Recent misconceptions about the ‘database search problem’: A probabilistic analysis using Bayesian networks

A collection of idioms for modeling activity level evaluations in forensic science

This paper presents a collection of idioms that is useful for modeling activity level evaluations in forensic science using Bayesian networks. The idioms are categorized into five groups: cause-consequence idioms, narrative idioms, synthesis idioms, hypothesis-conditioning idioms, and evidence-conditioning idioms. Each category represents a specific modeling objective. Furthermore, we support the use of an idiom-based approach and emphasize the relevance of our collection by combining several of the presented idioms to create a more comprehensive template model. This model can be used in cases involving transfer evidence and disputes over the actor and/or activity. Additionally, we cite literature that employs idioms in template models or case-specific models, providing the reader with examples of their use in forensic casework.

DNA database matches: A p versus np problem

The evidential value of a unique DNA database match has been extensively discussed. In principle the matter has been mathematically resolved, since the posterior odds on the match being with the trace donor are unambiguously defined. There are multiple ways to express these odds as a product of likelihood ratio and prior odds, and so the mathematics do not immediately tell us what to do in concrete cases, in particular which likelihood ratio to choose for reporting. With p the random match probability for the matching person, if innocent, and n the database size, both 1/p, originating from a suspect-centered framework, and 1/(np), originating from a database-centered framework, arise as likelihood ratio. Both have been defended and both have been criticized in the literature. We will clarify the situation by not introducing models and choices of prior probabilities until they are needed. This allows to derive the posterior odds in their most general form, which applies whenever we know that a single person among a list is not excluded as potential trace donor. We show that we need only three probabilities, that pertain to the observed match, to the database, and to the matching person respectively. How these required probabilities behave in a given context, then, differs from one situation to another. This is understandable since database searches may be done under various circumstances. They may be carried out with or without a suspect already in mind and, depending on the operational procedures, one may or may not be informed about the personal details of the person who gives the match. We show how to evaluate the required probabilities in all such cases. We will motivate why we believe that for some database searches, the 1/p likelihood ratio is more natural, whereas for others, 1/(np) seems the more sensible choice. This is not motivated by the mathematics: mathematically, the approaches are equivalent. It is motivated by considering which model best reflects the actual situation, taking into account what question was asked to begin with, and by the practical consideration of judging which likelihood ratio comes closer to the posterior odds based on the information available in the case. This article is intended to be both a research and a review article, and we end with an in-depth discussion of various arguments that have been brought forward in favor or against either 1/p or 1/(np).

Genotyping and interpretation of STR-DNA: Low-template, mixtures and database matches-Twenty years of research and development

The introduction of Short Tandem Repeat (STR) DNA was a revolution within a revolution that transformed forensic DNA profiling into a tool that could be used, for the first time, to create National DNA databases. This transformation would not have been possible without the concurrent development of fluorescent automated sequencers, combined with the ability to multiplex several loci together. Use of the polymerase chain reaction (PCR) increased the sensitivity of the method to enable the analysis of a handful of cells. The first multiplexes were simple: 'the quad', introduced by the defunct UK Forensic Science Service (FSS) in 1994, rapidly followed by a more discriminating 'six-plex' (Second Generation Multiplex) in 1995 that was used to create the world's first national DNA database. The success of the database rapidly outgrew the functionality of the original system - by the year 2000 a new multiplex of ten-loci was introduced to reduce the chance of adventitious matches. The technology was adopted world-wide, albeit with different loci. The political requirement to introduce pan-European databases encouraged standardisation - the development of European Standard Set (ESS) of markers comprising twelve-loci is the latest iteration. Although development has been impressive, the methods used to interpret evidence have lagged behind. For example, the theory to interpret complex DNA profiles (low-level mixtures), had been developed fifteen years ago, but only in the past year or so, are the concepts starting to be widely adopted. A plethora of different models (some commercial and others non-commercial) have appeared. This has led to a confusing 'debate' about the 'best' to use. The different models available are described along with their advantages and disadvantages. A section discusses the development of national DNA databases, along with details of an associated controversy to estimate the strength of evidence of matches. Current methodology is limited to searches of complete profiles - another example where the interpretation of matches has not kept pace with development of theory. STRs have also transformed the area of Disaster Victim Identification (DVI) which frequently requires kinship analysis. However, genotyping efficiency is complicated by complex, degraded DNA profiles. Finally, there is now a detailed understanding of the causes of stochastic effects that cause DNA profiles to exhibit the phenomena of drop-out and drop-in, along with artefacts such as stutters. The phenomena discussed include: heterozygote balance; stutter; degradation; the effect of decreasing quantities of DNA; the dilution effect.

A more straightforward derivation of the LR for a database search

Matching DNA profiles of an accused person and a crime scene trace are one of the most common forms of forensic evidence. A number of years ago the so-called 'DNA controversy' was concerned with how to quantify the value of such evidence. Given its importance, the lack of understanding of such a basic issue was quite surprising and concerning. Deriving the equation for the likelihood ratio of a DNA database match in a much more direct and simple way is the topic of this paper. As it is much easier to follow it is hoped that this derivation will contribute to the understanding.

A Bayesian network approach to the database search problem in criminal proceedings

Background

The ‘database search problem’, that is, the strengthening of a case - in terms of probative value - against an individual who is found as a result of a database search, has been approached during the last two decades with substantial mathematical analyses, accompanied by lively debate and centrally opposing conclusions. This represents a challenging obstacle in teaching but also hinders a balanced and coherent discussion of the topic within the wider scientific and legal community. This paper revisits and tracks the associated mathematical analyses in terms of Bayesian networks. Their derivation and discussion for capturing probabilistic arguments that explain the database search problem are outlined in detail. The resulting Bayesian networks offer a distinct view on the main debated issues, along with further clarity.

Methods

As a general framework for representing and analyzing formal arguments in probabilistic reasoning about uncertain target propositions (that is, whether or not a given individual is the source of a crime stain), this paper relies on graphical probability models, in particular, Bayesian networks. This graphical probability modeling approach is used to capture, within a single model, a series of key variables, such as the number of individuals in a database, the size of the population of potential crime stain sources, and the rarity of the corresponding analytical characteristics in a relevant population.

Results

This paper demonstrates the feasibility of deriving Bayesian network structures for analyzing, representing, and tracking the database search problem. The output of the proposed models can be shown to agree with existing but exclusively formulaic approaches.

Conclusions

The proposed Bayesian networks allow one to capture and analyze the currently most well-supported but reputedly counter-intuitive and difficult solution to the database search problem in a way that goes beyond the traditional, purely formulaic expressions. The method’s graphical environment, along with its computational and probabilistic architectures, represents a rich package that offers analysts and discussants with additional modes of interaction, concise representation, and coherent communication.