Adaptive optics (AO) corrected image restoration is particularly difficult, as it suffers from the lack of knowledge on the point spread function (PSF) in addition to usual difficulties. An efficient approach is to marginalize the object out of the problem and to estimate the PSF and (object and noise) hyperparameters only, before deconvolving the image using these estimates. Recent works have applied this marginal myopic deconvolution method, based on the maximum a posteriori estimator, combined with a parametric model of the PSF, to a series of AO-corrected astronomical and satellite images. However, this method does not enable one to infer global uncertainties on the parameters. We propose a PSF estimation method, which consists in choosing the minimum mean square error estimator and computing the latter as well as the associated uncertainties thanks to a Markov chain Monte Carlo algorithm. We validate our method by means of realistic simulations, in both astronomical and satellite observation contexts. Finally, we present results on experimental images for both applications: an astronomical observation on Very Large Telescope/spectro-polarimetric high-contrast exoplanet research with the Zimpol instrument and a ground-based LEO satellite observation at Côte d’Azur Observatory’s 1.52 m telescope with Office National d'Etudes et de Recherches Aérospatiales’s ODISSEE AO bench.