We explore the constraints on the three-nucleon force (3NF) of chiral effective field theory $\left(\chi \mathrm{EFT}\right)$ that are provided by bound-state observables in the $A=3$ and $A=4$ sectors. Our statistically rigorous analysis incorporates experimental error, computational method uncertainty, and the uncertainty due to truncation of the $\chi \mathrm{EFT}$ expansion at next-to-next-to-leading order. A consistent solution for the ${}^3\mathrm{H}$ binding energy, the ${}^4\mathrm{He}$ binding energy and radius, and the ${}^3\mathrm{H}\beta$-decay rate can only be obtained if $\chi \mathrm{EFT}$ truncation errors are included in the analysis. The $\beta$-decay rate is the only one of these that yields a nondegenerate constraint on the 3NF low-energy constants, which makes it crucial for the parameter estimation. We use eigenvector continuation for fast and accurate emulation of no-core shell model calculations of the few-nucleon observables. This facilitates sampling of the posterior probability distribution, allowing us to also determine the distributions of the parameters that quantify the truncation error. We find a $\chi \mathrm{EFT}$ expansion parameter of $Q=0.33\pm 0.06$ for these observables.

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• Binding energy & masses
• Effective field theory
• Few-body systems
• Nuclear forces
• Nucleon-nucleon interactions
• A ≤ 5
• Bayesian methods