The interpretation of elemental composition measurements from forensic glass evidence: II

A robust interpolation-based method for forensic soil provenancing: A Bayesian likelihood ratio approach

Soil is a complex and spatially variable material that has a demonstrated potential as a useful evidence class in forensic casework and intelligence operations. Here, the capability to spatially constrain police search areas and prioritise resources by triaging areas as low and high interest is advantageous. Conducted between 2017 and 2021, a forensically relevant topsoil survey (0-5 cm depth; 1 sample per 1 km2) was carried out over Canberra, Australia, aiming to document the distribution of chemical elements in an urban/suburban environment, and of acting as a testbed for investigating various aspects of forensic soil provenancing. Geochemical data from X-Ray Fluorescence (XRF; for total major oxides) and Inductively Coupled Plasma-Mass Spectrometry (ICP-MS; for trace elements) following a total digestion (HF + HNO3) of the fused XRF beads were obtained from the survey's 685 topsoil samples (plus 138 additional quality control samples and six "Blind" simulated evidentiary samples). Using those "Blind" samples, we document a likelihood ratio approach where for each grid cell the analytical similarity between the grid cell and evidentiary sample is attributed from a measure of overlap between the two Cauchy distributions, including appropriate uncertainties. Unlike existing methods that base inclusion/exclusion on an arbitrary threshold (e.g., ± three standard deviations), our approach is free from strict binary or Boolean thresholds, providing an unconstrained gradual transition dictated by the analytical similarity. Using this provenancing model, we present and evaluate a new method for upscaling from a fine (25 m x 25 m) interpolated grid to a more appropriate coarser (500 m x 500 m) grid. In addition, an objective method using Random Match Probabilities for ranking individual variables to be used for provenancing prior to receiving evidentiary material was demonstrated. Our results show this collective procedure generates more consistent and robust provenance maps when applied to two different interpolation algorithms (e.g., inverse distance weighting, and natural neighbour), with different grid placements (e.g., grid shifts to the north or east) and by different theoretical users (e.g., different computer systems, or forensic geoscientists).

Expert Algorithm for Substance Identification Using Mass Spectrometry: Application to the Identification of Cocaine on Different Instruments Using Binary Classification Models

This is the second of two manuscripts describing how general linear modeling (GLM) of a selection of the most abundant normalized fragment ion abundances of replicate mass spectra from one laboratory can be used in conjunction with binary classifiers to enable specific and selective identifications with reportable error rates of spectra from other laboratories. Here, the proof-of-concept uses a training set of 128 replicate cocaine spectra from one crime laboratory as the basis of GLM modeling. GLM models for the 20 most abundant fragments of cocaine were then applied to 175 additional test/validation cocaine spectra collected in more than a dozen crime laboratories and 716 known negative spectra, which included 10 spectra of three diastereomers of cocaine. Spectral similarity and dissimilarity between the measured and predicted abundances were assessed using a variety of conventional measures, including the mean absolute residual and NIST's spectral similarity score. For each spectral measure, GLM predictions were compared to the traditional exemplar approach, which used the average of the cocaine training set as the consensus spectrum for comparisons. In unsupervised models, EASI provided better than a 95% true positive rate for cocaine with a 0% false positive rate. A supervised binary logistic regression model provided 100% accuracy and no errors using EASI-predicted abundances of only four peaks at m/z 152, 198, 272, and 303. Regardless of the measure of spectral similarity, error rates for identifications using EASI were superior to the traditional exemplar/consensus approach. As a supervised binary classifier, EASI was more reliable than using Mahalanobis distances.

A multivariate extension to the standard 4σ criterion for comparison of forensic glass evidence

This manuscript presents a more accurate and easy to implement multivariate generalisation of the international standard 4σ forensic glass comparison technique. Many crimes result in glass breaking, and the broken glass found at a crime scene can be important forensic evidence. The chemical composition of this glass can be measured to establish whether it can be distinguished from glass fragments found on a suspect's clothing. The chemical composition can be measured using laser ablation-inductively coupled plasma mass spectrometry. A commonly used method to compare fragments of glass is the 4σ interval criterion. This method, however, compares each element individually and does not take advantage of the multivariate nature of this data. We introduce a multivariate extension to this method, which makes use of the correlation structure between the elements. We demonstrate that this method results in an improvement in the false positive rate, with only a small compromise in the false negative rate. The improvement in false positive rate is desirable as false positives translate to misleading evidence against a potentially innocent defendant. The multivariate generalisation improves accuracy while retaining a similar interpretation, and so is suitable to present in court.

