The photometric lightcurve and phase curve of an asteroid refer to the variation of the asteroid’s disk-integrated brightness as a function of time and of the phase angle (the Sun-Object-Observer angle), respectively. They depend on the shape and rotation state of the asteroid, as well as the scattering properties of the asteroid’s surface. It follows that the shape, rotation state, and scattering properties can be estimated from the observations, to an extent allowed by the data available. For general convex shapes comprising large numbers of parameters, we develop Markov-chain Monte Carlo (MCMC) samplers based on the simulation of virtual observations. We then demonstrate the utilization of the inverse methods for four asteroids with sparse photometry available from Data Release 2 of the ESA Gaia mission: (21) Lutetia, (26) Proserpina, (585) Bilkis, and (2867) Steins. With the help of the H, G1, G2 photometric function, we devise a surface reflection coecient that gives rise to realistic disk-integrated phase curves. This allows us to derive phase curve parameters that are independent of the illumination and observation geometry. These proper phase curve parameters may allow for photometric classication of asteroids.