Sampling--how big a sample?

It is thought that, in a consignment of discrete units, a certain proportion of the units contain illegal material. A sample of the consignment is to be inspected. Various methods for the determination of the sample size are compared. The consignment will be considered as a random sample from some super-population of units, a certain proportion of which contain drugs. For large consignments, a probability distribution, known as the beta distribution, for the proportion of the consignment which contains illegal material is obtained. This distribution is based on prior beliefs about the proportion. Under certain specific conditions the beta distribution gives the same numerical results as an approach based on the binomial distribution. The binomial distribution provides a probability for the number of units in a sample which contain illegal material, conditional on knowing the proportion of the consignment which contains illegal material. This is in contrast to the beta distribution which provides probabilities for the proportion of a consignment which contains illegal material, conditional on knowing the number of units in the sample which contain illegal material. The interpretation when the beta distribution is used is much more intuitively satisfactory. It is also much more flexible in its ability to cater for prior beliefs which may vary given the different circumstances of different crimes. For small consignments, a distribution, known as the beta-binomial distribution, for the number of units in the consignment which are found to contain illegal material, is obtained, based on prior beliefs about the number of units in the consignment which are thought to contain illegal material. As with the beta and binomial distributions for large samples, it is shown that, in certain specific conditions, the beta-binomial and hypergeometric distributions give the same numerical results. However, the beta-binomial distribution, as with the beta distribution, has a more intuitively satisfactory interpretation and greater flexibility. The beta and the beta-binomial distributions provide methods for the determination of the minimum sample size to be taken from a consignment in order to satisfy a certain criterion. The criterion requires the specification of a proportion and a probability.     

Comparison of Frequentist Methods for Estimating the Total Weight of Consignments of Drugs

Abstract: A topic in forensic statistics is the estimation of the total weight of consignments of drugs based on subsamples of which a certain fraction may not contain drugs at all. The frequentist approach to this concentrates on obtaining confidence intervals for the total weight, based on estimation of the fraction of drugs and the mean and variance of the weights of drug units. The current study shows that the resulting confidence intervals are basically unreliable, since they are based on an underestimation of the variation of the underlying statistical process. Two alternatives are given that yield asymptotically correct results. These are not reliable for small subsamples either, though, because of the inherent multimodal behaviour of the sample mean. In cases where a relatively large fraction of the consignment contains no drugs, the confidence intervals reported in the literature should not be used in practice.     

Representative drug sampling: sample size calculations revisited

Calculating the required number of samples to be tested from a consignment of pills suspected of containing drugs can be performed from a Bayesian perspective. Procedures in literature are based on the outstanding work of Aitken. However, in the mathematical treatment of the problem, the limitedness of the consignment is not systematically used. The current Technical Note addresses this problem. A suitable prior distribution for the number of positive pills is derived, being a betabinomial distribution with the consignment size as one of the parameters. A hypergeometric likelihood is used, as sampling generally proceeds without replacement. The betabinomial posterior distribution is mathematically identical to the predictive distribution as reported elsewhere. The currently used large consignment approximation can be derived from the betabinomial posterior, but the quality is not optimal when compared to the exact betabinomial-based results. A new approximation is derived, with better properties, as illustrated in some examples.     

A statistical approach to drug sampling: a case study.

In many countries it is left to the discretion of the court to accept or reject conclusions based on sampling procedures as applied to the total drug exhibit. As an alternative to this subjective approach, a statistical basis is presented using binomial and hypergeometric distributions to determine a lower limit for the proportion of units in a population which contains a drug, at a given confidence level. A method for calculating the total weight of a drug present in a population within a given confidence interval is also presented. In the event of no failures (all units sampled contain a drug), a sample size of six or seven units is generally sufficient to state that a proportion of at least 0.70 of the population contains a drug at a confidence level of at least 90%. When failures do occur in the sample, point estimation is used as the basis for selecting the appropriate sample size.     

NIST Mass Spectrometry Data Center standard reference libraries and software tools: Application to seized drug analysis

The standard reference libraries and associated custom software provided by the National Institute of Standards and Technology's Mass Spectrometry Data Center (NIST MSDC) are described with a focus on assisting the seized drug analyst with the identification of fentanyl-related substances (FRS). These tools are particularly useful when encountering novel substances when no certified sample is available. The MSDC provides three standard reference mass spectral libraries, as well as six software packages for mass spectral analysis, reference library searching, data interpretation, and measurement uncertainty estimation. Each of these libraries and software packages are described with references to the original publications provided. Examples of fentanyl identification by gas chromatography–mass spectrometry (GC–MS) and by direct analysis in real-time (DART) mass spectrometry are given. A link to online tutorials is provided.     

