The Missing Person problem through the lens of information theory

Missing person cases typically require a genetic kinship test to determine the relationship between an unidentified individual and the relatives of the missing person. When not enough genetic evidence has been collected the lack of statistical power of these tests might lead to unreliable results. This is particularly true when just a few distant relatives are available for genotyping. In this contribution, we considered a Bayesian network approach for kinship testing and proposed several information theoretic metrics in order to quantitatively evaluate the information content of pedigrees. We show how these statistics are related to the widely used likelihood ratio values and could be employed to efficiently prioritize family members in order to optimize the statistical power in missing person problems. Our methodology seamlessly integrates with Bayesian modeling approaches, like the GENis platform that we have recently developed for high-throughput missing person identification tasks. Furthermore, our approach can also be easily incorporated into Elston-Stewart forensic frameworks. To facilitate the application of our methodology, we have developed the forensIT package, freely available on CRAN repository, which implements all the methodologies described in our manuscript.

Interpretation of DNA data within the context of UK forensic science - investigation

This article is the second part of a review of the interpretation of DNA data in forensic science. The first part describes the evaluation of autosomal profile for criminal trials where an evidential weight is assigned to the profile of a person of interest (POI) and a crime-scene profile. This part describes the state of the art and future advances in the interpretation of forensic DNA data for providing intelligence information during an investigation. Forensic DNA is crucial in the investigative phase of an undetected crime where a POI needs to be identified. A sample taken from a crime scene is profiled using a range of forensic DNA tests. This review covers investigation using autosomal profiles including searching national and international crime and reference DNA databases. Other investigative methodologies described are kinship analysis; familial searching; Y chromosome (Y-STR) and mitochondrial (mtDNA) profiles; appearance prediction and geographic ancestry; forensic genetic genealogy; and body identification. For completeness, the evaluation of Y-STRs, mtDNA and kinship analysis are briefly described. Taken together, parts I and II, cover the range of interpretation of DNA data in a forensic context.

Evaluating DNA evidence possibly involving multiple (mixed) samples, common donors and related contributors

Forensic DNA profiling is used in various circumstances to evaluate support for two competing propositions with the assignment of a likelihood ratio. Many software implementations exist that tackle a range of inference problems spanning identification and relationship testing. We propose a flexible likelihood ratio framework that caters to inference problems in forensic genetics. The framework allows for investigation of the degree of support for the contribution of multiple persons to multiple samples allowing for persons to be related according to a pedigree, including inbred relationships. We explain how a number of routine as well as more complex problems can be treated within this framework.

Evaluating forensic biology results given source level propositions

The evaluation of forensic evidence can occur at any level within the hierarchy of propositions depending on the question being asked and the amount and type of information that is taken into account within the evaluation. Commonly DNA evidence is reported given propositions that deal with the sub-source level in the hierarchy, which deals only with the possibility that a nominated individual is a source of DNA in a trace (or contributor to the DNA in the case of a mixed DNA trace). We explore the use of information obtained from examinations, presumptive and discriminating tests for body fluids, DNA concentrations and some case circumstances within a Bayesian network in order to provide assistance to the Courts that have to consider propositions at source level. We use a scenario in which the presence of blood is of interest as an exemplar and consider how DNA profiling results and the potential for laboratory error can be taken into account. We finish with examples of how the results of these reports could be presented in court using either numerical values or verbal descriptions of the results.

Learning about Bayesian networks for forensic interpretation: an example based on the 'the problem of multiple propositions'

Both, Bayesian networks and probabilistic evaluation are gaining more and more widespread use within many professional branches, including forensic science. Notwithstanding, they constitute subtle topics with definitional details that require careful study. While many sophisticated developments of probabilistic approaches to evaluation of forensic findings may readily be found in published literature, there remains a gap with respect to writings that focus on foundational aspects and on how these may be acquired by interested scientists new to these topics. This paper takes this as a starting point to report on the learning about Bayesian networks for likelihood ratio based, probabilistic inference procedures in a class of master students in forensic science. The presentation uses an example that relies on a casework scenario drawn from published literature, involving a questioned signature. A complicating aspect of that case study - proposed to students in a teaching scenario - is due to the need of considering multiple competing propositions, which is an outset that may not readily be approached within a likelihood ratio based framework without drawing attention to some additional technical details. Using generic Bayesian networks fragments from existing literature on the topic, course participants were able to track the probabilistic underpinnings of the proposed scenario correctly both in terms of likelihood ratios and of posterior probabilities. In addition, further study of the example by students allowed them to derive an alternative Bayesian network structure with a computational output that is equivalent to existing probabilistic solutions. This practical experience underlines the potential of Bayesian networks to support and clarify foundational principles of probabilistic procedures for forensic evaluation.

