The “leaky noisy-OR” function is a common and popular method used to simplify the elicitation of complex conditional probability tables in Bayesian networks involving Boolean variables. It has proven to be useful for approximating the required relationship in many real-world situations where there is a set of two or more variables that are potential causes of a single effect variable. However, one of the properties of leaky noisy-OR is Conditional Inter-causal Independence (CII). This property means that the `explaining away' behavior-one of the most powerful benefits of BN inference-is not present when the effect variable is observed as false. Yet, for many real-world problems where the leaky noisy-OR has been considered, this behavior would be expected, meaning that leaky noisy-OR is deficient as an approximation of the required relationship in such cases. There have been previous attempts to adapt the noisy-OR to resolve this problem. However, they require too many additional parameters to be elicited. We describe a simple but powerful extension to leaky noisy-OR that requires only a single additional parameter. While it does not solve the CII problem in all cases, it does resolve most of the explaining away deficiencies that occur in practice. The problem and solution is illustrated using an example from intelligence analysis.

Numerous methods have been proposed to simplify the problem of eliciting complex conditional probability tables in Bayesian networks. One of the most popular methods -“Noisy-OR”- approximates the required relationship in many real-world situations between a set of variables that are potential causes of an effect variable. However, the Noisy-OR function has the conditional inter-causal independence (CII) property which means that `explaining away' behavior-one of the most powerful benefits of BN inference-is not present when the effect variable is observed as false. Hence, for many real-world problems where the Noisy-OR has been used or proposed, it may be deficient as an approximation of the required relationship. However, there is a very simple alternative solution, namely to define the variables as ranked nodes and to use the ranked node weighted average function. This does not have the CII property-instead, we prove it has the conditional anti-correlation property required to ensure that explaining away works in all cases. Moreover, ranked node variables are not restricted to binary states, and hence provide a more comprehensive and general solution to Noisy-OR in all cases.

A technique for compositing computer generated images of buildings and background images created from aerial photographs is described. The aerial photo data are mapped onto a terrain model based on cartographic data. The technique can be used to pre-evaluate visual impact of large scale construction by means of not only still images but also animations.The technique can be briefly described as follows: 1) an accurate, three-dimensional terrain model is created based on cartographic data. 2) a hierarchy of aerial photo data at various resolutions is mapped onto the terrain model as a texture. 3) the height of trees is taken into account in regions near the viewpoint. 4) allowing intersections of terrain models with constructions facilitates geometric adjustments and shadowing.