行政委托内涵之重构

到目前为止,我国尚没有一部统一的法律对行政委托进行规制,致使行政委托领域中的问题较为突出。我们只有重新界定行政委托的内涵,确定委托主体和受托主体的范围及其权利义务,明确行政委托的委托依据,限制行政委托的委托事项,把实践界和理论界的认识统一到一个层面上来,才能真正地解决问题,才能促进行政委托行为的规范化和制度化。     

动产交付制度研究

交付是动产物权的主要公示方法,也是源自古代仍活跃于现代的物权制度。动产交付的主要功能是公示,其法律效力有对抗要件主义和生效要件主义之别,我国立法应坚持生效要件主义的一贯立场并将之在物权法中做彻底性规定,确认现实交付、简易交付、拟制交付三种交付类型,不规定占有改定和指示交付。交付行为属于表意行为与事实行为的结合,当事人交付动产的意思表示与交付动产的义务是不同的两个问题。动产交付的公信力即动产占有的公信力,主要表现为物权的正确性推定和对第三人的信赖利益的保障。动产交付请求权性质上为债权请求权,包括请求交什的权利和请求更正交付的权利。我国物权法还要赋予第三人以交付异议请求权。     

The difference between drug money and a "lifetime's savings"

In many countries, monies suspected of being associated with drug trafficking can be seized by the authorities. One of the ways of investigating this association is through the analysis of seized banknotes for traces of controlled drugs. We report three studies which may assist the expert in assessing whether banknotes contaminated with diamorphine are part of the general population of notes in circulation or whether they show unusual contamination patterns which require explanation. Study 1 is based on three plausible contamination scenarios as they may occur during the various stages of an illicit drug transaction and seizure. It shows that notes which have been in direct contact with visible traces of diamorphine show significantly higher contamination to those in more indirect contact with the drug. Study 2 investigates the transfer of diamorphine from one highly contaminated note to other notes in a bundle over a period of 10 weeks with and without agitation. It was found that the total amount of drug transferred was smaller than 6% and no more than 4 out of a bundle of 10 previously clean notes became lightly contaminated. Based on extensive background data, study 3 proposes a probabilistic model to assess whether an observed proportion of diamorphine bearing banknotes is likely to have been contaminated by chance. The model predicts that there is only a 0.3% chance that a bundle of 100 notes from the general banknote population contains more than six contaminated specimens. Jointly, the three studies give useful indications for the spread of contamination throughout a sample and the amounts of heroin which may be expected given plausible contamination scenarios.     

Suicide of a body packer

The smuggling of illicit drugs by means of body packing has become a common problem at European airports. Europe is considered to be the fastest growing market for cocaine worldwide, and the air route is the most frequently used method of trafficking cocaine. Smuggling illicit drugs by use of body packing is considered to be a high toxicological hazard because of the risk of leakage or a package bursting. We report about the first case of suicide of a body packer by re-ingesting the content of excreted cocaine packages. The consequence of this case is that the death scene investigation and autopsy assessments in case of a body packer's death should always consider the possibility of re-ingested packages. Detention personnel should be instructed by forensic and criminalistic experts to take preventive measures.     

Correction to Tzidony and Ravreby (1992): A Statistical Approach to Drug Sampling: A Case Study

Abstract:  In 1992, Tzidony and Ravreby presented a confidence interval for the total weight of a seizure of illicit drugs present in a population. Their approach has subsequently been applied by several researchers in the field. The formula on which their approach is based does, however, not fully take into account the proportion of drug units found in the sample. In this paper, a modification is presented that consistently uses the correct sample size in all terms of the confidence interval, based on the proportion of drug units found in the sample. The effective sample size is smaller than the original sample size, and this should consequently be accounted for in the estimation of the standard error and in the corresponding t -distribution. The new confidence interval is again based on the assumption that the proportion of drug units in the population is known after sampling.     

Three-dimensional computer-assisted craniometrics: a comparison of the uncertainty in measurement induced by surface reconstruction performed by two computer programs

Digital investigation of anthropological material through computed tomography (CT) offers several new opportunities in morphometrics. However, an object measured with computer-assisted methods does not necessarily exactly match the original one. The scanning and surface reconstruction of the object induce some alterations, and data acquisition is prone to measurement uncertainty. The purpose of this research is to evaluate the intra- and inter-observers variations in medical CT scan measurements of a known-size phantom and two dry crania. Two software packages, AMIRA and Treatment and Increased Vision for Medical Imaging (TIVMI), which use different techniques of surface reconstructions, were compared. The mean difference between the measurements was lower for TIVMI, using an objective algorithm based on the half-maximum height (HMH) protocol in three dimensions (3D). AMIRA can induce up to a 4% error in known measurements and 5% uncertainty in dry skull measurements. This study emphasises the risk of object shape alteration in each step of its digitisation.     

