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Foundations for Bayesian networks
, 2001
"... Bayesian networks are normally given one of two types of foundations: they are either treated purely formally as an abstract way of representing probability functions, or they are interpreted, with some causal interpretation given to the graph in a network and some standard interpretation of probabi ..."
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Cited by 11 (7 self)
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Bayesian networks are normally given one of two types of foundations: they are either treated purely formally as an abstract way of representing probability functions, or they are interpreted, with some causal interpretation given to the graph in a network and some standard interpretation of probability given to the probabilities specified in the network. In this chapter I argue that current foundations are problematic, and put forward new foundations which involve aspects of both the interpreted and the formal approaches. One standard approach is to interpret a Bayesian network objectively: the graph in a Bayesian network represents causality in the world and the specified probabilities are objective, empirical probabilities. Such an interpretation founders when the Bayesian network independence assumption (often called the causal Markov condition) fails to hold. In §2 I catalogue the occasions when the independence assumption fails, and show that such failures are pervasive. Next, in §3, I show that even where the independence assumption does hold objectively, an agent’s causal knowledge is unlikely to satisfy the assumption with respect to her subjective probabilities, and that slight differences between an agent’s subjective Bayesian network and an objective Bayesian network can lead to large differences between probability distributions determined by these networks. To overcome these difficulties I put forward logical Bayesian foundations in §5. I show that if the graph and probability specification in a Bayesian network are thought of as an agent’s background knowledge, then the agent is most rational if she adopts the probability distribution determined by the
Understanding of what engineers “do
 LSE Centre for Natural and Social Sciences, www.lse.ac.uk/Depts/cpnss/proj_causality.htm
, 2002
"... presented at ..."
Precise Propagation of Upper and Lower Probability Bounds in
, 2000
"... In this paper we consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our algorithms, we propagate the lower and upper probability bounds associated with the conditional assertions of a given knowledge base, automatically obtaining the ..."
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In this paper we consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our algorithms, we propagate the lower and upper probability bounds associated with the conditional assertions of a given knowledge base, automatically obtaining the precise probability bounds for the derived conclusions of the inference rules. This allows a more flexible and realistic use of System P in default reasoning and provides an exact illustration of the degradation of the inference rules when interpreted in probabilistic terms. We also examine the disjunctive Weak Rational Monotony of System P + proposed by Adams in his extended probability logic. Keywords: Nonmonotonic reasoning, System P, Conditional probability bounds, Precise propagation,
Reassessing Accuracy Rates for Median Decision Procedures
"... specificity, sensitivity, predictive values, probability bounds, fundamental theorem of prevision, linear programming, quadratic programming We reexamine the procedure of median decision making in the context of radiological determination of asbestosis by three Breaders. Our assessment addresses t ..."
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specificity, sensitivity, predictive values, probability bounds, fundamental theorem of prevision, linear programming, quadratic programming We reexamine the procedure of median decision making in the context of radiological determination of asbestosis by three Breaders. Our assessment addresses the specificity, sensitivity and predictive values from this procedure compared to merely an individual radiologist’s diagnosis. Conditional exchangeability of the radiologists ’ classifications is recognised as more appropriate than independence which is often presumed. The framework of de Finetti’s fundamental theorem of probability makes the analysis tractable when it is formulated in terms of a linear programming problem, yielding coherent bounds on probabilities of interest even when a complete distribution is not specified. Further natural assertions motivate a partial ordering of conditional probabilities. In this context the computation of bounds develops into a quadratic programming problem. Using sensible assertions, the median decision procedure is found to be relatively weaker than has been thought based on the presumption of independence of radiologists ’ assessments. However that presumption is also shown to overstate the predictive qualities of individual diagnoses. We reevaluate substantive claims about the use of median Xray decisions as an indicator of cancer. 1