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Social networks and other large sparse date sets pose significant challenges for statistical inference, as many standard statistical methods for testing model/data fit are not applicable in such settings. Motivated by the goodness of fit problem for general log linear models, we focus on the problem of deriving Markov and Graver bases dynamically, since computation of the entire basis is infeasible in many practical settings. We present a dynamic approach to explore the fiber of a statistical model, based on the toric geometry of hypergraphs. This viewpoint offers a new combinatorial way to encode Graver bases. The talk will conclude with an example for the $p_1$ model for social networks, a statistical model of random directed graphs that allows for reciprocated edges. *This is joint work with E. Gross and D. Stasi.