimental design", | |
| "sec_num": "4.2" | |
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| "text": "For example, from the 40 speakers of the test database (D test ), 40 SS comparisons and 1560 independent (e.g. not-overlapping) DS comparisons are possible.", | |
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| "section": "General experimental design", | |
| "sec_num": "4.2" | |
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| "text": "The LR of each comparison was estimated using the Multivariate Likelihood Ratio (MVLR) formula, which is one of the standard formulae used in FVC (Ishihara & Kinoshita 2008 , Rose 2006 , Morrison & Kinoshita 2008 , Rose et al. 2004 . Although the reader needs to refer to Aitken and Lucy (2004) for the full mathematical exposition of the MVLR formula, this formula estimates a single LR from multiple variables (e.g. 16 MFCC), discounting the correlation among them.", | |
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| "text": "(Ishihara & Kinoshita 2008", | |
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| "text": ", Rose 2006", | |
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| "text": ", Morrison & Kinoshita 2008", | |
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| "text": ", Rose et al. 2004", | |
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| "text": "Aitken and Lucy (2004)", | |
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| "section": "Likelihood ratio calculation", | |
| "sec_num": "4.3" | |
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| "text": "The numerator of the MVLR formula calculates the likelihood (= probability) of evidence, which is the difference between the offender and suspect speech samples, when it is assumed that both of the samples have the same origin (or the prosecution hypothesis (H p ) is true). For that, you need the feature vectors of the offender and suspect samples and the within-group (= speaker) variance, which is given in the form of a variance/covariance matrix. The same feature vectors of the offender and suspect samples and the between-group (= speaker) variance are used in the denominator of the formula to estimate the likelihood of getting the same evidence when it is assumed that they have different origins (or the defence hypothesis (H d ) is true). These withingroup and between-group variances are estimated from the background dataset (D background ). The MVLR formula assumes normality for withingroup variance while it uses a kernel-density model for between-group variance.", | |
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| "section": "Likelihood ratio calculation", | |
| "sec_num": "4.3" | |
| }, | |
| { | |
| "text": "As explained earlier, each speaker has two sets of ten /e:/ segments, and 16 MFCC values were extracted. Thus, we can use a maximum of ten feature vectors to model each session of each speaker. In this study, we randomly generated X feature vectors (X = {2,4,6,8,10}) for each ses-sion of each speaker 300 times using the normal distribution function modelled with the mean vector (\uf06d) and variance/covariance matrix (\uf065) obtained from the original databases ({D test , D background , D development }). Figure 1 is an example showing 300 randomly generated first two MFCC values (c1 and c2) from the normal distribution function based on the statistics (\uf06d and \uf065) obtained from the first session of the first speaker in the test database. Experiments were repeatedly conducted using randomly generated feature vectors, as explained above. Two experiments: Experiments 1 and 2 were conducted in this study. In Experiment 1, we investigated how the token number (the number of feature vectors) of each speaker's session affects the performance of the FVC system. In Experiment 1, the same token number ({2,4,6,8,10}) was used across the test, background and development databases.", | |
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| "text": "Figure 1", | |
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| "section": "Repeated experiments using Monte Carlo simulations", | |
| "sec_num": "4.4" | |
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| { | |
| "text": "In Experiment 2, Experiment 1 was repeated with different token numbers in the background database ({2,4,6,8,10}) with the token number of the test and development databases kept constant. The aim of Experiment 2 was to investigate how the number of tokens in the background database affects the performance of the FVC system.", | |
| "cite_spans": [], | |
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| "section": "Repeated experiments using Monte Carlo simulations", | |
| "sec_num": "4.4" | |