Response to: DNA identification by pedigree likelihood ratio accommodating population substructure and mutations

Mutation models are important in many areas of genetics including forensics. This letter criticizes the model of the paper 'DNA identification by pedigree likelihood ratio accommodating population substructure and mutations' by Ge et al. (2010). Furthermore, we argue that the paper in some cases misrepresents previously published papers.

Please see related letter: http://www.investigativegenetics.com/content/2/1/8.

Efficient maximum likelihood pedigree reconstruction

A simple and efficient algorithm is presented for finding a maximum likelihood pedigree using microsatellite (STR) genotype information on a complete sample of related individuals. The computational complexity of the algorithm is at worst (O(n(3)2(n))), where n is the number of individuals. Thus it is possible to exhaustively search the space of all pedigrees of up to thirty individuals for one that maximizes the likelihood. A priori age and sex information can be used if available, but is not essential. The algorithm is applied in a simulation study, and to some real data on humans.

Probabilistic evidential assessment of gunshot residue particle evidence (Part I): likelihood ratio calculation and case pre-assessment using Bayesian networks

Well developed experimental procedures currently exist for retrieving and analyzing particle evidence from hands of individuals suspected of being associated with the discharge of a firearm. Although analytical approaches (e.g. automated Scanning Electron Microscopy with Energy Dispersive X-ray (SEM-EDS) microanalysis) allow the determination of the presence of elements typically found in gunshot residue (GSR) particles, such analyses provide no information about a given particle's actual source. Possible origins for which scientists may need to account for are a primary exposure to the discharge of a firearm or a secondary transfer due to a contaminated environment. In order to approach such sources of uncertainty in the context of evidential assessment, this paper studies the construction and practical implementation of graphical probability models (i.e. Bayesian networks). These can assist forensic scientists in making the issue tractable within a probabilistic perspective. The proposed models focus on likelihood ratio calculations at various levels of detail as well as case pre-assessment.

Object-oriented Bayesian networks for paternity cases with allelic dependencies

This study extends the current use of Bayesian networks by incorporating the effects of allelic dependencies in paternity calculations. The use of object-oriented networks greatly simplify the process of building and interpreting forensic identification models, allowing researchers to solve new, more complex problems. We explore two paternity examples: the most common scenario where DNA evidence is available from the alleged father, the mother and the child; a more complex casewhere DNA is not available from the alleged father, but is available from the alleged father's brother. Object-oriented networks are built, using HUGIN, for each example which incorporate the effects of allelic dependence caused by evolutionary relatedness.

Validation of software for calculating the likelihood ratio for parentage and kinship

Although the likelihood ratio is a well-known statistical technique, commercial off-the-shelf (COTS) software products for its calculation are not sufficiently validated to suit general requirements for the competence of testing and calibration laboratories (EN/ISO/IEC 17025:2005 norm) per se. The software in question can be considered critical as it directly weighs the forensic evidence allowing judges to decide on guilt or innocence or to identify person or kin (i.e.: in mass fatalities). For these reasons, accredited laboratories shall validate likelihood ratio software in accordance with the above norm. To validate software for calculating the likelihood ratio in parentage/kinship scenarios I assessed available vendors, chose two programs (Paternity Index and familias) for testing, and finally validated them using tests derived from elaboration of the available guidelines for the field of forensics, biomedicine, and software engineering. MS Excel calculation using known likelihood ratio formulas or peer-reviewed results of difficult paternity cases were used as a reference. Using seven testing cases, it was found that both programs satisfied the requirements for basic paternity cases. However, only a combination of two software programs fulfills the criteria needed for our purpose in the whole spectrum of functions under validation with the exceptions of providing algebraic formulas in cases of mutation and/or silent allele.

