Impact of hyperon mixing on neutron star structure based on Skyrme-type equations of state: Systematic analysis of $\mathrm{\Lambda }NN$ and $\mathrm{\Lambda }\mathrm{\Lambda }N$ three-body forces with Bayesisan inference

We study hyperonic density-dependent three-body effects in cold neutron-star matter using a Skyrme energy-density-functional framework. In beta-equilibrated $npe\mu \mathrm{\Lambda }$ matter, the effective $\mathrm{\Lambda }NN$ and $\mathrm{\Lambda }\mathrm{\Lambda }N$ terms are varied separately in the $(\beta ,A_3)$ and $(\gamma ,C_3)$ planes, and each tabulated equation of state is used in Tolman–Oppenheimer–Volkoff calculations. The calculated $P$–$\epsilon$ branches are classified by monotonicity and extremum structure. The $\mathrm{\Lambda }\mathrm{\Lambda }N$ term does not affect the $\mathrm{\Lambda }$-onset condition, but modifies the finite-$\mathrm{\Lambda }$ post-onset EOS: increasing $C_3$ generally stiffens the post-onset branch and raises $M_{\max }$ in mechanically admissible regions, whereas increasing $\gamma$ reduces this enhancement at fixed $C_3$. In contrast, the $\mathrm{\Lambda }NN$ term shifts the $\mathrm{\Lambda }$-onset density and modifies the post-onset EOS simultaneously, producing organized branch-limited and Maxwell-candidate regions for some reference interactions. Representative two-extrema cases are examined with Maxwell constructions. We also perform an exploratory Bayesian analysis using neutron-star mass–radius information alone and apply XGBoost–SHAP surrogate diagnostics to summarize parameter sensitivities. Within the adopted likelihood and prior ranges, the posterior weight tends to favor sizable hyperonic three-body repulsion, and the SHAP analysis identifies $A_3$ and $C_3$ as important controls of $M_{\text{max}}$ and $R_{2.0}$. These results show that maximum-mass recovery in hyperonic neutron stars is not a single mechanism: $M_{\text{max}}$ maps must be interpreted together with onset behavior, branch admissibility, and extremum-count diagnostics. *shortened due to the arXiv’s word limit.