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| "text": "A logistic-regression calibration (Br\u00fcmmer & du Preez 2006) was applied to the derived LRs from the MVLR formula. Given two sets of LRs derived from the SS and DS comparisons and a decision boundary, calibration is a normalisation procedure involving linear monotonic shifting and scaling of the LRs relative to the decision boundary so as to minimise a cost function. The FoCal toolkit 1 was used for the logisticregression calibration in this study (Br\u00fcmmer & du Preez 2006) . The logistic-regression weight was obtained from the development database.", | |
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| "text": "(Br\u00fcmmer & du Preez 2006)", | |
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| "text": "(Br\u00fcmmer & du Preez 2006)", | |
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| "section": "Calibration", | |
| "sec_num": "4.5" | |
| }, | |
| { | |
| "text": "The performance of the FVC system was assessed in terms of its validity (= accuracy) and reliability (= precision) using the log-likelihoodratio cost (C llr ) and the 95% credible intervals (CI) as the metrics of validity and reliability, respectively.", | |
| "cite_spans": [], | |
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| "section": "Evaluation of performance: validity and reliability", | |
| "sec_num": "4.6" | |
| }, | |
| { | |
| "text": "Suppose that you have speech samples collected from two speakers at two different sessions which are denoted as S1.1, S1.2, S2.1, and S2.2, where S = speaker, and 1 & 2 = the first and second sessions (S1.1 refers to the first session recording collected from (S)peaker1, and S1.2 the second session from that same speaker). From these speech samples, two independent (not overlapping) DS comparisons are possible; S1.1 vs. S2.1 and S1.2 vs. S2.2. Further suppose that you conducted two separate FVC tests in the same way, but using two different features (Features 1 and 2), and that you obtained the log 10 LRs given in Table 1 for these two DS comparisons.", | |
| "cite_spans": [], | |
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| "text": "Table 1", | |
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| "section": "Evaluation of performance: validity and reliability", | |
| "sec_num": "4.6" | |
| }, | |
| { | |
| "text": "DS comparison Feature 1 Feature 2 S1.1 vs. S2.1 -3.5 -2.1 S1.2 vs. S2.2 -3.3 0.2 Table 1 : Example LRs used to explain the concept of validity and reliability.", | |
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| "section": "Evaluation of performance: validity and reliability", | |
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| "text": "Since the comparisons given in Table 1 are DS comparisons, the desired log 10 LR value would be lower than 0, and the greater the negative log 10 LR value is, the better the system is, as it more strongly supports the correct hypothesis. For Feature 1, both of the comparisons received log 10 LR < 0 while for Feature 2, only one of them got log 10 LR < 0. Feature 1 is better not only in that both log 10 LR values are smaller than 0 (supporting the correct hypothesis) but also in that they are further away from unity (log 10 LR = 0) than the log 10 LR values of Feature 2. Thus, it can be said that the validity (= accuracy) of Feature 1 is higher than that of Feature 2. This is the basic concept of validity. Morrison (2011b: 93) argues that classification-accuracy/classification-error rates, such as equal error rate (EER), are inappropriate for use within the LR framework because they implicitly refer to posterior probabilitieswhich is the province of the trier-of-factrather than LRswhich is the province of forensic scientistsand \"they are based on a categorical threshholding, error versus non-error, rather than a gradient strength of evidence.\" In this study, the loglikelihood-ratio cost (C llr ), which is a gradient metric based on LR for assessing the validity of the system performance was used. See Equation 2) for calculating C llr (Br\u00fcmmer & du Preez 2006) . In Equation 2), N Hp and N Hd are the numbers of SS and of DS comparisons, and LR i and LR j are the LRs derived from the SS and DS comparisons, respectively. If the system is producing desired LRs, all the SS comparisons should produce LRs greater than 1, and the DS comparisons should produce LRs less than 1. In this approach, LRs which support counter-factual hypotheses are given a penalty. The size of this penalty is determined according to how significantly the LRs deviate from the neutral point.", | |
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| "text": "That is, an LR supporting a counter-factual hypothesis with greater strength will be penalised more heavily than the ones which are closer to unity, because they are more misleading. The FoCal toolkit 1 was also used for calculating C llr in this study (Br\u00fcmmer & du Preez 2006) . The lower the C llr value is, the better the performance.", | |
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| "text": "llr ( p \u2211 log ( L i ) p i for p true d \u2211 log ( L ) d for d true ) 2)", | |
