After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form decisions from incomplete data in diagnostic problems has highlighted probabilistic methods [5] which compute posterior probabilities from prior distributions in a way similar to Bayes Rule, and thus are called Bayesian methods. This paper documents the use of a Bayesian method in a real time problem which is similar to medical diagnosis in that there is a need to form decisions and take some action without complete knowledge of conditions in the problem domain. This particular method has a limitation which is discussed.

A primary motivation for reasoning under uncertainty is to derive decisions in the face of inconclusive evidence. However, Shafer's theory of belief functions, which explicitly represents the underconstrained nature of many reasoning problems, lacks a formal procedure for making decisions. Clearly, when sufficient information is not available, no theory can prescribe actions without making additional assumptions. Faced with this situation, some assumption must be made if a clearly superior choice is to emerge. In this paper we offer a probabilistic interpretation of a simple assumption that disambiguates decision problems represented with belief functions. We prove that it yields expected values identical to those obtained by a probabilistic analysis that makes the same assumption. In addition, we show how the decision analysis methodology frequently employed in probabilistic reasoning can be extended for use with belief functions.

We introduce a graceful approach to probabilistic inference called bounded conditioning. Bounded conditioning monotonically refines the bounds on posterior probabilities in a belief network with computation, and converges on final probabilities of interest with the allocation of a complete resource fraction. The approach allows a reasoner to exchange arbitrary quantities of computational resource for incremental gains in inference quality. As such, bounded conditioning holds promise as a useful inference technique for reasoning under the general conditions of uncertain and varying reasoning resources. The algorithm solves a probabilistic bounding problem in complex belief networks by breaking the problem into a set of mutually exclusive, tractable subproblems and ordering their solution by the expected effect that each subproblem will have on the final answer. We introduce the algorithm, discuss its characterization, and present its performance on several belief networks, including a complex model for reasoning about problems in intensive-care medicine.

Considerable attention has been given to the problem of non-monotonic reasoning in a belief function framework. Earlier work (M. Ginsberg) proposed solutions introducing meta-rules which recognized conditional independencies in a probabilistic sense. More recently an e-calculus formulation of default reasoning (J. Pearl) shows that the application of Dempster's rule to a non-monotonic situation produces erroneous results. This paper presents a new belief function interpretation of the problem which combines the rules in a way which is more compatible with probabilistic results and respects conditions of independence necessary for the application of Dempster's combination rule. A new general framework for combining conflicting evidence is also proposed in which the normalization factor becomes modified. This produces more intuitively acceptable results.

A. Abstract Control Strategies for hierachical treelike probabilistic inference networks are formulated and investigated. Strategies that utilize staged look-ahead and temporary focus on subgoals are formalized and refined using the Depth Vector concept that serves as a tool for defining the'virtual tree' regarded by the control strategy. The concept is illustrated by four types of control strategies for three-level trees that are characterized according to their Depth Vector, and according to the way they consider intermediate nodes and the role that they let these nodes play. INFERENTl is a computerized inference system written in Prolog, which provides tools for exercising a variety of control strategies. The system also provides tools for simulating test data and for comparing the relative average performance under different strategies.

Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the conclusions are much weaker than those computed from complete probability distributions, they are still valuable for suggesting potential actions, eliminating obviously inferior plans, identifying important tradeoffs, and explaining probabilistic models.

The JIEDDO Analytic Decision Engine (JADE) is a flexible software toolkit for studying the performance of sensor configurations for the detection of person-borne explosive compounds and other threat substances. JADE is designed to enable performance and tradeoff analyses between different, user-specified scenarios with given sensor placements and data fusion networks. JADE contains fundamental physics-based models of several sensor technologies of interest, such as nonlinear acoustic and radar-based detectors, along with a data fusion system that we focus on in this paper. The fusion system consists of a static component that combines the decisions of individual sensors at a fixed point in time, and a dynamic, time-dependent component that in turn fuses the outputs of the static structure at different times. The static component is based on a probabilistic graphical model, or Bayesian network, and accepts probability matrices from the physicsbased sensor models as inputs (the details of which are abstracted from the fusion system). Its outputs are fed into the dynamic fusion framework, which is based on sequential hypothesis testing and produces performance metrics for the entire, fused sensor configuration. The purpose of the system is to determine the performance of a given fusion structure, as opposed to doing fusion on actual measurements.

We propose a novel approach for nonlinear regression using a two-layer neural network (NN) model structure with sparsity-favoring hierarchical priors on the network weights. We present an expectation propagation (EP) approach for approximate integration over the posterior distribution of the weights, the hierarchical scale parameters of the priors, and the residual scale. Using a factorized posterior approximation we derive a computationally efficient algorithm, whose complexity scales similarly to an ensemble of independent sparse linear models. The approach enables flexible definition of weight priors with different sparseness properties such as independent Laplace priors with a common scale parameter or Gaussian automatic relevance determination (ARD) priors with different relevance parameters for all inputs. The approach can be extended beyond standard activation functions and NN model structures to form flexible nonlinear predictors from multiple sparse linear models. The effects of the hierarchical priors and the predictive performance of the algorithm are assessed using both simulated and real-world data. Comparisons are made to two alternative models with ARD priors: a Gaussian process with a NN covariance function and marginal maximum a posteriori estimates of the relevance parameters, and a NN with Markov chain Monte Carlo integration over all the unknown model parameters.

We discuss the Dempster-Shafer theory of evidence. We introduce a concept of monotonicity which is related to the diminution of the range between belief and plausibility. We show that the accumulation of knowledge in this framework exhibits a nonmonotonic property. We show how the belief structure can be used to represent typical or commonsense knowledge.

In this paper, the feasibility of using finite totally ordered probability models under Alelinnas's Theory of Probabilistic Logic [Aleliunas, 1988] is investigated. The general form of the probability algebra of these models is derived and the number of possible algebras with given size is deduced. Based on this analysis, we discuss problems of denominator-indifference and ambiguity-generation that arise in reasoning by cases and abductive reasoning. An example is given that illustrates how these problems arise. The investigation shows that a finite probability model may be of very limited usage.