Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and structural observability theorems are developed and algorithms are formulated. Controllability and observability are fundamental concepts in dynamic systems (Luenberger 1979). Controllability corresponds to the ability to control a system while observability analyzes the inferability of its variables. Both properties can be determined by the ranks of the system matrices. Structural controllability and observability, on the other hand, analyze the property of a system with its structure only, without the specific knowledge of the values of its elements (tin 1974, Shields and Pearson 1976). The structural analysis explores the connection between the structure of a model and the functional dependence among its elements. It is useful in comprehending problem and formulating solution by challenging the underlying intuitions and detecting inconsistency in a model. This type of qualitative reasoning can sometimes provide insight even when there is insufficient numerical information in a model.

In Moral, Campos (1991) and Cano, Moral, Verdegay-Lopez (1991) a new method of conditioning convex sets of probabilities has been proposed. The result of it is a convex set of non-necessarily normalized probability distributions. The normalizing factor of each probability distribution is interpreted as the possibility assigned to it by the conditioning information. From this, it is deduced that the natural value for the conditional probability of an event is a possibility distribution. The aim of this paper is to study methods of transforming this possibility distribution into a probability (or uncertainty) interval. These methods will be based on the use of Sugeno and Choquet integrals. Their behaviour will be compared in basis to some selected examples.

Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization algorithm. When the model is conditionally conjugate, the coordinate updates are easily derived and in closed form. However, many models of interest---like the correlated topic model and Bayesian logistic regression---are nonconjuate. In these models, mean-field methods cannot be directly applied and practitioners have had to develop variational algorithms on a case-by-case basis. In this paper, we develop two generic methods for nonconjugate models, Laplace variational inference and delta method variational inference. Our methods have several advantages: they allow for easily derived variational algorithms with a wide class of nonconjugate models; they extend and unify some of the existing algorithms that have been derived for specific models; and they work well on real-world datasets. We studied our methods on the correlated topic model, Bayesian logistic regression, and hierarchical Bayesian logistic regression.

This paper introduces a set of algorithms for Monte-Carlo Bayesian reinforcement learning. Firstly, Monte-Carlo estimation of upper bounds on the Bayes-optimal value function is employed to construct an optimistic policy. Secondly, gradient-based algorithms for approximate upper and lower bounds are introduced. Finally, we introduce a new class of gradient algorithms for Bayesian Bellman error minimisation. We theoretically show that the gradient methods are sound. Experimentally, we demonstrate the superiority of the upper bound method in terms of reward obtained. However, we also show that the Bayesian Bellman error method is a close second, despite its significant computational simplicity.

In this paper we address the uncertainty issues involved in the low-level vision task of image segmentation. Researchers in computer vision have worked extensively on this problem, in which the goal is to partition (or segment) an image into regions that are homogeneous or uniform in some sense. This segmentation is often utilized by some higher level process, such as an object recognition system. We show that by considering uncertainty in a Bayesian formalism, we can use statistical image models to build an approximate representation of a probability distribution over a space of alternative segmentations. We give detailed descriptions of the various levels of uncertainty associated with this problem, discuss the interaction of prior and posterior distributions, and provide the operations for constructing this representation.

Dynamic network models (DNMs) are belief networks for temporal reasoning. The DNM methodology combines techniques from time series analysis and probabilistic reasoning to provide (1) a knowledge representation that integrates noncontemporaneous and contemporaneous dependencies and (2) methods for iteratively refining these dependencies in response to the effects of exogenous influences. We use belief-network inference algorithms to perform forecasting, control, and discrete event simulation on DNMs. The belief network formulation allows us to move beyond the traditional assumptions of linearity in the relationships among time-dependent variables and of normality in their probability distributions. We demonstrate the DNM methodology on an important forecasting problem in medicine. We conclude with a discussion of how the methodology addresses several limitations found in traditional time series analyses.

In this paper, we present a Bayesian channel estimation algorithm for multicarrier receivers based on pilot symbol observations. The inherent sparse nature of wireless multipath channels is exploited by modeling the prior distribution of multipath components' gains with a hierarchical representation of the Bessel K probability density function; a highly efficient, fast iterative Bayesian inference method is then applied to the proposed model. The resulting estimator outperforms other state-of-the-art Bayesian and non-Bayesian estimators, either by yielding lower mean squared estimation error or by attaining the same accuracy with improved convergence rate, as shown in our numerical evaluation.

We present a mechanism for constructing graphical models, specifically Bayesian networks, from a knowledge base of general probabilistic information. The unique feature of our approach is that it uses a powerful first-order probabilistic logic for expressing the general knowledge base. This logic allows for the representation of a wide range of logical and probabilistic information. The model construction procedure we propose uses notions from direct inference to identify pieces of local statistical information from the knowledge base that are most appropriate to the particular event we want to reason about. These pieces are composed to generate a joint probability distribution specified as a Bayesian network. Although there are fundamental difficulties in dealing with fully general knowledge, our procedure is practical for quite rich knowledge bases and it supports the construction of a far wider range of networks than allowed for by current template technology.

The Noisy-Or model is convenient for describing a class of uncertain relationships in Bayesian networks [Pearl 1988]. Pearl describes the Noisy-Or model for Boolean variables. Here we generalize the model to nary input and output variables and to arbitrary functions other than the Boolean OR function. This generalization is a useful modeling aid for construction of Bayesian networks. We illustrate with some examples including digital circuit diagnosis and network reliability analysis.

One of the most difficult aspects of modeling complex dilemmas in decision-analytic terms is composing a diagram of relevance relations from a set of domain concepts. Decision models in domains such as medicine, however, exhibit certain prototypical patterns that can guide the modeling process. Medical concepts can be classified according to semantic types that have characteristic positions and typical roles in an influence-diagram model. We have developed a graph-grammar production system that uses such inherent interrelationships among medical terms to facilitate the modeling of medical decisions.