Light-field stereo matching problems are commonly modeled by Markov Random Fields (MRFs) for statistical inference of depth maps. Nevertheless, most previous approaches did not adapt to image statistics but instead adopted fixed model parameters. They explored explicit vision cues, such as depth consistency and occlusion, to provide local adaptability and enhance depth quality. However, such additional assumptions could end up confining their applicability, e.g. algorithms designed for dense view sampling are not suitable for sparse one. In this paper, we get back to MRF fundamentals and develop an empirical Bayesian framework-Robust Pseudo Random Field-to explore intrinsic statistical cues for broad applicability. Based on pseudo-likelihoods with hidden soft-decision priors, we apply soft expectation-maximization (EM) for good model fitting and perform hard EM for robust depth estimation. We introduce novel pixel difference models to enable such adaptability and robustness simultaneously. Accordingly, we devise a stereo matching algorithm to employ this framework on dense, sparse, and even denoised light fields. It can be applied to both true-color and grey-scale pixels. Experimental results show that it estimates scene-dependent parameters robustly and converges quickly. In terms of depth accuracy and computation speed, it also outperforms state-of-the-art algorithms constantly.