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| "text": "Both of the DS comparisons given in Table 1 are the comparisons between S1 and S2. Thus, you can expect that the LR values obtained for these two DS comparisons should be similar as they are comparing the same speakers. However, you can see that the log 10 LR values based on Feature 1 are closer to each other (-3.5 and -3.3) than those based on Feature 2 (-2.1 and 0.2). In other words, the reliability (= precision) of Feature 1 is higher than that of Feature 2. This is the basic concept of reliability. As a metric of reliability, we used credible intervals, the Bayesian analogue of frequentist confidence intervals (Morrison 2011b) . In this study, we calculated 95% credible intervals (CI) in the parametric manner based on the deviation-from-mean values collected from all of the DS comparison pairs. For example, CI = 1.23 and log 10 LR = 2 means that it is 95% certain that it is at least log 10 LR = Figure 2 : Tippett plot showing the uncalibrated (dashed curves) and calibrated (solid curves) LRs plotted separately for the SS (black) and DS (grey) comparisons (a), and Tippett plot showing the calibrated LRs with \uf0b195% CI band (grey dotted lines) superimposed on the DS LRs (b). X-axis = log 10 LR; Y=axis = cumulative proportion. C llr value was calculated from the calibrated LRs and CI value was calculated only for the calibrated DS LRs. 0.77 (= 2-1.23) and it is not greater than log 10 LR = 3.23 (= 2+1.23) for this particular comparison. The smaller the credible intervals, the better the reliability is.", | |
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| "text": "Before presenting the results of Experiments 1 and 2, we conducted an experiment using the original databases (D test , D background , D development ) . The results of this experiment are given as Tippett plots in Figure 2 with the C llr and CI values. In these Tippett plots, the log 10 LRs, which are equal to or greater than the value indicated on the X-axis, are cumulatively plotted, separately for the SS and DS comparisons. Tippett plots graphically show how strongly the derived LRs not only support the correct hypothesis but also misleadingly support the contrary-to-fact hypothesis. In Figure 2a , calibrated and uncalibrated LRs are plotted together in order to show what sorts of effect the logistic-regression calibration brings to the uncalibrated LRs, and in Figure 2b , the calibrated LRs are plotted together with \uf0b1CI band on the DS LRs.", | |
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| "start": 110, | |
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| "text": "(D test , D background , D development )", | |
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| "text": "Figure 2", | |
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| "text": "Theoretically speaking, the crossing point of the SS and DS LRs should be on log 10 LR = 0, but you can see the crossing point of the uncalibrated SS and DS LRs are far away from it in Figure 2b . In this circumstance, it is difficult to interpret the given LR appropriately as the theoretical threshold (log 10 LR = 0) and the obtained threshold (log 10 LR = ca. -7 in the uncalibrated LRs of Figure 2b ) are completely different. A calibration technique needs to be applied in this situation. Please note that the calibrated SS and DS LRs given in Figure 2 are very well calibrated. The C llr value was calculated using these calibrated SS and DS LRs, and it was 0.396. The CI was calculated based on calibrated DS LRs, and it was 4.026.", | |
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| "start": 185, | |
| "end": 194, | |
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| "text": "The results of Experiment 1 are graphically presented in Figure 3 in terms of C llr and CI. In Figure 3a, the C llr and CI values obtained from the Monte Carlo simulations (repeated 300 times) are plotted altogether with their mean values for each of the five different token numbers ({2,4,6,8,10}) . The numerical values for the mean values are given in Table 2 together with their standard deviation (sd) values. Please note that the same token number was used across the test, background and development databases (test = background = development = {2,4,6,8,10}) in Experiment 1.", | |
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| "text": "({2,4,6,8,10})", | |
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| "text": "What we can observe from Figure 3a and Table 2 is that the validity of the system (C llr ) improves as the token number increases whereas the reliability of the system (CI) deteriorates. That is, there is a trade-off between the validity and reliability of the system. The improvement in validity as a function of the token number is nonlinear in that there is a large improvement from the token number = {2} to {4} (0.66->0.51) Figure 3 : The C llr and CI values of the 300 repeated Monte Carlo simulations are plotted separately for the different token numbers {2,4,6,8,10} with their mean values (large filled circles) (a). The mean C llr and CI values of the 300 repeated Monte Carlo simulations (big empty circles) differing in the token numbers ({2,4,6,8,10}) of the background database (b). X-axis = C llr ; Y-axis = CI; test, back and dev = test, background and development databases.", | |
