Qualitative approaches to quantifying probabilistic networks

A probabilistic network consists of a graphical representation (a directed graph) of the important variables in a domain of application, and the relationships between them, together with a joint probability distribution over the variables. A probabilistic network allows for computing any probability of interest. The joint probability distribution factorises into conditional probability distributions such that for each variable represented in the graph a distribution is specified conditional on all possible combinations of the variable's parents in the graph. Even for a moderate sized probabilistic network, thousands of probabilities need to be specified. Often the only source of probabilistic information is the knowledge and experience of experts. People, even experts, are known not be very good at assessing probabilities, and often dislike expressing their estimates as numbers. To overcome this problem, we propose two qualitative approaches to quantifying probabilistic networks. The first approach is abstracting away from probabilities by using qualitative probabilistic networks. The second approach is to allow the use of verbal expressions of probability during elicitation. In qualitative probabilistic networks, the arcs of the directed graph are augmented with signs: `+',`-', `0', and `?', indicating the direction of shift in probability for the variable at one end of the arc, given a shift in values of the variable at the other end of the arc. For example, a positive influence of variable A on variable B indicates that higher values for B become more likely given higher values for A. Qualitative probabilistic networks allow for reasoning with probabilistic networks in a qualitative way, thereby enabling us to check the robustness of the network's structure before probabilities are assessed. In addition, the qualitative signs provide constraints on the probabilities to be elicited. Qualitative networks are, however, not very expressive and therefore easily result in uninformative answers (`?'s) during reasoning. We will suggest several refinements of the formalism of qualitative probabilistic networks that enhance their expressiveness and applicability. To make probability elicitation easier on experts, we allow them to state verbal probability expressions, such as "probable" and "impossible", as well as numbers. To this end, we have augmented a vertical probability elicitation scale with verbal expressions. These expressions, and their position on the scale, are the result of several studies we conducted. The scale, together with other ingredients such as text-fragments describing the probability to be assessed and grouping of the probabilities that should sum to 1, is used in a newly designed probability elicitation method. The method provides for the elicitation of initial rough assessments. Assessments for which the outcome of the network is very sensitive can be refined using additional experts and/or the more conventional elicitation methods. Our method has been used with two experts in oncology in the construction of a probabilistic network for oesophageal carcinoma and allows us to elicit a large number of probabilities in little time. The experts felt comfortable with the method and evaluations of the resulting network have shown that it performs quite well with the rough assessments

Representing and Evaluating Legal Narratives with Subscenarios in a Bayesian network

In legal cases, stories or scenarios can serve as the context for a crime when reasoning with evidence. In order to develop a scientifically founded technique for evidential reasoning, a method is required for the representation and evaluation of various scenarios in a case. In this paper the probabilistic technique of Bayesian networks is proposed as a method for modeling narrative, and it is shown how this can be used to capture a number of narrative properties. Bayesian networks quantify how the variables in a case interact. Recent research on Bayesian networks applied to legal cases includes the development of a list of legal idioms: recurring substructures in legal Bayesian networks. Scenarios are coherent presentations of a collection of states and events, and qualitative in nature. A method combining the quantitative, probabilistic approach with the narrative approach would strengthen the tools to represent and evaluate scenarios. In a previous paper, the development of a design method for modeling multiple scenarios in a Bayesian network was initiated. The design method includes two narrative idioms: the scenario idiom and the merged scenarios idiom. In this current paper, the method of Vlek, et al. (2013) is extended with a subscenario idiom and it is shown how the method can be used to represent characteristic features of narrative

Про участь НАН України в розробці наукових основ сталого розвитку України

Наведено основні напрями наукових досліджень установ НАН України з проблеми збереження навколишнього середовища і сталого розвитку України, що виконувались наприкінці ХХ та на початку ХХІ століть в світлі рішень Конференції ООН з навколишнього середовища і розвитку у Ріо-де-Жанейро (червень 1992 р.) та Всесвітнього саміту зі сталого розвитку в Йоганнесбурзі (26 серпня — 4 вересня 2002 р.). На основі узагальнення результатів опитування установ НАН України в 2005 році проведено кількісний (наукометричний) аналіз їх участі у вирішенні зазначеної міждисциплінарної проблеми за п’ятирічний період за рядом показників (фінансове і кадрове забезпечення досліджень, використання їх результатів, патентно-ліцензійна та видавнича діяльність тощо) і сформульовано пропозиції щодо здійснення відповідних заходів з підвищення ефективності використання фінансових і матеріальних ресурсів при виконанні наукових досліджень з проблеми, підвищення їх координації та результативності.Приведены основные направления научных исследований учреждений НАН Украины по проблеме сохранения окружающей среды и стойкого развития Украины, которые выполнялись в конце ХХ и в начале XXI столетий в свете решений Конференции ООН по окружающей среде и развитию в Рио-де-Жанейро (июнь 1992 г.) и Всемирного саммита по устойчивому развитию в Иоганнесбурге (26 августа — 4 сентября 2002 г.). На основе обобщения результатов опроса учреждений НАН Украины в 2005 году проведен количественный (наукометрический) анализ их участия в решении указанной междисциплинарной проблемы за пятилетний период по ряду показателей (финансовое и кадровое обеспечение исследований, использование их результатов, патентно-лицензионная и издательская деятельность и др.) и сформулированы предложения о выполнении соответствующих мероприятий по повышению эффективности использования финансовых и материальных ресурсов при выполнении научных исследований по проблеме, повышению их координации и результативности.Main areas for research in institutes of the Ukrainian NAS are shown, devoted to environmental protection and sustained development in Ukraine, performed at the end of XX and the beginning of XXI centuries in light of the decision taken by the UN Conference in Rio de Janeiro (June 1992) and the World Summit on Sustained Development in Johannesburg (26 August – 4 September 2002). On the basis of results from a survey on institutes of the Ukrainian NAS, conducted in 2005, a scientometric analysis of their contributions in solving the above interdisciplinary problem is made, covering the 5-year period, by several indicators (research funding and personnel, applications of results, patenting, licensing, printing and publishing etc.), and measures are offered to enhance the efficiency of relevant research in terms of resource utilization, coordination and produced results

A method for explaining Bayesian networks for legal evidence with scenarios

In a criminal trial, a judge or jury needs to reason about what happened based on the available evidence, often including statistical evidence. While a probabilistic approach is suitable for analysing the statistical evidence, a judge or jury may be more inclined to use a narrative or argumentative approach when considering the case as a whole. In this paper we propose a combination of two approaches, combining Bayesian networks with scenarios. Whereas a Bayesian network is a popular tool for analysing parts of a case, constructing and understanding a network for an entire case is not straightforward. We propose an explanation method for understanding a Bayesian network in terms of scenarios. This method builds on a previously proposed construction method, which we slightly adapt with the use of scenario schemes for the purpose of explaining. The resulting structure is explained in terms of scenarios, scenario quality and evidential support. A probabilistic interpretation of scenario quality is provided using the concept of scenario schemes. Finally, the method is evaluated by means of a case study