Application of SBI-NPE to real NICER data. Left: 23 burst spectra covered by the restricted prior, indicated by the region in gray. Right: recovered spectral parameters with SBI-NPE and XSPEC. The agreement between the different methods is remarkable. The figure shows the number of counts per spectrum (top), the normalization of the power law, the temperature of the back body in keV, and at the bottom the black-body normalization translated to a radius (in km) assuming a distance to the source of 8 kpc. Single-round inference is performed with a training sample of 23 × 5000 spectra, derived from a restrictor, constraining the number of counts in the spectra to be between 100 and 10 000 counts (red filled circles). Single-round inference is also performed with a training sample of 23 × 2500 spectra, generated from a restrictor build from a quick inference (green filled circles). XSPEC best-fit results are shown with blue filled circles.