| "cite_spans": [], | |
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| { | |
| "start": 25, | |
| "end": 34, | |
| "text": "Figure 3a", | |
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| "text": "whereas there is not much improvement between the token number = {6} and the token number = {10} (0.45->0.44->0.43). That is, if you have six repeated tokens (e.g. six yes tokens for each session of each speaker) in the databases, the performance of the system can be expected to be as good as when you have as many as ten repeated tokens.", | |
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| "text": "Another observation that can be made is that the C llr and CI values are more widely scattered when the token number is {6,8,10} than {2,4}. This point can be seen in the sd values given in Table 2 in that, for example, the sd values of the C llr and CI are far smaller when the token number is {2} (0.073 and 0.427, respectively) than when the token number is {10} (0.090 and 0.700, respectively). That is, the performance of the system widely fluctuates when the token number is high (e.g. {6,8,10}).", | |
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| "text": "In Experiment 2, Experiment 1 was repeated five times with the five different token numbers ({2,4,6,8,10}) in the background database. The results of Experiment 2 are given in Figure 3b in which only the mean C llr and CI values are plotted in order to prevent the figure from becoming too crowded. The numerical values of Figure 3b are given in Table 3 . For example, the experiment with the token number of {10} in the test and development databases was repeated five times, differing the token number in the background database (background = {2,4,6,8,10}) , and then the mean C llr and CI values of these five experiments are plotted in the same colour (gold for the token number of {10} in the test and development databases) in Figure 3b .", | |
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| "start": 92, | |
| "end": 106, | |
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| "text": "We can observe from Figure 3b and Table 3 that each experimental set (e.g. test = development = 8, background = {2,4,6,8,10}) has one result which is very different in performance from the other four results. For example, the results of the token number of {10} in the test and development databases with the token numbers of {4,6,8,10} in the background database are more or less the same (C llr = ca. 0.44 and CI = ca. 3.3) whereas they are significantly better in terms of C llr than the result with the token number of {2} in the background database (= 0.77). In fact, regardless of the token number in the test and development databases, the performance of the system is worse when there are only two repeated tokens in the background database than when there are four or more repeated tokens ({4,6,8,10}) (refer to the arrows given in Figure 3b ). Figure 3b .", | |
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| "text": "Figure 3b", | |
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| "text": "Furthermore, this difference in performance between the token numbers of {4,6,8,10} and that of {2} in the background database becomes greater as the number of tokens used in the test and development databases increases. For example, as can be seen in Table 3 , the difference in question is relatively small for the test and development databases = {2} (C llr = 0.66 and CI = 1.65 for the background = {2}; average C llr = 0.61 and average CI = 1.81 for the background = {4,6,8,10}) whereas it is far larger for the test and development databases = {10} (C llr = 0.77 and CI = 1.39 for the background = {2}; average C llr = 0.43 and average CI = 3.32 for the background = {4,6,8,10} Figure 3a (only mean values).", | |
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| "start": 252, | |
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| "text": "Table 3", | |
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| "text": "As far as the C llr values are concerned, the performance never deteriorates as the size increases from the background = {4} to {10}. Whereas there are some very small fluctuations in performance in terms of the CI values from the background = {4} to {10}. The reasons for these fluctuations are not clear at this stage.", | |
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| "text": "The results of Experiment 2 tell us that, if you have four repeated tokens (e.g. four yes tokens for each session of each speaker) in the background database, the system can achieve as good a performance as when you have ten repeated tokens. However, if you have only two repeated tokens in the background database, it will result in an underperformance of the system in comparison to when you have four or more repeated tokens.", | |