Death by obstruction: sudden death resulting from impromptu ingestion of drugs

Over an 18-month period, the department of Forensic Medicine and Science at the University of Glasgow investigated four rather unusual drug-related deaths. In all cases, death was due to the obstruction of the airway by a foreign body after an attempt to evade arrest. In all cases, the obstruction was drug packages of various shapes and sizes. Results of toxicology revealed levels of drugs that may have had a significant respiratory effect on the deceased in three of the cases. Rupturing of the packages and hence leakage of drugs being conducive to death was obvious in only one case.     

Bayesian networks and probabilistic reasoning about scientific evidence when there is a lack of data

Bayesian networks (BNs) are a kind of graphical model that formally combines elements of graph and probability theory. BNs are a mathematically and statistically rigorous technique allowing their user to define a pictorial representation of assumed dependencies and influences among a set of variables deemed to be relevant for a particular inferential problem. The formalism allows one to process newly acquired evidence according to the rules of probability calculus. Applications of BNs have been reported in various forensic disciplines. However, there seems to be some reluctance to consider BNs as a more general framework for representing and evaluating sources of uncertainties associated with scientific evidence. Notably, BNs are widely thought of as an essentially numerical method, requiring "exact" numbers with a high "accuracy". The present paper aims to draw the reader's attention to the point that the availability of hard numerical data is not a necessary requirement for using BNs in forensic science. An abstraction of quantitative BNs, known as qualitative probabilistic networks (QPNs), and sensitivity analyses are presented and their potential applications discussed. As a main difference to their quantitative counterpart, QPNs contain qualitative probabilistic relationships instead of numerical relations. Sensitivity analyses consist of varying the probabilities assigned to one or more variables and evaluating the effect on one or more other variables of interest. Both QPNs and sensitivity analyses appear to be useful concepts that permit one to work in contexts with acute lack of numerical data and where reasoning consistent with the laws of probability should nevertheless be performed.     

Headspace concentrations of explosive vapors in containers designed for canine testing and training: theory, experiment, and canine trials

It is a common misconception that the amount of explosive is the chief contributor to the quantity of vapor that is available to trained canines. In fact, this quantity (known as odor availability) depends not only on the amount of explosive material, but also the container volume, explosive vapor pressure and temperature. In order to better understand odor availability, headspace experiments were conducted and the results were compared to theory. The vapor-phase concentrations of three liquid explosives (nitromethane, nitroethane and nitropropane) were predicted using the Ideal Gas Law for containers of various volumes that are in use for canine testing. These predictions were verified through experiments that varied the amount of sample, the container size, and the temperature. These results demonstrated that the amount of sample that is needed to saturate different sized containers is small, predictable and agrees well with theory. In general, and as expected, once the headspace of a container is saturated, any subsequent increase in sample volume will not result in the release of more vapors. The ability of canines to recognize and alert to differing amounts of nitromethane has also been studied. In particular, it was found that the response of trained canines is independent of the amount of nitromethane present, provided it is a sufficient quantity to saturate the container in which it is held.     

Evaluating probabilistic genotyping for low-pass DNA sequencing

Most genomic methods consider the sample genotype. Data are evaluated at some location, and if the signal strength is sufficient, a genotype call is made. Conversely, sites that lack sufficient signal are treated as missing data. Such methods for genotype calling are binary, and this dichotomy limits genomic analyses to relatively high-coverage (and high-cost) massively parallel sequencing (MPS) data. It follows that bioinformatic methods that rely on genotypes may not be ideal for trace DNA samples, such as those sometimes encountered in forensic investigations, but even when applicable such analyses can be expensive. However, there are some genomic analyses where having many uncertain genotypes (with measured uncertainty) assayed over the entirety of the genome may be more powerful than current multi-locus approaches that consider a limited number of well-characterized markers. Methods for such problems may rely on genotype likelihood, which expresses the likelihood of alternative genotype calls in addition to the most likely call. One application that can benefit from genotype likelihoods is kinship analysis. NgsRelate is a bioinformatic tool that infers pairwise relatedness using a probabilistic genotyping framework, which accommodates the uncertainty associated with genotype calls for low-pass MPS data. Here, NgsRelate was used to infer kinship coefficients from low-pass whole genome sequencing data from a known pedigree. Multiple samples in a titration series (ranging from 50 ng to 0.5 ng) on a single MPS S4 flow cell were assessed. A reproducible scientific bioinformatic workflow was developed to evaluate kinship coefficients considering up to 3rd degree relatives. NgsRelate was found to provide robust assessments of kinship. Further, the use of low-pass MPS data provides a more cost-effective way to conduct forensic investigations.     

Probabilistic expert systems for handling artifacts in complex DNA mixtures

This paper presents a coherent probabilistic framework for taking account of allelic dropout, stutter bands and silent alleles when interpreting STR DNA profiles from a mixture sample using peak size information arising from a PCR analysis. This information can be exploited for evaluating the evidential strength for a hypothesis that DNA from a particular person is present in the mixture. It extends an earlier Bayesian network approach that ignored such artifacts. We illustrate the use of the extended network on a published casework example.     