Statistical comparison of mass spectra for identification of amphetamine-type stimulants

A method for the statistical comparison of mass spectral data is demonstrated for applications in controlled substance analysis. The method uses an unequal variance t-test at each mass-to-charge ratio in the scan range to determine if two spectra are statistically associated or discriminated. If the two spectra are associated, a random-match probability is calculated to estimate the likelihood that the mass spectral fragmentation pattern in question occurs by random chance alone. If the two spectra are discriminated, the fragment ions responsible for the discrimination are determined. In this work, mass spectral data from case samples containing amphetamine, methamphetamine, 3,4-methylenedioxyamphetamine (MDA), 3,4-methylenedioxymethamphetamine (MDMA), phentermine, and psilocin were investigated. All spectra were collected in an accredited forensic laboratory using routine methods for controlled substance analysis. Using the statistical method, spectra of case samples were statistically associated to the corresponding reference standard at the 99.9% confidence level. In these instances, random-match probabilities ranged from 10^-39 to 10^-29, indicating the probability that the characteristic fragmentation pattern occurred by random chance is extremely small. Further, spectra of case samples were discriminated from other reference standards at the 99.9% or 99.0% confidence level, with 1-26 ions responsible for discrimination in each comparison.

Lead isotope ratios for bullets, forensic evaluation in a Bayesian paradigm

Forensic science is a discipline concerned with collection, examination and evaluation of physical evidence related to criminal cases. The results from the activities of the forensic scientist may ultimately be presented to the court in such a way that the triers of fact understand the implications of the data. Forensic science has been, and still is, driven by development of new technology, and in the last two decades evaluation of evidence based on logical reasoning and Bayesian statistic has reached some level of general acceptance within the forensic community. Tracing of lead fragments of unknown origin to a given source of ammunition is a task that might be of interest for the Court. Use of data from lead isotope ratios analysis interpreted within a Bayesian framework has shown to be suitable method to guide the Court to draw their conclusion for such task. In this work we have used isotopic composition of lead from small arms projectiles (cal. .22) and developed an approach based on Bayesian statistics and likelihood ratio calculation. The likelihood ratio is a single quantity that provides a measure of the value of evidence that can be used in the deliberation of the court.

Mixed effects modelling for glass category estimation from glass refractive indices

520 Glass fragments were taken from 105 glass items. Each item was either a container, a window, or glass from an automobile. Each of these three classes of use are defined as glass categories. Refractive indexes were measured both before, and after a programme of re-annealing. Because the refractive index of each fragment could not in itself be observed before and after re-annealing, a model based approach was used to estimate the change in refractive index for each glass category. It was found that less complex estimation methods would be equivalent to the full model, and were subsequently used. The change in refractive index was then used to calculate a measure of the evidential value for each item belonging to each glass category. The distributions of refractive index change were considered for each glass category, and it was found that, possibly due to small samples, members of the normal family would not adequately model the refractive index changes within two of the use types considered here. Two alternative approaches to modelling the change in refractive index were used, one employed more established kernel density estimates, the other a newer approach called log-concave estimation. Either method when applied to the change in refractive index was found to give good estimates of glass category, however, on all performance metrics kernel density estimates were found to be slightly better than log-concave estimates, although the estimates from log-concave estimation prossessed properties which had some qualitative appeal not encapsulated in the selected measures of performance. These results and implications of these two methods of estimating probability densities for glass refractive indexes are discussed.

Compositional data analysis for elemental data in forensic science

Discrimination of material based on elemental composition was achieved within a compositional data (CoDa) analysis framework in a form appropriate for use in forensic science. The methods were carried out on example data from New Zealand nephrite. We have achieved good separation of the in situ outcrops of nephrite from within a well-defined area. The most significant achievement of working within the CoDa analysis framework is that the implications of the constraints on the data are acknowledged and dealt with, not ignored. The full composition was reduced based on collinearity of elements, principal components analysis (PCA) and scalings from a backwards linear discriminant analysis (LDA). Thus, a descriptive subcomposition was used for the final discrimination, using LDA, and proved to be more successful than using the full composition. The classification based on the LDA model showed a mean error rate of 2.9% when validated using a 10 repeat, three-fold cross-validation. The methods presented lend objectivity to the process of interpretation, rather than relying on subjective pattern matching type approaches.

A two-level model for evidence evaluation

A random effects model using two levels of hierarchical nesting has been applied to the calculation of a likelihood ratio as a solution to the problem of comparison between two sets of replicated multivariate continuous observations where it is unknown whether the sets of measurements shared a common origin. Replicate measurements from a population of such measurements allow the calculation of both within-group and between-group variances/covariances. The within-group distribution has been modelled assuming a Normal distribution, and the between-group distribution has been modelled using a kernel density estimation procedure. A graphical method of estimating the dependency structure among the variables has been used to reduce this highly multivariate problem to several problems of lower dimension. The approach was tested using a database comprising measurements of eight major elements from each of four fragments from each of 200 glass objects and found to perform well compared with previous approaches, achieving a 15.2% false-positive rate, and a 5.5% false-negative rate. The modelling was then applied to two examples of casework in which glass found at the scene of the criminal activity has been compared with that found in association with a suspect.