One of the biggest issues in the study of Bayesian inference of neutron star (NS) equations of state (EoSs) is the choice of Bayesian priors. Given today’s measurement accuracy of neutron star mass and radii, the understanding of NS EoSs is unavoidably influenced by our choice of the prior. What’s the difference of these priors? How to quantify the difference of these priors? In this work, we show the radii of two NSs observed by NICER observations (PSR J0740+6620 and PSR 0030+0451) are correlated (in both Bayesian prior and posterior) if these two NSs are built upon standard EoS models that have been widely used in astronomical studies (e.g. the piece-wise speed of sound and the piece-wise polytropic EoSs). On the other hand, the correlation of the NS radii (again, in both prior and posterior) can be significantly weakened when additional degrees of freedom concerning the first-order phase transitions are added into the EoSs. We propose an observable quantity, $D_L$, which measures the extent to which the linear correlation of the radii of two NSs is weakened. The strength of $D_L$ of “standard” EoSs and those with strong phase transitions(PT) are obviously different. Consequently, the $D_L$ may be used as a “sensor” of PT. By comparing the probability distribution of the $D_L$ extracted from NICER observations and the $D_L$ distribution of standard EoSs, we can quantitatively obtain the identification probability of finding beyond-standard EoS models in NICER observations, which is 48% with 5% false alarm rate.