Quantifying activities in a food web or ecological network, and related aspects of dependence, has largely been either descriptive or deterministic. Although schemes exist for assessing the reliability of such quantification, many are far from being statistical in nature. Statistical modeling approaches are explored, with a focus on the ecosystem aspects of a food web. By employing Bayesian melding, we provide a new statistical inferential approach for understanding ecological networks in the context of mass balance. Our approach embodies the traditional deterministic views on network relations, yet it is developed on the basis of proper statistical inference that allows the estimation of physical quantities and probabilistic assessment of the estimation. We describe our approach, and illustrate it with a mass balance dataset. The practical advantage of our approach is a more realistic understanding of the network by incorporating natural measurement variability into deterministic beliefs about the relationships among measurements. The resulting inference thus forms a more honest representation of the true state of nature, and provides a formal assessment of balance before data are passed on to later stages of an ecological network analysis (ENA). We also demonstrate that general Bayesian inference for ENA can yield new ecological insight that may not be available through standard classical inference. Copyright © 2009 John Wiley & Sons, Ltd.