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Considerable effort has been devoted to the empirical estimation of species interaction strengths. This effort has focused primarily on statistical significance testing and on obtaining point estimates of parameters that contribute to interaction strength magnitude, leaving characterizations of estimation uncertainty and distinctions between the deterministic and stochastic contributions to variation largely unconsidered. Here we consider a means of quantifying interaction strength uncertainty by formulating an observational method for estimating per capita attack rates as a Bayesian statistical model. This formulation permits the explicit incorporation of multiple sources of uncertainty. In doing so we highlight the informative nature of several so-called non-informative prior choices in modeling the sparse data typical of predator feeding surveys and provide evidence for the superior performance of a new neutral prior choice. A case study application shows that while Bayesian point estimates may be made to correspond with those obtained by frequentist approaches, estimation uncertainty as described by the 95% intervals is more biologically realistic using the Bayesian method in that the lower bounds of the Bayesian posterior intervals for the attack rates do not include zero when the occurrence of a given predator-prey interaction is in fact observed. This contrasts with bootstrap confidence intervals that often do contain zero in such cases. The Bayesian approach provides a straightforward, probabilistic characterization of interaction strength uncertainty. In doing so it provides a framework for considering both the deterministic and stochastic drivers of species interactions and their impact on food web dynamics.