Influence diagrams are ideal knowledge representations for Bayesian statistical models. However, these diagrams are difficult for end users to interpret and to manipulate. We present a user-based architecture that enables end users to create and to manipulate the knowledge representation. We use the problem of physicians' interpretation of two-arm parallel randomized clinical trials (TAPRCT) to illustrate the architecture and its use. There are three primary data structures. Elements of statistical models are encoded as subgraphs of a restricted class of influence diagram. The interpretations of those elements are mapped into users' language in a domain-specific, user-based semantic interface, called a patient-flow diagram, in the TAPRCT problem. Pennitted transformations of the statistical model that maintain the semantic relationships of the model are encoded in a metadata-state diagram, called the cohort-state diagram, in the TAPRCT problem. The algorithm that runs the system uses modular actions called construction steps. This framework has been implemented in a system called THOMAS, that allows physicians to interpret the data reported from a TAPRCT.

In recent years the belief network has been used increasingly to model systems in Al that must perform uncertain inference. The development of efficient algorithms for probabilistic inference in belief networks has been a focus of much research in AI. Efficient algorithms for certain classes of belief networks have been developed, but the problem of reporting the uncertainty in inferred probabilities has received little attention. A system should not only be capable of reporting the values of inferred probabilities and/or the favorable choices of a decision; it should report the range of possible error in the inferred probabilities and/or choices. Two methods have been developed and implemented for determining the variance in inferred probabilities in belief networks. These methods, the Approximate Propagation Method and the Monte Carlo Integration Method are discussed and compared in this paper.

In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit conditions and the implicit conditions of probability assignments `me properly distinguished, it follows that Bayes' theorem is not a generally applicable revision rule. Upon properly distinguishing belief revision from belief updating, we see that Jeffrey's rule and its variations are not revision rules, either. Without these distinctions, the limitation of the Bayesian approach is often ignored or underestimated. Revision, in its general form, cannot be done in the Bayesian approach, because a probability distribution function alone does not contain the information needed by the operation.

Bayesian belief networks can be used to represent and to reason about complex systems with uncertain, incomplete and conflicting information. Belief networks are graphs encoding and quantifying probabilistic dependence and conditional independence among variables. One type of reasoning of interest in diagnosis is called abductive inference (determination of the global most probable system description given the values of any partial subset of variables). In some cases, abductive inference can be performed with exact algorithms using distributed network computations but it is an NP-hard problem and complexity increases drastically with the presence of undirected cycles, number of discrete states per variable, and number of variables in the network. This paper describes an approximate method based on genetic algorithms to perform abductive inference in large, multiply connected networks for which complexity is a concern when using most exact methods and for which systematic search methods are not feasible. The theoretical adequacy of the method is discussed and preliminary experimental results are presented.

As belief networks are used to model increasingly complex situations, the need to automatically construct them from large databases will become paramount. This paper concentrates on solving a part of the belief network induction problem: that of learning the quantitative structure (the conditional probabilities), given the qualitative structure. In particular, a theory is presented that shows how to propagate inference distributions in a belief network, with the only assumption being that the given qualitative structure is correct. Most inference algorithms must make at least this assumption. The theory is based on four network transformations that are sufficient for any inference in a belief network. Furthermore, the claim is made that contrary to popular belief, error will not necessarily grow as the inference chain grows. Instead, for QBN belief nets induced from large enough samples, the error is more likely to decrease as the size of the inference chain increases.

Relevance-based explanation is a scheme in which partial assignments to Bayesian belief network variables are explanations (abductive conclusions). We allow variables to remain unassigned in explanations as long as they are irrelevant to the explanation, where irrelevance is defined in terms of statistical independence. When multiple-valued variables exist in the system, especially when subsets of values correspond to natural types of events, the over specification problem, alleviated by independence-based explanation, resurfaces. As a solution to that, as well as for addressing the question of explanation specificity, it is desirable to collapse such a subset of values into a single value on the fly. The equivalent method, which is adopted here, is to generalize the notion of assignments to allow disjunctive assignments. We proceed to define generalized independence based explanations as maximum posterior probability independence based generalized assignments (GIB-MAPs). GIB assignments are shown to have certain properties that ease the design of algorithms for computing GIB-MAPs. One such algorithm is discussed here, as well as suggestions for how other algorithms may be adapted to compute GIB-MAPs. GIB-MAP explanations still suffer from instability, a problem which may be addressed using ?approximate? conditional independence as a condition for irrelevance.

Tree structures have been shown to provide an efficient framework for propagating beliefs [Pearl,1986]. This paper studies the problem of finding an optimal approximating tree. The star decomposition scheme for sets of three binary variables [Lazarsfeld,1966; Pearl,1986] is shown to enhance the class of probability distributions that can support tree structures; such structures are called tree-decomposable structures. The logarithm scoring rule is found to be an appropriate optimality criterion to evaluate different tree-decomposable structures. Characteristics of such structures closest to the actual belief network are identified using the logarithm rule, and greedy and exact techniques are developed to find the optimal approximation.

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.

Two algorithms are presented for "compiling" influence diagrams into a set of simple decision rules. These decision rules define simple-to-execute, complete, consistent, and near-optimal decision procedures. These compilation algorithms can be used to derive decision procedures for human teams solving time constrained decision problems.

In previous work we developed a method of learning Bayesian Network models from raw data. This method relies on the well known minimal description length (MDL) principle. The MDL principle is particularly well suited to this task as it allows us to tradeoff, in a principled way, the accuracy of the learned network against its practical usefulness. In this paper we present some new results that have arisen from our work. In particular, we present a new local way of computing the description length. This allows us to make significant improvements in our search algorithm. In addition, we modify our algorithm so that it can take into account partial domain information that might be provided by a domain expert. The local computation of description length also opens the door for local refinement of an existent network. The feasibility of our approach is demonstrated by experiments involving networks of a practical size.