Implementing statistical learning methods through Bayesian networks (Part 2): Bayesian evaluations for results of black toner analyses in forensic document examination

This paper presents and discusses the use of Bayesian procedures – introduced through the use of Bayesian networks in Part I of this series of papers – for ‘learning’ probabilities from data. The discussion will relate to a set of real data on characteristics of black toners commonly used in printing and copying devices. Particular attention is drawn to the incorporation of the proposed procedures as an integral part in probabilistic inference schemes (notably in the form of Bayesian networks) that are intended to address uncertainties related to particular propositions of interest (e.g., whether or not a sample originates from a particular source). The conceptual tenets of the proposed methodologies are presented along with aspects of their practical implementation using currently available Bayesian network software.     

Development of a specific fragmentation pattern-based quadrupole-Orbitrap™ mass spectrometry method to screen drugs in illicit products

Over the past decade, illicit drugs have been founded in marketed products, which pose a risk to public health. In particular, newly designed analogues synthesized by chemical modification of parent compounds to avoid detection by authorities are frequently detected worldwide. Although many analytical methods for determination of drugs have been reported, analytical methods using high-resolution mass spectrometry, which has the advantage of rapid screening and accurate identification of new substances, are necessary to control illicit drugs in marketed products. In this study, a rapid analytical method using an Orbitrap™ mass spectrometer for identification of illicit drugs in marketed products was developed. The 32 drugs were classified as benzodiazepine-, synthetic cannabinoid-, amphetamine- and benzylpiperazine-type drugs according to their chemical structures, and from their fragmentation patterns in tandem mass spectrometry spectra of an established method. The method validation gave a limit of detection of 0.06–5.30 ng/mL and a limit of quantification of 0.18–16.50 ng/mL, high linearity (R² > 0.994) and mean recoveries of spiked matrix-blank samples ranging from 83.7% to 117.1%. Approximately 71% of 21 samples collected over 3 years were found to individually contain one of four types of benzodiazepines or two different synthetic cannabinoids. In one case, levels as high as 827.2 mg/g were measured suggesting adulteration at high levels, which suggests that potential illicit products containing drugs should be regularly screened to protect public health.     

Factors influencing the contamination of UK banknotes with drugs of abuse

Bank of England banknotes sampled from different locations in the UK have been analysed for the presence of cocaine, diamorphine (DAM), Delta(9)-tetrahydrocannabinol (THC) and 3,4-methylenedioxymethamphetamine (MDMA). A database of the contamination detected is routinely used as a benchmark against which the contamination detected on seized banknotes can be compared. Evidence presented at court details how banknotes seized from a suspect may differ from banknotes in general circulation in terms of their contamination with controlled drugs. A question arising from such evidence is whether seized banknotes could have become contaminated through being in circulation in drug "hot spots". In order to address this issue, a Plackett-Burman experimental design was used to investigate the influence of source location and other factors on banknote contamination with drugs of abuse. Banknotes were drawn from banks in eight regions throughout the UK. Each location could be described by a unique combination of the factors under investigation, namely whether the location was rural or urban, in the North or South of the UK, and whether it was a port of entry. The socio-economic class and the proportion of drug offenders in the area and the denomination of the banknotes were also considered as potentially influential factors. Indices were calculated to describe the degree to which samples were contaminated with different drugs, and normal probability plots were used to identify the factors that could account for the contamination observed. Whilst some factors were more influential than others, it was shown that, at the 95% confidence level, none of the proposed factors were significant influences on the contamination. Cocaine contamination on banknotes has been shown to follow a log-normal distribution. It was, therefore, possible to calculate F- and t-statistics to compare the cocaine contamination on the entire sample set with that detected on a second sample set consisting of banknotes all drawn from a single bank branch. It was shown that both inter-bank samples and intra-bank samples had similar variance and similar contamination levels at the 95% confidence level. This suggests that there are no significant regional trends in the contamination of banknotes with drugs of abuse across the UK.     

Identification and separation of DNA mixtures using peak area information

We introduce a new methodology, based upon probabilistic expert systems, for analysing forensic identification problems involving DNA mixture traces using quantitative peak area information. Peak area is modelled with conditional Gaussian distributions. The expert system can be used for ascertaining whether individuals, whose profiles have been measured, have contributed to the mixture. It can also be used to predict DNA profiles of unknown contributors by separating the mixture into its individual components. The potential of our probabilistic methodology is illustrated on case data examples and compared with alternative approaches. The advantages are that identification and separation issues can be handled in a unified way within a single probabilistic model and the uncertainty associated with the analysis is quantified. Further work, required to bring the methodology to a point where it could be applied to the routine analysis of casework, is discussed.