Inferring higher-order interaction structure from observations of dynamics is a central challenge in complex systems, particularly when data are scarce, noisy, or concentrated in lower-dimensional regions of state space. We develop Bayes-THIS, a Bayesian extension of Taylor-based Hypergraph Inference using SINDy (THIS) that replaces threshold-based sparse regression with sparse Bayesian regression using automatic relevance determination. This yields adaptive, term-wise shrinkage and a posterior over inferred Taylor expansion coefficients that encode the presence or absence of interactions. Across numerical experiments, Bayes-THIS improves inference in low-data, high-noise, and ill-conditioned regimes. The Bayesian formulation also enables two capabilities absent from the original THIS framework: a posterior predictive diagnostic for assessing whether a dataset contains higher-order signal distinguishable from noise, and a posterior interval rule for pruning weakly supported hyperedges. Finally, we examine a separate, structural limitation of Taylor-based hypergraph reconstruction: higher-order interactions can produce spurious lower-order signatures that are indistinguishable from genuine lower-order edges. We find that the severity of this non-identifiability depends on cross-order support, showing that structural properties of the target hypergraph can be as important as data quality in determining what can be inferred from dynamics within this framework.

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