ALBERT

Description: The role played by the required level of statistical significance in the scientific method should not be seen as analogous to that played by the standard of proof in the legal process.

Description: The Supreme Court ruled in Matrixx that statistical significance is not necessary to show that a drug caused an adverse reaction. Five circuit court decisions holding otherwise preceded this decision. This paper examines the extent to which the Supreme Court’s reasoning differed from those of the circuit courts.

Description: Unlike the evaluation of single items of scientific evidence, the formal study and analysis of the joint evaluation of several distinct items of forensic evidence has to date received some punctual, rather than systematic, attention. Questions about the (i) relationships among a set of (usually unobservable) propositions and a set of (observable) items of scientific evidence, (ii) the joint probative value of a collection of distinct items of evidence as well as (iii) the contribution of each individual item within a given group of pieces of evidence still represent fundamental areas of research. To some degree, this is remarkable since both, forensic science theory and practice, yet many daily inference tasks, require the consideration of multiple items if not masses of evidence. A recurrent and particular complication that arises in such settings is that the application of probability theory, i.e. the reference method for reasoning under uncertainty, becomes increasingly demanding. The present paper takes this as a starting point and discusses graphical probability models, i.e. Bayesian networks, as framework within which the joint evaluation of scientific evidence can be approached in some viable way. Based on a review of existing main contributions in this area, the article here aims at presenting instances of real case studies from the author’s institution in order to point out the usefulness and capacities of Bayesian networks for the probabilistic assessment of the probative value of multiple and interrelated items of evidence. A main emphasis is placed on underlying general patterns of inference, their representation as well as their graphical probabilistic analysis. Attention is also drawn to inferential interactions, such as redundancy, synergy and directional change. These distinguish the joint evaluation of evidence from assessments of isolated items of evidence. Together, these topics present aspects of interest to both, domain experts and recipients of expert information, because they have bearing on how multiple items of evidence are meaningfully and appropriately set into context.

Description: In its first foray into the labyrinth that causation in personal injury has become, the U.K. Supreme Court recently held obiter that statistical evidence alone could not establish causation. But in an earlier toxic tort case, the High Court had relied on epidemiological evidence to identify a cluster of birth defects arising in the vicinity of a contaminated land site. This recent British experience is then discussed within the wider context of the forensic role of ‘naked statistics’.

Description: Scales of conclusion in forensic interpretation play an important role in the interface between scientific work at a forensic laboratory and different bodies of the jurisdictional system of a country. Of particular importance is the use of a unified scale that allows interpretation of different kinds of evidence in one common framework. The logical approach to forensic interpretation comprises the use of the likelihood ratio as a measure of evidentiary strength. While fully understood by forensic scientists, the likelihood ratio may be hard to interpret for a person not trained in natural sciences or mathematics. Translation of likelihood ratios to an ordinal scale including verbal counterparts of the levels is therefore a necessary procedure for communicating evidence values to the police and in the courtroom. In this paper, we present a method to develop an ordinal scale for the value of evidence that can be applied to any type of forensic findings. The method is built on probabilistic reasoning about the interpretation of findings and the number of scale levels chosen is a compromise between a pragmatic limit and mathematically well-defined distances between levels. The application of the unified scale is illustrated by a number of case studies.

Description: In personal injury litigation, claimants may seek their compensation for future losses or expenses as a lump sum that is determined by the product of a multiplicand and a multiplier. The multiplicand represents the annual loss in earnings and other benefits, as assessed at the trial date, while the multiplier discounts future pecuniary values into a single present-day lump sum amount. At present, multipliers in the UK are calculated using actuarial methods and based on assumed mortality and interest rates. However, it is entirely possible that these assumptions are incorrect, and if they are, then all claimants who rely on the same set of actuarial multipliers will be affected. In this article, we investigate how the uncertainty surrounding mortality and interest rate assumptions affects the precision of actuarial multipliers. With the aid of stochastic models, we estimate the possible range of values that an actuarial multiplier can take.

Description: In this article we report and discuss a contextual problem solving task that was proposed to a class of 8th grade (13–14-year-old) students. These students had been developing a reasonable experience in the use of the spreadsheet to model relations within contextual problems and chose to use this tool to solve the mentioned problem, engaging in the process of translating relations between variables and combining them in chained models, while working with fractions, multiples and expressions. We intend to highlight the role of the spreadsheet in students’ processes of variable identification and translation of the problem conditions, their numerical approaches to algebraic models and their experimental forms of finding solutions to equations.

Description: This theoretical study is an attempt to explore the potential of the dynamic and interactive mathematics learning environments (DIMLE) in relation to the technological pedagogical content knowledge (TPACK) framework. DIMLE are developed with intent to support learning mathematics through free exploration in a less constrained environment. A typical DIMLE software package has interactivity and dynamism as key affordances; these are especially suitable for enhancing learning and teaching with technology of the essentially dynamic mathematics concepts. Moreover, we propose that DIMLE and their affordances should be studied under the TPACK framework because this framework is explicit in considering technology-supported mathematics learning as a qualitative add-on as contrasted to what would be a simple totalling of technological, pedagogical and mathematical knowledge. As an example, we focus in our discussion on using a DIMLE in order to support learner in development of the limit concept.