Context. As of today, hundreds of hot Jupiters have been found, yet the inflated radii of a large fraction of them remain unexplained. A number of mechanisms have been proposed to explain these anomalous radii, however most of these can only work under certain conditions and may not be sufficient to explain the most extreme cases. It is still unclear whether a single mechanism can sufficiently explain the entire distribution of radii, or whether a combination of these mechanisms is needed. Aims. We seek to understand the relationship of radius with stellar irradiation and mass and to find the range of masses over which hot Jupiters are inflated. We also aim to find the intrinsic physical scatter in their radii, caused by unobservable parameters, and to constrain the fraction of hot Jupiters that exhibit inflation. Methods. By constructing a hierarchical Bayesian model, we inferred the probabilistic relation between planet radius, mass, and incident flux for a sample of 286 gas giants. We separately incorporated the observational uncertainties of the data and the intrinsic physical scatter in the population. This allowed us to treat the intrinsic physical scatter in radii, due to latent parameters such as the heavy element fraction, as a parameter to be inferred. Results. We find that the planetary mass plays a key role in the inflation extent and that planets in the range ~0.37−0.98 M_J show the most inflated radii. At higher masses, the radius response to incident flux begins to decrease. Below a threshold of 0.37 ± 0.03 M_J we find that giant exoplanets as a population are unable to maintain inflated radii ≿1.4 R_J but instead exhibit smaller sizes as the incident flux is increased beyond 10⁶ W m⁻². We also find that below 1 M_J, there is a cut-off point at high incident flux beyond which we find no more inflated planets, and that this cut-off point decreases as the mass decreases. At incident fluxes higher than ~1.6 × 10⁶ W m⁻² and in a mass range 0.37−0.98 M_J, we find no evidence for a population of non-inflated hot Jupiters. Our study sheds a fresh light on one of the key questions in the field and demonstrates the importance of population-level analysis to grasp the underlying properties of exoplanets.