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Trajectory reconstruction in bloodstain pattern analysis is currently performed by assuming that blood drop trajectories are straight along directions inferred from stain inspection. Recently, several attempts have been made at reconstructing ballistic trajectories backwards, considering the effects of gravity and drag forces. Here, we propose a method to reconstruct the region of origin of impact blood spatter patterns that considers fluid dynamics and statistical uncertainties. The fluid dynamics relies on defining for each stain a range of physically possible trajectories, based on known physics of how drops deform, both in flight and upon slanted impact. Statistical uncertainties are estimated and propagated along the calculations, and a probabilistic approach is used to determine the region of origin as a volume most compatible with the backward trajectories. A publicly available data set of impact spatter patterns on a vertical wall with various impactor velocities and distances to target is used to test the model and evaluate its robustness, precision, and accuracy. Results show that the proposed method allows reconstruction of bloodletting events with distances between the wall and blood source larger than ∼1 m. The uncertainty of the method is determined, and its dependency on the distance between the blood source and the wall is characterized. Causes of error and uncertainty are discussed. The proposed method allows the consideration of stains indicating impact velocities that point downwards, which are typically not used for determining the height of the origin. Based on the proposed method, two practical recommendations on crime scene documentation are drawn. [ABSTRACT FROM AUTHOR]

Highlights • We find an inverse S-shape in stated subjective probabilities in a novel experiment. • Prelec's (1998) conditional invariant model provides the best fit. • We find a large degree of individual heterogeneity. Abstract We examine the nature of stated subjective probabilities in a complex, evolving context in which participants are not told what the actual probability is: we collect information on subjective expectations in a computerized car race game wherein participants must bet on a particular car but cannot influence the odds of winning once the race begins. In our setup, the actual probability of the good outcome (a win) can be determined based on computer simulations from any point in the process. We compare this actual probability to the subjective probability stated by participants at three different points in each of six races. In line with previous research in which participants have direct access to actual probabilities, we find that the inverse S-shaped curve relating subjective to actual probabilities is also evident in our far more complex situation, and that there is only a limited degree of learning through repeated play. We show that the model in the inverse S-shaped function family that provides the best fit to our data is Prelec's 1998 conditional invariant model. We also find that individuals who report a greater degree of ambiguity are more pessimistic and less responsive to actual changes in real probabilities. [ABSTRACT FROM AUTHOR]

Probabilistic Risk Assessment (PRA) has proven to be an invaluable tool for evaluating risks in complex engineered systems. However, there is increasing concern that PRA may not be adequate in situations with little underlying knowledge to support probabilistic representation of uncertainties. As analysts and policy makers turn their attention to deeply uncertain hazards such as climate change, a number of alternatives to traditional PRA have been proposed. This paper systematically compares three diverse approaches for risk analysis under deep uncertainty (qualitative uncertainty factors, probability bounds, and robust decision making) in terms of their representation of uncertain quantities, analytical output, and implications for risk management. A simple example problem is used to highlight differences in the way that each method relates to the traditional risk assessment process and fundamental issues associated with risk assessment and description. We find that the implications for decision making are not necessarily consistent between approaches, and that differences in the representation of uncertain quantities and analytical output suggest contexts in which each method may be most appropriate. Finally, each methodology demonstrates how risk assessment can inform decision making in deeply uncertain contexts, informing more effective responses to risk problems characterized by deep uncertainty. [ABSTRACT FROM AUTHOR]

Abstract: In engineering risk assessments, probability is the common tool used to describe the epistemic uncertainties about unknown quantities. Probability is considered a main component of risk. However, a number of alternative approaches exist for representing and describing uncertainties in risk assessments, including possibility theory and evidence theory. For these approaches and theories a probability-based risk definition cannot in general serve as a conceptual framework for risk assessments. A broader risk perspective is required. The purpose of the present paper is to present such a perspective and show how both the probabilistic and the alternative approaches and theories can be supported by this perspective. The key feature of this perspective is that uncertainty replaces probability in the definition of risk. [Copyright &y& Elsevier]

Uncertainty is highly relevant in environmental policy because on the one hand environmental problems are regarded as complex and require a long-term perspective and on the other hand the knowledge available to practitioners and policy makers alike is often fragmentary and not systemised. One key issue arising from this is the challenge to develop scientific decision support methods that are capable of dealing with uncertainty in a systematic and differentiated way, integrating scientific as well as practical knowledge. This paper introduces a conceptual framework for perceiving and describing uncertainty in environmental decision-making. The conceptual framework consists of a general definition of uncertainty along with five complementary perspectives on the phenomenon, each highlighting one specific aspect of it. By using the conceptual framework, decision-makers are able to reflect on their knowledge base with regard to its completeness and reliability and to gain a broad picture of uncertainty from various standpoints. The theoretical ideas presented here are complemented by two empirical studies looking at how uncertainty is dealt with in the implementation process of the EU Water Framework Directive. The rather abstract differentiations are illustrated by a number of examples in the form of interview statements and excerpts from the directive and official EU documents. [Copyright &y& Elsevier]

In knowledge-based systems, as particular systems for the making of decisions, the use of techniques to consider the uncertainty is of special interest. In this article, the problem of uncertainty is analysed in systems based on cases and a model that shows ways for its determination and handling using probabilistic techniques combined with concepts in the theory of the rough sets is proposed. The proposed model is based on a case-based structure, which allows a better retrieval of the cases. The ideas stated are explained through an example. [Copyright &y& Elsevier]