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Probabilistic graphical models are widely used to model complex systems withuncertainty. Traditionally, Gaussian directed graphical models are applied foranalysis of large networks with continuous variables since they can provideconditional and marginal distributions in closed form simplifying theinferential task. The Gaussianity and linearity assumptions are often adequate,yet can lead to poor performance when dealing with some practical applications.In this paper, we model each variable in graph G as a polynomial regression ofits parents to capture complex relationships between individual variables andwith utility function of polynomial form. Since the marginal posteriordistributions of individual variables can become analytically intractable, wedevelop a message-passing algorithm to propagate information throughout thenetwork solely using moments which enables the expected utility scores to becalculated exactly. We illustrate how the proposed methodology works in adecision problem in energy systems planning.

Propagating moments in probabilistic graphical models for decision support systems