Bayesian Networks (BN) provide robust probabilistic methods of reasoning under uncertainty, but despite their formal grounds are strictly based on the notion of conditional dependence, not much attention has been paid so far to their use in dependability analysis. The aim of this paper is to propose BN as a suitable tool for dependability analysis, by challenging the formalism with basic issues arising in dependability tasks. We will discuss how both modeling and analysis issues can be naturally dealt with by BN. Moreover, we will show how some limitations intrinsic to combinatorial dependability methods such as Fault Trees can be overcome using BN. This will be pursued through the study of a real-world example concerning the reliability analysis of a redundant digital Programmable Logic Controller (PLC) with majority voting 2:3

In previous work, we pointed out the limitations of standard Bayesian networks as a modeling framework for large, complex domains. We proposed a new, richly structured modeling language, {em Object-oriented Bayesian Netorks}, that we argued would be able to deal with such domains. However, it turns out that OOBNs are not expressive enough to model many interesting aspects of complex domains: the existence of specific named objects, arbitrary relations between objects, and uncertainty over domain structure. These aspects are crucial in real-world domains such as battlefield awareness. In this paper, we present SPOOK, an implemented system that addresses these limitations. SPOOK implements a more expressive language that allows it to represent the battlespace domain naturally and compactly. We present a new inference algorithm that utilizes the model structure in a fundamental way, and show empirically that it achieves orders of magnitude speedup over existing approaches.

Graphical models based on conditional independence support concise encodings of the subjective belief of a single agent. A natural question is whether the consensus belief of a group of agents can be represented with equal parsimony. We prove, under relatively mild assumptions, that even if everyone agrees on a common graph topology, no method of combining beliefs can maintain that structure. Even weaker conditions rule out local aggregation within conditional probability tables. On a more positive note, we show that if probabilities are combined with the logarithmic opinion pool (LogOP), then commonly held Markov independencies are maintained. This suggests a straightforward procedure for constructing a consensus Markov network. We describe an algorithm for computing the LogOP with time complexity comparable to that of exact Bayesian inference.

Influence diagrams serve as a powerful tool for modelling symmetric decision problems. When solving an influence diagram we determine a set of strategies for the decisions involved. A strategy for a decision variable is in principle a function over its past. However, some of the past may be irrelevant for the decision, and for computational reasons it is important not to deal with redundant variables in the strategies. We show that current methods (e.g. the "Decision Bayes-ball" algorithm by Shachter UAI98) do not determine the relevant past, and we present a complete algorithm. Actually, this paper takes a more general outset: When formulating a decision scenario as an influence diagram, a linear temporal ordering of the decisions variables is required. This constraint ensures that the decision scenario is welldefined. However, the structure of a decision scenario often yields certain decisions conditionally independent, and it is therefore unnecessary to impose a linear temporal ordering on the decisions. In this paper we deal with partial influence diagrams i.e. influence diagrams with only a partial temporal ordering specified. We present a set of conditions which are necessary and sufficient to ensure that a partial influence diagram is welldefined. These conditions are used as a basis for the construction of an algorithm for determining whether or not a partial influence diagram is welldefined.

Recently, researchers have demonstrated that "loopy belief propagation" - the use of Pearl's polytree algorithm in a Bayesian network with loops - can perform well in the context of error-correcting codes. The most dramatic instance of this is the near Shannon-limit performance of "Turbo Codes" - codes whose decoding algorithm is equivalent to loopy belief propagation in a chain-structured Bayesian network. In this paper we ask: is there something special about the error-correcting code context, or does loopy propagation work as an approximate inference scheme in a more general setting? We compare the marginals computed using loopy propagation to the exact ones in four Bayesian network architectures, including two real-world networks: ALARM and QMR. We find that the loopy beliefs often converge and when they do, they give a good approximation to the correct marginals. However, on the QMR network, the loopy beliefs oscillated and had no obvious relationship to the correct posteriors. We present some initial investigations into the cause of these oscillations, and show that some simple methods of preventing them lead to the wrong results.

We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian, which facilitates exact inference, and then iteratively adjust the variational parameters to improve the quality of the approximation. We demonstrate experimentally that this approximation is much faster than sampling, but comparable in accuracy. We also introduce a simple new technique for handling evidence, which allows us to handle arbitrary distributions on observed nodes, as well as achieving a significant speedup in networks with discrete variables of large cardinality.

As observations and student models become complex, educational assessments that exploit advances in technology and cognitive psychology can outstrip familiar testing models and analytic methods. Within the Portal conceptual framework for assessment design, Bayesian inference networks (BINs) record beliefs about students' knowledge and skills, in light of what they say and do. Joining evidence model BIN fragments- which contain observable variables and pointers to student model variables - to the student model allows one to update belief about knowledge and skills as observations arrive. Markov Chain Monte Carlo (MCMC) techniques can estimate the required conditional probabilities from empirical data, supplemented by expert judgment or substantive theory. Details for the special cases of item response theory (IRT) and multivariate latent class modeling are given, with a numerical example of the latter.

Solving symmetric Bayesian decision problems is a computationally intensive task to perform regardless of the algorithm used. In this paper we propose a method for improving the efficiency of algorithms for solving Bayesian decision problems. The method is based on the principle of lazy evaluation - a principle recently shown to improve the efficiency of inference in Bayesian networks. The basic idea is to maintain decompositions of potentials and to postpone computations for as long as possible. The efficiency improvements obtained with the lazy evaluation based method is emphasized through examples. Finally, the lazy evaluation based method is compared with the HUGIN and valuation-based systems architectures for solving symmetric Bayesian decision problems.

We introduce a new class of graphical representations, expected utility networks (EUNs), and discuss some of its properties and potential applications to artificial intelligence and economic theory. In EUNs not only probabilities, but also utilities enjoy a modular representation. EUNs are undirected graphs with two types of arc, representing probability and utility dependencies respectively. The representation of utilities is based on a novel notion of conditional utility independence, which we introduce and discuss in the context of other existing proposals. Just as probabilistic inference involves the computation of conditional probabilities, strategic inference involves the computation of conditional expected utilities for alternative plans of action. We define a new notion of conditional expected utility (EU) independence, and show that in EUNs node separation with respect to the probability and utility subgraphs implies conditional EU independence.

There is available an ever-increasing variety of procedures for managing uncertainty. These methods are discussed in the literature of artificial intelligence, as well as in the literature of philosophy of science. Heretofore these methods have been evaluated by intuition, discussion, and the general philosophical method of argument and counterexample. Almost any method of uncertainty management will have the property that in the long run it will deliver numbers approaching the relative frequency of the kinds of events at issue. To find a measure that will provide a meaningful evaluation of these treatments of uncertainty, we must look, not at the long run, but at the short or intermediate run. Our project attempts to develop such a measure in terms of short or intermediate length performance. We represent the effects of practical choices by the outcomes of bets offered to agents characterized by two uncertainty management approaches: the subjective Bayesian approach and the Classical confidence interval approach. Experimental evaluation suggests that the confidence interval approach can outperform the subjective approach in the relatively short run.