Decision theoretic properties of forensic identification: underlying logic and argumentative implications

The field of forensic science has profited from recent advances in the elicitation of various kinds probabilistic data. These provide the basis for implementing probabilistic inference procedures (e.g., in terms of likelihood ratios) that address the task of discriminating among competing target propositions. There is ongoing discussion, however, whether forensic identification, that is, a conclusion that associates a potential source (such as an individual or object) with a given item of scientific evidence (e.g., a biological stain or a tool mark), can, if ever, be based on purely probabilistic argument. With regard to this issue, the present paper proposes to analyze the process of forensic identification from a decision theoretic point of view. Existing probabilistic inference procedures are used therein as an integral part. The idea underlying the proposed analyses is that inference and decision are connected in the sense that the former is the point of departure for the latter. As such the approach forms a coordinated whole, that is a framework also known in the context as 'full Bayesian (decision) approach'. This study points out that, as a logical extension to purely probabilistic reasoning, a decision theoretic conceptualization of forensic identification allows the content and structure of arguments to be examined from a reasonably distinct perspective and common fallacious interpretations to be avoided.

Estimating mutation rates from paternity casework

We present a statistical methodology for making inferences about mutation rates from paternity casework. This takes account of a number of sources of potential bias, including hidden mutation, incomplete family triplets, uncertain paternity status and differing maternal and paternal mutation rates, while allowing a wide variety of mutation models. An object-oriented Bayesian network is used to facilitate computation of the likelihood function for the mutation parameters. This can process either full or summary genotypic information, both from complete putative father-mother-child triplets and from defective cases where only the child and one of its parents are observed. We use a dataset from paternity casework to illustrate the effects on inferences about mutation parameters of various types of biases and the mutation model assumed. In particular, we show that there can be relevant information in cases of unconfirmed paternity, and that excluding these, as has generally been done, can lead to biased conclusions.

Handling manipulated evidence

Bayesian Networks have been advocated as useful tools to describe the relations of dependence/independence among random variables and relevant hypotheses in a crime case. Moreover, they have been applied to help the investigator structure the problem and evaluate the impact of the observed evidence, typically with respect to the hypothesis of guilt of a suspect. In this paper we describe a model to handle the possibility that one or more pieces of evidence have been manipulated in order to mislead the investigations. This method is based on causal inference models, although it is developed in a different, specific framework.

Structured Incorporation of Prior Information in Relationship Identification Problems

The objective of this paper is to show how various sources of information can be modelled and integrated to address relationship identification problems. Applications come from areas as diverse as evolution and conservation research, genealogical research in human, plant and animal populations, and forensic problems including paternity cases, identification following disasters, family reunions and immigration issues. We propose assigning a prior probability distribution to the sample space of pedigrees, calculating the likelihood based on DNA data using available software and posterior probabilities using Bayes' Theorem. Our emphasis here is on the modelling of this prior information in a formal and consistent manner. We introduce the distinction between local and global prior information, whereby local information usually applies to particular components of the pedigree and global prior information refers to more general features. When it is difficult to decide on a prior distribution, robustness to various choices should be studied. When suitable prior information is not available, a flat prior can be used which will then correspond to a strict likelihood approach. In practice, prior information is often considered for these problems, but in a generally ad hoc manner. This paper offers a consistent alternative. We emphasise that many practical problems can be addressed using freely available software.

A probabilistic approach to the joint evaluation of firearm evidence and gunshot residues

The present paper addresses issues that affect both the separate as well as the joint evaluation of firearm evidence (i.e., marks) and gunshot residues (GSR). Mark evidence will be used as a basis to discriminate among barrels through which a bullet in question might have been shot whereas GSR will be used to draw inferences about the distance of firing. Particular attention is drawn to the coherent handling of uncertainties associated with the various parameters considered within each item of evidence. The proposed analysis relies on a probabilistic viewpoint that uses graphical models (i.e., Bayesian networks) as an aid to cope with the complexity induced by the number of variables considered. The paper discusses how an approach based on a probabilistic network environment can be used for the formal analysis and construction of arguments. Emphasis is made on the gain of insight into structural dependencies that may be uncovered when the evaluative process is extended beyond single items of scientific evidence.