This paper derives a formula for computing the conditional probability of a set of candidates, where a candidate is a set of disorders that explain a given set of positive findings. Such candidate sets are produced by a recent method for multidisorder diagnosis called symptom clustering. A symptom clustering represents a set of candidates compactly as a cartesian product of differential diagnoses. By evaluating the probability of a candidate set, then, a large set of candidates can be validated or pruned simultaneously. The probability of a candidate set is then specialized to obtain the probability of a single candidate. Unlike earlier results, the equation derived here allows the specification of positive, negative, and unknown symptoms and does not make assumptions about disorders not in the candidate.

We propose an abductive diagnosis theory that integrates probabilistic, causal and taxonomic knowledge. Probabilistic knowledge allows us to select the most likely explanation; causal knowledge allows us to make reasonable independence assumptions; taxonomic knowledge allows causation to be modeled at different levels of detail, and allows observations be described in different levels of precision. Unlike most other approaches where a causal explanation is a hypothesis that one or more causative events occurred, we define an explanation of a set of observations to be an occurrence of a chain of causation events. These causation events constitute a scenario where all the observations are true. We show that the probabilities of the scenarios can be computed from the conditional probabilities of the causation events. Abductive reasoning is inherently complex even if only modest expressive power is allowed. However, our abduction algorithm is exponential only in the number of observations to be explained, and is polynomial in the size of the knowledge base. This contrasts with many other abduction procedures that are exponential in the size of the knowledge base.

The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference, some extensions seem to be simply wrong and we use qualitative techniques to weed out the unwanted ones. In the area of diagnosis, however, the multiple explanations may all seem reasonable, however improbable. Choosing among them is a matter of quantitative preference. Quantitative preference works well in diagnosis when knowledge is modelled causally. Here we suggest a framework that combines probabilities and defaults in a single unified framework that retains the semantics of diagnosis as construction of explanations from a fixed set of possible hypotheses. We can then compute probabilities incrementally as we construct explanations. Here we describe a branch and bound algorithm that maintains a set of all partial explanations while exploring a most promising one first. A most probable explanation is found first if explanations are partially ordered.

A new probabilistic network construction system, DYNASTY, is proposed for diagnostic reasoning given variables whose probabilities change over time. Diagnostic reasoning is formulated as a sequential stochastic process, and is modeled using influence diagrams. Given a set O of observations, DYNASTY creates an influence diagram in order to devise the best action given O. Sensitivity analyses are conducted to determine if the best network has been created, given the uncertainty in network parameters and topology. DYNASTY uses an equivalence class approach to provide decision thresholds for the sensitivity analysis. This equivalence-class approach to diagnostic reasoning differentiates diagnoses only if the required actions are different. A set of network-topology updating algorithms are proposed for dynamically updating the network when necessary.

We present a general architecture for the monitoring and diagnosis of large scale sensor-based systems with real time diagnostic constraints. This architecture is multileveled, combining a single monitoring level based on statistical methods with two model based diagnostic levels. At each level, sources of uncertainty are identified, and integrated methodologies for uncertainty management are developed. The general architecture was applied to the monitoring and diagnosis of a specific nuclear physics detector at Lawrence Berkeley National Laboratory that contained approximately 5000 components and produced over 500 channels of output data. The general architecture is scalable, and work is ongoing to apply it to detector systems one and two orders of magnitude more complex.

Since exact probabilistic inference is intractable in general for large multiply connected belief nets, approximate methods are required. A promising approach is to use heuristic search among hypotheses (instantiations of the network) to find the most probable ones, as in the TopN algorithm. Search is based on the relative probabilities of hypotheses which are efficient to compute. Given upper and lower bounds on the relative probability of partial hypotheses, it is possible to obtain bounds on the absolute probabilities of hypotheses. Best-first search aimed at reducing the maximum error progressively narrows the bounds as more hypotheses are examined. Here, qualitative probabilistic analysis is employed to obtain bounds on the relative probability of partial hypotheses for the BN20 class of networks networks and a generalization replacing the noisy OR assumption by negative synergy. The approach is illustrated by application to a very large belief network, QMR-BN, which is a reformulation of the Internist-1 system for diagnosis in internal medicine.

Although the notion of diagnostic problem has been extensively investigated in the context of static systems, in most practical applications the behavior of the modeled system is significantly variable during time. The goal of the paper is to propose a novel approach to the modeling of uncertainty about temporal evolutions of time-varying systems and a characterization of model-based temporal diagnosis. Since in most real world cases knowledge about the temporal evolution of the system to be diagnosed is uncertain, we consider the case when probabilistic temporal knowledge is available for each component of the system and we choose to model it by means of Markov chains. In fact, we aim at exploiting the statistical assumptions underlying reliability theory in the context of the diagnosis of timevarying systems. We finally show how to exploit Markov chain theory in order to discard, in the diagnostic process, very unlikely diagnoses.

Numerous methods for probabilistic reasoning in large, complex belief or decision networks are currently being developed. There has been little research on automating the dynamic, incremental construction of decision models. A uniform value-driven method of decision model construction is proposed for the hierarchical complete diagnosis. Hierarchical complete diagnostic reasoning is formulated as a stochastic process and modeled using influence diagrams. Given observations, this method creates decision models in order to obtain the best actions sequentially for locating and repairing a fault at minimum cost. This method construct decision models incrementally, interleaving probe actions with model construction and evaluation. The method treats meta-level and baselevel tasks uniformly. That is, the method takes a decision-theoretic look at the control of search in causal pathways and structural hierarchies.

Recent research has found that diagnostic performance with Bayesian belief networks is often surprisingly insensitive to imprecision in the numerical probabilities. For example, the authors have recently completed an extensive study in which they applied random noise to the numerical probabilities in a set of belief networks for medical diagnosis, subsets of the CPCS network, a subset of the QMR (Quick Medical Reference) focused on liver and bile diseases. The diagnostic performance in terms of the average probabilities assigned to the actual diseases showed small sensitivity even to large amounts of noise. In this paper, we summarize the findings of this study and discuss possible explanations of this low sensitivity. One reason is that the criterion for performance is average probability of the true hypotheses, rather than average error in probability, which is insensitive to symmetric noise distributions. But, we show that even asymmetric, logodds-normal noise has modest effects. A second reason is that the gold-standard posterior probabilities are often near zero or one, and are little disturbed by noise.

A modelling language is described which is suitable for the correlation of information when the underlying functional model of the system is incomplete or uncertain and the temporal dependencies are imprecise. An efficient and incremental implementation is outlined which depends on cost functions satisfying certain criteria. Possibilistic logic and probability theory (as it is used in the applications targetted) satisfy these criteria.