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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
Interactive CourseofAction Planning using Causal Models
, 2004
"... Abstract. This paper describes a new technique for interactive planning for coalition operations under conditions of uncertainty. Our approach is based on the use of the Air Force Research Laboratory’s Causal Analysis Tool (CAT), a system for creating and analyzing causal models similar to Bayesian ..."
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Cited by 3 (2 self)
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Abstract. This paper describes a new technique for interactive planning for coalition operations under conditions of uncertainty. Our approach is based on the use of the Air Force Research Laboratory’s Causal Analysis Tool (CAT), a system for creating and analyzing causal models similar to Bayesian networks. In order to use CAT as a tool for planning for coalition operations, users go through an iterative process in which they use CAT to create and analyze alternative plans. One of the biggest difficulties is that the number of possible plans that must be analyzed is exponential in the number of possible actions that may or may not appear in those plans. In any planning problem of significant size, it is impossible for the user to create and analyze every possible plan; thus users can spend days arguing about which actions to include in their plans. To solve this problem, we have developed an approach to quickly compute upper and lower bounds on the probabilities of success associated with a partial plan, and use these probabilities to recommend which actions the user should include in the plan in order to get a complete plan. This provides an exponential reduction in the amount of time needed to find a complete plan. In our experiments, our approach generated recommendations that resulted in plans that have the highest probability of success in just a few minutes. 1 Problem and Significance In planning a coalition’s course of action (i.e., a plan for the coalition to execute to achieve a desired objective or
Interactive Planning under Uncertainty with Causal Modeling and Analysis
 OF ELECTRICAL, COMPUTER, AND SYSTEMS ENGINEERING AT RENSSELAER POLYTECHNIC INSTITUTE
, 2003
"... This paper describes a new technique for interactive planning under conditions of uncertainty. Our approach is based on the use of the Air Force Research Laboratory's Causal Analysis Tool (CAT), a system for creating and analyzing causal models similar to Bayes networks. In order to ..."
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Cited by 3 (0 self)
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This paper describes a new technique for interactive planning under conditions of uncertainty. Our approach is based on the use of the Air Force Research Laboratory's Causal Analysis Tool (CAT), a system for creating and analyzing causal models similar to Bayes networks. In order to
Acquiring and Assessing Knowledge from Multiple Experts Using Graphical Representations
, 2000
"... This chapter presents a thorough review of current practice in eliciting, representing and amalgamating knowledge from multiple experts, with a focus on the use of graphical representations to support the process. The important points of the discussion are illustrated by presenting a specific method ..."
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Cited by 1 (0 self)
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This chapter presents a thorough review of current practice in eliciting, representing and amalgamating knowledge from multiple experts, with a focus on the use of graphical representations to support the process. The important points of the discussion are illustrated by presenting a specific methodology for eliciting and combining knowledge from multiple experts. This methodology provides a statistically defensive summarization for assessment. The results of a pilot test of its implementation over the Internet are also presented. The chapter concludes with a discussion of the need for knowledge acquisition techniques that permit quantitative assessment of the quality of the rules developed based upon the acquired knowledge and subsequently embedded in decision support systems. 3 I.
A Causal Calculus
"... Given an arbitrary causal graph, some of whose nodes are observable and some unobservable, the problem is to determine whether the causal effect of one variable on another can be computed from the joint distribution over the observables and, if the answer is positive, to derive a formula for the ..."
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Given an arbitrary causal graph, some of whose nodes are observable and some unobservable, the problem is to determine whether the causal effect of one variable on another can be computed from the joint distribution over the observables and, if the answer is positive, to derive a formula for the causal effect. We introduce a calculus which, using a step by step reduction of probabilistic expressions, derives the desired formulas. 1 1 Introduction Networks employing directed acyclic graphs (DAGs) can be used to provide either 1. an economical scheme for representing conditional independence assumptions and joint distribution functions, or 2. a graphical language for representing causal influences. Although the professed motivation for investigating such models lies primarily in the second category, [Wright, 1921, Blalock, 1971, Simon, 1954, Pearl 1988], causal inferences have been treated very cautiously in the statistical literature [Lauritzen & Spiegelhalter 1988, Cox 1992,...