Bayesian inferences on covariant density functionals from multimessenger astrophysical data: The impacts of likelihood functions of low density matter constraints

We systematically investigate how the choice between Gaussian and uniform likelihood functions in Bayesian inference affects the inferred bulk properties of compact stars and nuclear matter within covariant density functional-based equations of state. To enable direct comparison between two approaches, we designed the uniform likelihood function with a Gaussian-equivalent normalization factor and marginalization behavior. Across three representative astrophysical scenarios, both approaches yield nearly identical mass-radius relations, density-pressure relations, and overlapping 95.4\% confidence level regions. We find significant variations in the predicted distributions of nuclear characteristics at nuclear saturation in the isoscalar channel, e.g., in nuclear compressibility $K_{\rm sat}$, whereas the isovector quantities, for example, proton fraction, are quite similar. Our results indicate that the influence of individual nuclear characteristics at saturation density on the global properties of compact stars is obscured by the integral nature of these quantities. This, in turn, underscores the need for dedicated nuclear experiments sensitive to these characteristics in order to better constrain their values.