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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]

This paper examines marginal-risk behavior in a decision-theoretic setting that is sufficiently general to accommodate any decision-making model representable by a certainty equivalent. The analysis shows that risk aversion in its usual sense is a special case of marginal-risk aversion associated with mean-preserving changes in gambles. Thus, marginal-risk behavior and risk behavior are not inherently different. Rather, they manifest similar behavior evaluated at different gambles. The paradox of marginal-risk-loving risk averters arises from mixing definitions of an "increase in risk". [ABSTRACT FROM AUTHOR]