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In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the possibility of local computation from the axioms. Next, we describe a propagation scheme for computing marginals of a valuation when we have a factorization of the valuation on a hypertree. Finally we show how the problem of computing marginals of joint probability distributions and joint belief functions fits the general framework. [ABSTRACT FROM AUTHOR]

This article discusses a potential application of radio frequency identification (RFID) and collaborative filtering for targeted advertising in grocery stores. Every day hundreds of items in grocery stores are marked down for promotional purposes. Whether these promotions are effective or not depends primarily on whether the customers are aware of them or not, and secondarily whether the customers are interested in the products or not. Currently, the companies are incapable of influencing the customers' decision-making process while they are shopping. However, the capabilities of RFID technology enable us to transfer the recommendation systems of e-commerce to grocery stores. In our model, using RFID technology, we get real time information about the products placed in the cart during the shopping process. Based on that information we inform the customer about those promotions in which the customer is likely to be interested in. The selection of the product advertised is a dynamic decision making process since it is based on the information of the products placed inside the cart while customer is shopping. Collaborative filtering will be used for the identification of the advertised product and Bayesian networks will be used for the application of collaborative filtering. We are assuming a scenario where all products have RFID tags, and grocery carts are equipped with RFID readers and screens that would display the relevant promotions. [ABSTRACT FROM AUTHOR]

In a Bayesian network with continuous variables containing a variable(s) that is a conditionally deterministic function of its continuous parents, the joint density function does not exist. Conditional linear Gaussian distributions can handle such cases when the deterministic function is linear and the continuous variables have a multi-variate normal distribution. In this paper, operations required for performing inference with nonlinear conditionally deterministic variables are developed. We perform inference in networks with nonlinear deterministic variables and non-Gaussian continuous variables by using piecewise linear approximations to nonlinear functions and modeling probability distributions with mixtures of truncated exponentials (MTE) potentials. [ABSTRACT FROM AUTHOR]