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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 ..."
Abstract

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
§3 Goodman’s New Problem of Induction 7
"... Journal of Logic, Language and Information, to appear Bayesian probability is normally defined over a fixed language or event space. But in practice language is susceptible to change, and the question naturally arises as to how Bayesian degrees of belief should change as language changes. I argue he ..."
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Journal of Logic, Language and Information, to appear Bayesian probability is normally defined over a fixed language or event space. But in practice language is susceptible to change, and the question naturally arises as to how Bayesian degrees of belief should change as language changes. I argue here that this question poses a serious challenge to Bayesianism. The Bayesian may be able to meet this challenge however, and I outline a practical method for changing degrees of belief over changes in
Automated Endoscope Navigation and Advisory System from medical
"... In this paper, we present a review of the research conducted by our group to design an automatic endoscope navigation and advisory system. The whole system can be viewed as a twolayer system. The first layer is at the signal level, which consists of the processing that will be performed on a series ..."
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In this paper, we present a review of the research conducted by our group to design an automatic endoscope navigation and advisory system. The whole system can be viewed as a twolayer system. The first layer is at the signal level, which consists of the processing that will be performed on a series of images to extract all the identifiable features. The information is purely dependent on what can be extracted from the 'raw ' images. At the signal level, the first task is performed by detecting a single dominant feature, lumen. Few methods of identifying the lumen are proposed. The first method used contour extraction. Contours are extracted by edge detection, thresholding and linking. This method required images to be divided into overlapping squares (8 by 8 or 4 by 4) where line segments are extracted by using a Hough transform. Perceptual criteria such as proximity, connectivity, similarity in orientation, contrast and edge pixel intensity, are used to group edges both strong and weak. This approach is called perceptual grouping. The second method is based on a region extraction using split and merge approach using spatial domain data. An nlevel (for a 2n by 2n image) quadtree based pyramid structure is constructed to find the most homogenous large dark region, which in most cases corresponds to the lumen. The algorithm constructs the quadtree from the bottom (pixel) level upward, recursively and computes the mean and variance of image regions corresponding to quadtree nodes. On reaching the root, the largest uniform seed region, whose mean corresponds to a lumen is selected that is grown by merging with its neighboring regions.