When performing regression or classification, we are interested in the conditional probability distribution for an outcome or class variable Y given a set of explanatoryor input variables X. We consider Bayesian models for this task. In particular, we examine a special class of models, which we call Bayesian regression/classification (BRC) models, that can be factored into independent conditional (y|x) and input (x) models. These models are convenient, because the conditional model (the portion of the full model that we care about) can be analyzed by itself. We examine the practice of transforming arbitrary Bayesian models to BRC models, and argue that this practice is often inappropriate because it ignores prior knowledge that may be important for learning. In addition, we examine Bayesian methods for learning models from data. We discuss two criteria for Bayesian model selection that are appropriate for repression/classification: one described by Spiegelhalter et al. (1993), and another by Buntine (1993). We contrast these two criteria using the prequential framework of Dawid (1984), and give sufficient conditions under which the criteria agree.

In most current applications of belief networks, domain knowledge is represented by a single belief network that applies to all problem instances in the domain. In more complex domains, problem-specific models must be constructed from a knowledge base encoding probabilistic relationships in the domain. Most work in knowledge-based model construction takes the rule as the basic unit of knowledge. We present a knowledge representation framework that permits the knowledge base designer to specify knowledge in larger semantically meaningful units which we call network fragments. Our framework provides for representation of asymmetric independence and canonical intercausal interaction. We discuss the combination of network fragments to form problem-specific models to reason about particular problem instances. The framework is illustrated using examples from the domain of military situation awareness.

There is a brief description of the probabilistic causal graph model for representing, reasoning with, and learning causal structure using Bayesian networks. It is then argued that this model is closely related to how humans reason with and learn causal structure. It is shown that studies in psychology on discounting (reasoning concerning how the presence of one cause of an effect makes another cause less probable) support the hypothesis that humans reach the same judgments as algorithms for doing inference in Bayesian networks. Next, it is shown how studies by Piaget indicate that humans learn causal structure by observing the same independencies and dependencies as those used by certain algorithms for learning the structure of a Bayesian network. Based on this indication, a subjective definition of causality is forwarded. Finally, methods for further testing the accuracy of these claims are discussed.

A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is directly represented by a Bayesian network. By using a powerful way of specifying conditional probability distributions in these networks, the resulting formalism is more expressive than the previous ones. Particularly, it provides for constraints on equalities of events, and it allows to define complex, nested combination functions.

Bayesian approaches to learn the graphical structure of Bayesian Belief Networks (BBNs) from databases share the assumption that the database is complete, that is, no entry is reported as unknown. Attempts to relax this assumption involve the use of expensive iterative methods to discriminate among different structures. This paper introduces a deterministic method to learn the graphical structure of a BBN from a possibly incomplete database. Experimental evaluations show a significant robustness of this method and a remarkable independence of its execution time from the number of missing data.

Bayesian networks provide a modeling language and associated inference algorithm for stochastic domains. They have been successfully applied in a variety of medium-scale applications. However, when faced with a large complex domain, the task of modeling using Bayesian networks begins to resemble the task of programming using logical circuits. In this paper, we describe an object-oriented Bayesian network (OOBN) language, which allows complex domains to be described in terms of inter-related objects. We use a Bayesian network fragment to describe the probabilistic relations between the attributes of an object. These attributes can themselves be objects, providing a natural framework for encoding part-of hierarchies. Classes are used to provide a reusable probabilistic model which can be applied to multiple similar objects. Classes also support inheritance of model fragments from a class to a subclass, allowing the common aspects of related classes to be defined only once. Our language has clear declarative semantics: an OOBN can be interpreted as a stochastic functional program, so that it uniquely specifies a probabilistic model. We provide an inference algorithm for OOBNs, and show that much of the structural information encoded by an OOBN--particularly the encapsulation of variables within an object and the reuse of model fragments in different contexts--can also be used to speed up the inference process.

Conditioning is the generally agreed-upon method for updating probability distributions when one learns that an event is certainly true. But it has been argued that we need other rules, in particular the rule of cross-entropy minimization, to handle updates that involve uncertain information. In this paper we re-examine such a case: van Fraassen's Judy Benjamin problem, which in essence asks how one might update given the value of a conditional probability. We argue that -- contrary to the suggestions in the literature -- it is possible to use simple conditionalization in this case, and thereby obtain answers that agree fully with intuition. This contrasts with proposals such as cross-entropy, which are easier to apply but can give unsatisfactory answers. Based on the lessons from this example, we speculate on some general philosophical issues concerning probability update.

We present a method for calculation of myopic value of information in influence diagrams (Howard & Matheson, 1981) based on the strong junction tree framework (Jensen, Jensen & Dittmer, 1994). The difference in instantiation order in the influence diagrams is reflected in the corresponding junction trees by the order in which the chance nodes are marginalized. This order of marginalization can be changed by table expansion and in effect the same junction tree with expanded tables may be used for calculating the expected utility for scenarios with different instantiation order. We also compare our method to the classic method of modeling different instantiation orders in the same influence diagram.

Performance prediction or forecasting sporting outcomes involves a great deal of insight into the particular area one is dealing with, and a considerable amount of intuition about the factors that bear on such outcomes and performances. The mathematical Theory of Evidence offers representation formalisms which grant experts a high degree of freedom when expressing their subjective beliefs in the context of decision-making situations like performance prediction. Furthermore, this reasoning framework incorporates a powerful mechanism to systematically pool the decisions made by individual subject matter experts. The idea behind such a combination of knowledge is to improve the competence (quality) of the overall decision-making process. This paper reports on a performance prediction experiment carried out during the European Football Championship in 1996. Relying on the knowledge of four predictors, Evidence Theory was used to forecast the final scores of all 31 matches. The results of this empirical study are very encouraging.

By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function describing the interactions between a parameter variable, an observation variable and a random source, and P is a probability distribution for the random source. Unlike traditional functional models, generalized functional models do not require that there is only one value of the parameter variable that is compatible with an observation and a realization of the random source. As a consequence, the results of the analysis of a generalized functional model are not expressed in terms of probability distributions but rather by support and plausibility functions. The analysis of a generalized functional model is very logical and is inspired from ideas already put forward by R.A. Fisher in his theory of fiducial probability.