In this paper we give a short theoretical description of the general predictive adaptive arithmetic coding technique. The links between this technique and the works of J. Rissanen in the 80's, in particular the BIC information criterion used in parametrical model selection problems, are established. We also design lossless and lossy coding techniques of images. The lossless technique uses a mix between fixed-length coding and arithmetic coding and provides better compression results than those separate methods. That technique is also seen to have an interesting application in the domain of statistics since it gives a data-driven procedure for the non-parametrical histogram selection problem. The lossy technique uses only predictive adaptive arithmetic codes and shows how a good choice of the order of prediction might lead to better results in terms of compression. We illustrate those coding techniques on a raw grayscale image.