This paper presents Bayesian parameter estimation for the mass and equatorial radius of the millisecond pulsar PSR J0030+0451, based on pulse-profile modeling of X-ray spectral-timing data from the Neutron Star Interior Composition Explorer (NICER). The analysis involves relativistic ray-tracing of thermal emission from hot regions on the pulsar's surface, which are modeled as two distinct regions. The study explores various shapes and topologies for these regions, inferring their parameters along with the pulsar's mass and radius. The results indicate that one hot region has a small angular extent, while the other is more extended. The inferred mass is $ 1.34_{-0.16}^{+0.15}~M_{\odot} $ and the equatorial radius is $ 12.71_{-1.19}^{+1.14}~km $, with the compactness $ GM/R_{eq}c^{2}=0.156_{-0.010}^{+0.008} $. The analysis uses the X-ray Pulsation Simulation and Inference (X-PSI) package, which combines Bayesian modeling with statistical sampling software. The study also compares results with earlier analyses of PSR J0030+0451 using XMM-Newton data. The results provide insights into the pulsar's structure and the equation of state of dense matter. The paper discusses the implications of these findings for understanding neutron star physics, pulsar emission mechanisms, and stellar evolution. The analysis highlights the importance of high-quality data and computational resources in constraining pulsar parameters. The study also addresses the challenges of modeling complex surface radiation fields and the need for further research to improve constraints on pulsar properties.This paper presents Bayesian parameter estimation for the mass and equatorial radius of the millisecond pulsar PSR J0030+0451, based on pulse-profile modeling of X-ray spectral-timing data from the Neutron Star Interior Composition Explorer (NICER). The analysis involves relativistic ray-tracing of thermal emission from hot regions on the pulsar's surface, which are modeled as two distinct regions. The study explores various shapes and topologies for these regions, inferring their parameters along with the pulsar's mass and radius. The results indicate that one hot region has a small angular extent, while the other is more extended. The inferred mass is $ 1.34_{-0.16}^{+0.15}~M_{\odot} $ and the equatorial radius is $ 12.71_{-1.19}^{+1.14}~km $, with the compactness $ GM/R_{eq}c^{2}=0.156_{-0.010}^{+0.008} $. The analysis uses the X-ray Pulsation Simulation and Inference (X-PSI) package, which combines Bayesian modeling with statistical sampling software. The study also compares results with earlier analyses of PSR J0030+0451 using XMM-Newton data. The results provide insights into the pulsar's structure and the equation of state of dense matter. The paper discusses the implications of these findings for understanding neutron star physics, pulsar emission mechanisms, and stellar evolution. The analysis highlights the importance of high-quality data and computational resources in constraining pulsar parameters. The study also addresses the challenges of modeling complex surface radiation fields and the need for further research to improve constraints on pulsar properties.