The extended Recursive Noisy OR model: Static and dynamic considerations

Abstract

Many engineering problems rely on causal reasoning to analyze the interactions among the numerous causes/variables. Probabilistic graphical models (e.g., Bayesian networks) are widely used for such analyses, but the conditional probability tables (CPTs) grow exponentially with respect to the number of variables (nodes). Several canonical models have been developed to reduce the amount of information needed to complete the CPTs. In this paper, the Extended Recursive Noisy OR (ERNOR) is developed. It is an improved version of the long-established RNOR, in that it resolves the asymmetry problem when the number of causes exceeds three. Like RNOR, it is not restricted to the independence of causal influence, thus synergy can be considered. The dynamic form of the ERNOR is also developed, which provides a continuous causal influence function. This function is dependent on cumulative distributions that represent the presence level of each time-dependent cause, useful for models that do not rely on CPTs. The derivation of the ERNOR is presented, and it is contrasted with its predecessor, the RNOR.