| "cite_spans": [], | |
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| { | |
| "text": "This study investigated how the offender and suspect sample sizes (or the within-speaker sample size) influences the performance of an FVC system. In order to answer this question, two experiments based on Monte Carlo simulations: Experiments 1 and 2, were conducted.", | |
| "cite_spans": [], | |
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| "section": "Conclusions and Future Directions", | |
| "sec_num": "6" | |
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| "text": "In Experiment 1, five different token numbers ({2,4,6,8,10}) were used in the databases to see how the performance of the system would be influenced by the token number. The results demonstrated that 1) there was a trade-off between the validity (C llr ) and reliability (CI) of the system; 2) there was a large improvement in the validity between the token number = {2} and the token number = {4} whereas no large improvement was observed from the token number = {6} to the token number = {10}. That is, if we have six repetitions of the target segment/word (e.g. yes), the system validity is almost as good as when we have ten repetitions.", | |
| "cite_spans": [ | |
| { | |
| "start": 46, | |
| "end": 60, | |
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| "section": "Conclusions and Future Directions", | |
| "sec_num": "6" | |
| }, | |
| { | |
| "text": "In Experiment 2, Experiment 1 was repeated by changing the token number ({2,4,6,8,10}) of the background database while keeping the same token number for the test and development databases. The results of Experiment 2 demonstrated that regardless of the token number in the test and development databases, the system with the token number = {2} in the background database significantly underperformed in accuracy when compared to the systems with the token number = {4,6,8,10}, of which the performances were very similar. The results of Experiment 2 also demonstrated that the above-mentioned discrepancy in performance between two repeated tokens ({2}) and four or more repeated tokens ({4,6,8,10}) becomes wider as the token number of the test and development databases increases.", | |
| "cite_spans": [], | |
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| "section": "Conclusions and Future Directions", | |
| "sec_num": "6" | |
| }, | |
| { | |
| "text": "These results suggest that when we compile a database which can be used as background population data, we do not need many repetitions in the database as a model based on four repeated tokens can achieve very similar results as one based on ten repeated tokens. However, if we have only two repeated tokens in the background database, we need to be aware that the performance will be compromised, even if you have many repetitions in the test and development databases.", | |
| "cite_spans": [], | |
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| "section": "Conclusions and Future Directions", | |
| "sec_num": "6" | |
| }, | |
| { | |
| "text": "In this study, we mainly focused on the token numbers of the test and background databases. However, it goes without saying that the token number of the development database is also important to the performance of a system. We need to look into this point as well.", | |
| "cite_spans": [], | |
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| "section": "Conclusions and Future Directions", | |
| "sec_num": "6" | |
| }, | |
| { | |
| "text": "In this study, although some other techniques are available for the estimate of LRs, the MVLR formula was used. For example, Morrison (2011a) reported that the procedures based on the Gaussian Mixture Model -Universal Background Model (GMM-UBM) outperformed those based on MVLR procedures, and that the GMM-UBM resulted in an improvement in both the validity and reliability (without trade-offs between them). Since the GMM-UBM is another popular way of estimating LRs in FVC, it is important to investigate the relationship between its performance and the sample size as well.", | |
| "cite_spans": [ | |
| { | |
| "start": 125, | |
| "end": 141, | |
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| "section": "Conclusions and Future Directions", | |
| "sec_num": "6" | |
| }, | |
| { | |
| "text": "https://sites.google.com/site/nikobrummer/focal", | |
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| "text": "The author appreciates the very detailed comments and suggestions made by the three anonymous reviewers.", | |
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| "section": "Acknowledgments", | |
| "sec_num": null | |
| } | |
| ], | |
| "bib_entries": { | |
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