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This article discusses arc reversals in hybrid Bayesian networks with deterministic variables. Hybrid Bayesian networks contain a mix of discrete and continuous chance variables. In a Bayesian network representation, a continuous chance variable is said to be deterministic if its conditional distributions have zero variances. Arc reversals are used in making inferences in hybrid Bayesian networks and influence diagrams. We describe a framework consisting of potentials and some operations on potentials that allows us to describe arc reversals between all possible kinds of pairs of variables. We describe a new type of conditional distribution function, called partially deterministic, if some of the conditional distributions have zero variances and some have positive variances, and show how it can arise from arc reversals.

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Abstract. 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' decisionmaking 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.

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