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 can work only under certain conditions , and may not be enough to explain the most extreme cases .
It is still unclear whether a single mechanism is enough to explain the entire distribution of radii , or whether a combination of them 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 infer the probabilistic relation between planet radius , mass and incident flux for a sample of 286 gas giants .
We separately incorporate the observational uncertainties of the data and the intrinsic physical scatter in the population .
This allows 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 , with planets in the range \sim 0.37 - 0.98 \si { \Mj } showing the most inflated radii .
At higher masses , the radius response to incident flux begins to decrease .
Below a threshold of 0.37 \pm 0.03 \si { \Mj } we find that giant exoplanets as a population are unable to maintain inflated radii \gtrapprox 1.4 \si { \Rj } but instead exhibit smaller sizes as the incident flux is increased beyond 10 ^ { 6 } \si { Wm ^ { -2 } } .
We also find that below 1 \si { \Mj } , there is a cutoff point at high incident flux beyond which we find no more inflated planets , and that this cutoff point decreases as the mass decreases .
At incident fluxes higher than \sim 1.6 \times 10 ^ { 6 } \si { Wm ^ { -2 } } and in a mass range 0.37 - 0.98 \si { \Mj } , 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 .

Conclusions :